Study on Sampling and CLT

Okay, so good afternoon everyone. So last time we've finished discussing about the introduction to hypothesis testing. And of course, you've learned from the previous topic na ang tinatest lang nating hypothesis is the null hypothesis. Kasi ang basic assumption natin, when we get a sample or acquire a sample from a population, the sample represents the population. So basically, there is no significant difference. Doon sa karakteristika. ng sample and population. Now, if you will apply a particular treatment doon sa sample, and you are expecting na merong impact yung treatment at magbabago yung characteristics ng sample, now the goal here is to reject the null. And to conclude na dapat merong significant difference yung sample and population, or merong significant impact or effect yung treatment doon sa sample na kinuha natin from the population. And then, of course, As we all know, we reject the null hypothesis kapag is it greater than or less than the significance level or alpha. Nag-i-in sa chatbox natin. Is it less than or greater than the significance level or the alpha level? So for example, nag-compute tayo ng z and then kinuha natin yung probability value. So ano ba dapat? What is the value of the p? Is it less than or greater than the significance level? Greater than daw ang nagsabi sa chat. Ano ba sabi? When the P is... Ano? When the P is... Okay. Diba sabi? When the P is low, the hoe must go. So dapat, the P is less than the alpha or the significance level. So sa example natin last time, less than... 0.05 or less than 0.01. So, depende kung anong isaset ninyong alpha level. Okay? So, now, ila-level up natin ng kaunti yung natutunan nyo last week about hypothesis testing. So, we will be moving forward with the next topic. We have here the hypothesis test with means of samples. So, ano ba yung mga learning objectives natin in this particular topic? So, the first one, of course, We will be defining the distribution of sample means. So later on, makikita ninyo kung ano ba yung ibig sabihin ko about the distribution of sample means or the sampling distribution. So meron tayong panibagong distribution na kailangan maintindihan bago tayo mag-proceed with the calculation or bago tayo mag-proceed with the formula ng Z-test. And then we will explain or I will explain to you how the central limit theorem or the CLT na tinatawag in statistics, specifies the shape, the central tendency, and the variability for the distribution of sample means or the sampling distribution. And then you need to understand the basic logic behind hypothesis testing for means of samples or gagamitin natin yung formula ng Z-test. And then you need to show competency in calculating, analyzing, and interpreting the results of a Z-test. and you will learn how to report Z-test results in research articles, specifically in APA format. Now, sa previous topic natin, when we are doing hypothesis testing, kung maaalala ninyo, meron tayong population, and then kumuha lang tayo ng isang individual from that population. And of course, alam naman natin in research, hindi naman isang individual lang. Yung ginagamit natin kapag nag-i-investigate tayo halimbawa ng particular phenomenon. Multiple individuals yung kinukuha natin in research. Unless gagawa kayo ng qualitative research, konti lang talaga yung kailangan. Minsan isa kung case study. Pero kung quantitative research, hindi pwedeng isa lang. Kadalasan, more than one yung individuals na kinukuha natin. from the population. Now, meron tayong malaking problema in that particular case. So, share ko yung whiteboard ko. Ayan. So, sa mga previous topics natin, we have a population and meron tayong distribution of scores, di ba? So, sa x-axis, nandito yung mga scores or yung x. And then, of course, kapag naka-normal curve siya, yung gitna niyan is the mean of the population and then we have The standard distance ng score from the mean, the standard deviation of the population. So, ang ginawa natin last time, kumuha tayo sa population ng isang score or isang individual, tapos ginawa yung score niya, tapos compare natin kung saan magpo-fall itong particular score na to. Sa high probability value ba or sa low probability value. So, ito okay lang kasi isang score lang to, isang individual lang to. Okay lang i-compare natin itong isang score na to dito sa distribution ng scores. Pero may problem tayo dito sa actual research. Kasi sa actual research, again, multiple individuals yung kinukuha natin from the population. Or malaki yung sample size na kinukuha natin. Halimbawa, n is equals to 64 yung kinuha natin. And ang ginagawa natin, from these 64 respondents, kukunin natin yung mean, halimbawa, ng dependent variable na minimesure. So for example, I want to conduct a study wherein meron akong ipapakitang picture sa inyo or photograph ng isang tao and then babanggitin ko dun bago ko imeasure yung dependent variable na gusto ko imeasure sa inyo babanggitin ko yung positive personality qualities nung nasa picture. So this is our independent variable or kukwasa independent variable. Ah sige, independent variable to kasi this is an experiment. So babanggitin ko muna yung positive personality qualities nung nasa picture na ipapakita ko sa inyo. And then, afterwards, i-rate nyo yung attractiveness ng taong nasa picture. So, halimbawa, sinabi ko na mabait siya, may sense of humor, matalino. Ayan. And then, afterwards, may bigyan nyo ng rating sa attractiveness. So, dito, halimbawa, kumuha tayo ng 64 respondents. Kukunin natin yung attractiveness rating for each respondent, and then kukunin natin yung mean ng 64 respondents na yun from that particular questionnaire. Now, meron tayong problem kasi, unang-una, itong mean ng 64 respondents na to, hindi natin pwede i-compare sa distribution ng scores na to. Kasi again, puro ito individual scores. X. Para kang nagko-compare ng apple sa orange. Diba? Magkaiba ang x sa m. So hindi natin pwedeng gamitin yung steps na ginawa natin last time wherein we will be comparing this particular sample dun sa population. Kasi again, mean na yung kinukuha natin sa samples. X lang yung kinukuha natin noong nakaraan. Okay? So kailangan natin ng panibagong distribution kung saan natin i-co-compare itong mean ng sample na to. Does that make sense? Nakakuha ba yun? Press 0 kung hindi, press 1 kung nakakuha ninyo. Ayan. So, wala nakakuha nun. Okay, so again, kapag multiple individuals na yung kinuha nyo from the population, kukunin nyo na yung mean ng sample na yun. Okay, so yung last hypothesis testing kasi natin, isang individual lang yung kinuha natin. Tapos, compare natin doon sa individual scores. na naka-distribute sa normal curve. Pero ngayon, hindi na pwede kasi nga again, multiple individuals na ito. So sa multiple individuals na ito, yung mean, i-co-compare mo sa individual scores, sa x. Magkaiba ang m at saka yung x. So hindi natin pwedeng gamitin yung distribution ng individual scores. So we need another distribution wherein doon natin i-co-compare ngayon yung mean ng sum. Okay? Kasi yun yung last time, score ng sample yung compare natin sa individual scores na naka-plot sa normal curve or sa histogram. So okay lang yun. Kasi puro x yun eh. Diba? Puro x-es yun nandito. Tapos kumuha tayo ng isa, x yung score ng isang individual, kikocompare natin. Okay lang kasi puro x yung nasa x-axis natin. Puro scores yung nasa x-axis or individual scores. Pero ngayon, hindi na pwede. Kasi again, we will be dealing with multiple individuals. Mean na to ng sample mismo, ng multiple individuals in a particular sample. So, hindi pwedeng i-compare ang mean sa x or sa individual score. Nakukuha? Press 0 kung hindi, press 1 kung nakukuha ninyo. Ayan. So now, we need another distribution. So in this topic, meron tayong another distribution na tinatawag nating distribution of sample means. Okay, so pag sinabi natin distribution of sample means This is a particular distribution or gagawa tayo halimbawa ng histogram or gagawa tayo ng distribution na puro mean ang nasa x-axis. Kasi nung last time, puro individual scores lang. Puro x or xs. Ngayon, puro means yung nasa x-axis natin instead of individual scores. So another term for the distribution of sample means is the sampling distribution. So ito na yung gagamitin natin, comparison distribution, kapag nag-hypothesis testing tayo. Lalo kapag ang n natin is not 1. Kapag more than 1 yung n natin. So again, this is also called the sampling distribution. This is a particular distribution obtained by selecting all the possible samples of a specific size from a population. So let me demonstrate kung ano bang ibig sabihin nung... sampling distribution na yan. So, paano ba yan ginagawa? So, kunyari, meron tayong population na merong 1,000 individuals. So, syempre, meron niyang specified parameters. Alimbawa, meron niyang specific mean and meron niyang specific standard deviation. So, let's say ang mean nito ay nasa 55. itong population na ito. So, pag kumuha ako ng sample dito, halimbawa, kuha ako ng sample na 30, kukuha na natin ito ng mean and SD. Tapos, pwede ulit akong kumuha ng another set of 30, na merong ibang mean and SD rin yun. Pwede rin akong kumuha ng another set of samples, 30 pa rin, meron niyang specified mean and SD. So napakadami kong pwedeng set of samples na makuha from 1,000 na population size. And each sample, alam natin na may iba-ibang mean and SD yan. So for example, kumuha ko ng 30 samples dito sa 1,000 na population, pwedeng ang mean niyan around 53. Itong 30 na another kukunin ko, pwedeng 54. Ito pwedeng 55. Ito pwedeng 56. At alam natin na merong discrepancy. yung sample mean sa population mean because of, anong tawag doon, sa discrepancy na yun? Okay, because of sampling error. So, ito yung sinasabi ko sa inyo. Kapag gumukuha tayo ng sample from the population, pwede tayo makakuha ng different means in different set of samples. So, yung different set of samples na yan, pwede natin i-plot yan into a histogram. So, halimbawa, ito. So, kumuha ako ng apat na set ng samples. So, 53 yung mean nito, ito 54, ito 55, ito 56. So, gagawa ako ngayon ng distribution of sample means. Wherein, ang nasa x-axis, puro mean ng bawat sample na to. So, for example, we have 53, 54, 55, 56. Tapos yun na sa y-axis, frequency pa rin. So, ito na yung tinatawag nating distribution of sample means. So, ang distribution of sample means, yan ay parang collection ng mga different means from different samples na pwede nyong makuha from the population. So, kalimbawa dito, meron tayong isang 53, meron tayong isang 54, may 55, may 56. So, pwede yan. So, the more samples na kukuni natin from the population, merong mabubuong shape yan. Yung distribution of sample means. Na mamaya ipapakita ko rin sa inyo. Okay? So, nakukuha nyo ba yung concept ng distribution of sample means? Press 0 kung hindi, press 1 kung nakukuha ninyo. Ayan. Okay. So, now, sige, i-level up pa natin yung sampling distribution. So imagine meron tayong population na merong size na 4. So apat lang yung nasa population. At ito yung mga scores na nasa population. 2, 4, 6, and 8. So now kunin natin ngayon yung population mean. Nung dataset na ito. Yung 2, 4, 6, and 8. So meron tayong size na population na 4. And then ito yung scores na nandun sa population. 2, 4. 6 and 8. So, ilan yung mean natin for the population? So, add nyo lang and then over n, that would be the mean. So, 2 plus 4 plus 6 plus 8 over 4, that would be ilan? We have 5. So, ito ang population mean natin. Now, halimbawa, mag-research ako. Kukuha ko ng sample. Ang kailangan kong sample ay dalawa lang. Okay? So, napakadaming permutation yung pwede natin makuha from this population size of 4. Diba? Specifically, kapag ginamit natin yung sampling with replacement. Naaalala nyo yung sampling with replacement? Kuha ka ng sample, ibabalik mo. So gagamitin natin yung sampling with replacement in this sample size of 2. So ano bang pwede nating permutation na makuha dito? Kapag halimbawa, dalawa lang yung kukunin natin from 4 na population size. So kuha ko ng isa, halimbawa, randomly. Nakuha ko si 2. And then ibabalik ko si 2. Pagkakuha ko ulit, pwede ko makuha si 2 ulit. So ito yung dalawang individual in this sample size na 2. Pwede rin kuha ko ng 2, tapos binalik ko ulit. Ang nakuha ko naman si 4. So ito yung sample 1 natin, sample 2, sample 3, sample 4. Ano pang pwede? Pwede rin 2 at saka 6. Pwede rin 2 and 8. So meron tayong... Apat dito. Pero pwede rin tayo makakuha ng another sample wherein 4 yung unang makukuha natin tapos 2. Pwede rin 4 and 4. Wait lang ha. Burahin ko lang to. Pwede rin 4 and 4. Pwede rin 4 and 6. Pwede rin 4 and 8. Ano pa? Meron pa bang ibang combination? Pwede rin tayong makakuha ng another sample. Salimbawa, si 6 and 2, 6 and 4, 6 and 6, 6 and 8. Pwede rin 8 and 2, 8 and 4, 8 and 6, tsaka 8 and 8. So, meron tayong mabubuong how many samples? How many sets of samples? Meron tayong 16 sets of samples na pwede mabuo. Dito sa population na size na 4, tapos ang kukunin lang natin na sample size is 2. So now, kukunin nyo yung mean ng bawat set ng sample. So kunin natin yung mean ng bawat set ng sample. Ayan. So pakicompute. So ito demonstrate ko lang sa inyo yung sampling distribution. So 2 plus 2 divided by 2, that would be 4. 2 plus 4 is 6, divided by 2 is 3. 2, 3, 4 lang ito, and then ito 5. Ito ay 6 plus 2 is 8, over 2 is 4. So may pattern naman ito. So 4 plus 2 is 6, over 2 is 3. So 4, 5, and 6. Okay, itong kabila. 6 plus 2 is 8 over 2, that would be 4. 5, 6, and then 7. So, pasang ko na ko itong 5, 6, 7. Again, min lang ito nito. Itong mga bawat pairs. Ayan. So, 8 plus 2 is 10 over 2, 5. So, 5, 6, 7, and then 8. Okay? So, pakidouble check kung pareho tayo na nakuha ang sagot. Press 1 na lang kung... nakuha ninyo. So, each sample or each set of sample, kailangan nyo kunin yung mean. Okay na? Ayan. Wait lang ah. Monitor lang natin temperature. 74 degrees Celsius. Okay. How about the others? So, pakidouble check kung pareho tayo na nakuha ah. So, si sample 1, ang mean niya is 2. Sample 2, ang mean niya is 3, 4, 5, and so on. Pareho? Ayan. So now, gagawa natin ngayon ng distribution itong mga sample means. Okay, so gagawa tayo ngayon ng distribution of sample means or the sampling distribution. So ang pinakamataas natin ay 8, ano, na mean. Pinakamababa is 2. Okay, so gawa tayo ngayon dito sa baba For example, gagawa ako ngayon ng distribution of sample means. So we have 2, 3, 4, 5, 6, 7, and then 8. And nandito yung frequency. We have 1, 2, 3, 4, and then 5. So pakibilang kung ilan yung 2 na mean sa example natin. So tinan natin kung ilan yung 2. na mean. So we have 1. Tama, 1 lang. Pakidouble check. 1 nga lang ba? Press 0 kung hindi, press 1 kung 1 lang. Okay. So isa lang siya. So lagay tayo ngayon ng histogram. Ayan. So isa lang yung ating 2. How about yung 3? Ilan yung 3 natin? Pakilagay sa chatbox para hindi ko natitignan sa taas. Cross-check na lang natin mamaya. Ilan yung 3? Dalawa, no? So we have 1 and then we have 2. How about yung 4? Tatlo. Okay, 1, 2, and then we have 3. Ang taas naman yung 3. Ayan, haya mo na. Okay, 5. Ilan yung 5 natin? Apat, no? Tama, apat? Okay, apat. So, 1, 2, 3, and then, ang taas naman nun. And then, 4. Ayan. And then, yung 6. Tatlo rin. I think tatlo lang yung 6 dyan. And then, dalawa yung 7. Isa yung 8. Tama? Tama ba? Ganito bang magiging itsura ng histogram natin? Anong napansin ninyo? Anong napansin ninyo sa shape ng distribution? Symmetrical and unimodal? Anong piramid doon? Walang ganun shape ng distribution. Piramid. Meron tayong normal curve. So, if you can acquire all the possible set of samples from a population, makakabuo kayo ng normal distribution. At tulad sa example natin, gumamit tayo ng sampling with replacement, kinuha natin yung all possible permutations or all possible samples or set of samples from the population, eto yung nakuha natin yung distribution. N equals, we have an N is equals to 2, diba? Kumuha tayo ng tig to 2, kinuha natin yung mean, eto yung distribution of sample means. At normally distributed siya. Kapag nakuha nyo yung lahat ng possible set of samples or means of samples. Now, meron tayong characteristics ng sampling distribution. So, the first characteristic na kailangan nyong malaman about this sampling distribution, pakita ko lang yung ano ko. presentation. So the first characteristic ng sampling distribution or the distribution of sample means is the mean of the distribution of means or the sampling distribution is the same as the mean of the population. Naniniwala ba kayo na yung mean ng sampling distribution kanina, the same lang yung mean ng population natin. Itest natin ngayon. Kasi yun yung rule number one. Sabi, itong mean daw ng sampling distribution, yung mean daw ng sampling distribution, equal lang daw sa mean ng population. So, ang mean ng population natin kanina is 5. So, tingnan natin kung totoo ang sinasabi na ang mean ng sampling distribution is equal to the mean of the population. So, kunin natin yung mean netong distribution of means or the sampling distribution. So, 2 plus 3 plus 4 plus 5 plus 3 plus 4 plus 5 plus 6, plus 4 plus 5 plus 6 plus 7, plus 5 plus 6 plus 7 plus 8, that would be 80. Pag pinag-add nyo lahat ng mean. Over 16, meron tayong 16 na sample, or samples, ilan ang nakuha ninyo? Okay, that would be 5. Okay? So, ang mean nito is 5 din. So, that's the first rule. Nakukuha, press 0 kung hindi, press 1 kung nakukuha na niya. So, the mean of the sampling distribution or the mean of the distribution of means is the same with the population mean. Okay, next. The next rule is... The variance naman ng sampling distribution. So the variance of the sampling distribution or the variance of the distribution of means is equal to the variance of the population over the sample size. So inote nyo muna yung formula bago natin kunin mamay. So inote nyo muna ito ha. So yung variance daw ng sampling distribution is equal to the variance of the population over N or the sample size. And then press 1 na lang sa chat box kung nanote nyo na yung formula. So this is the variance of the distribution of means, kaya may sub M sa baba. It's equals to the variance of the population over N. Now, paano natin kukunin yung standard deviation ng sampling distribution? So isquare root lang natin ito. So makakancel to. Makakancel to. So yung standard deviation ng sampling distribution is equals to the standard deviation of the population over the square root of n. Okay? So yan. So inote nyo tong formula. Okay? So that's rule 2b. The standard deviation of the sampling distribution or the... or the distribution of sample means is the square root of the variance of the distribution of means. Or, ganito na lang, para mas madali. The standard deviation of the sampling distribution is equals to the standard deviation of the population over square root of n. Now, ang tawag natin dito, itong sigma sub m, or the standard deviation of the sampling distribution, yan po yung tinatawag natin, standard error of... of the mean or the SEM. Although meron pang another SEM in statistics, pero ngayon, ito lang muna tandaan ninyo. Standard error of the mean or standard error. So ano ba ang standard error? Okay? So ang standard error, pagpalagay natin muna yung term na error lang. Okay? So yung error, parang yun yung discrepancy, parang sa sampling error. Yun yung discrepancy. So yung standard error, in-estimate niya, Ina-estimate niya kung gaano ba kalaki yung deviation ng sampling distribution mean doon sa population mean. So again, the standard error will tell us how much ba nagde-deviate yung mga mean from the distribution of sample means from the population mean. Yun yung sinasabi niya. So diba ang dami nating pinlat na means kanina. sa sampling distribution natin. So, yung standard error, siya yung nagbibigay sa atin ng estimate kung gaano ba kalaki yung difference or distance, alimbawa, itong mga sample means na ito from the population mean. Nakukuha? Press 0 kung hindi, press 1 kung nakukuha na ito. Okay? Ayan. Now, The last rule in determining the characteristics of the sampling distribution or the distribution of means is the shape of the sampling distribution or the shape of the distribution of means is approximately normal if either each sample is of 30 or more individuals. So kapag daw, Ang sample size is greater than or equal to 30 in each sample na kinuha natin from the population. Kapag ginawa nyo ng sampling distribution, approximately normally distributed yung shape ng distribution. So, pinakita ko sa inyo kanina. Although hindi yun n is equals to 30. Pero, kinuha kasi natin yung lahat ng... possible sample na pwedeng makuha sa population, yun po ang nagiging shape. kapag pinlat natin yun sa distribution. So, sa example ko kanina, since nakuha natin lahat ng possible means from all possible sample or set of samples, normally distributed lagi ang lalabas dyan. Okay? Ayan. Another one, kung ang population ninyo ay skewed, Or halimbawa, uniform. Kung sinabing uniform, walang mode. Pare-pareha sila ng frequency. O kaya halimbawa, meron pa isang exponential. Ang itsura na ay parang pa ganito. Hindi, parang baliktad. Kalimutan ko itsura ng exponential distribution. So pagpalagay na lang natin ito muna ang tatlo. Kapag skewed ang distribution or uniform, halimbawa. Kapag daw kumuha tayo, halimbawa... From this particular population, basta ang ating n is greater than or equal to 30. So halimbawa, kumuha tayo dito sa skewed distribution ng isang sample set na 30 or above. So kumuha tayo ng napakadaming set of samples na tig to 30 or above. Kapag daw ginawan nyo ng sampling distribution or distribution of means, still magiging normally distributed siya. Okay? Nakakuha? So again, kahit anong shape ng distribution, kunyari skewed or uniform yung distribution natin, or rectangular, kapag kumuha ka dyan ng mga different sets of sample, basta raw greater than or equal to 30 yung kukunin ninyo. Kapag ginawan daw yan ng sampling distribution, or distribution of means, it will follow a normal curve. Okay? Malinaw? Press 0 kung hindi, press 1 kung malinaw. Ayan. Another one, paano naman po kung yung population na pinanggalingan ng samples ay normally distributed? So, kung ang population nyo ay normally distributed or normal curve yung shape niya, kahit anong size, ng sample ninyo, regardless of size, kahit hindi 30, kapag nag-plot kayo ngayon ng distribution of sample means, approximately normally distributed siya. Yun yung sinasabi ng concept na tinatawag na CLT or the Central Limit Theorem. Narinig nyo na ba yung term? Yung Central Limit Theorem? Ayan. Narinig nyo na yung term na central limit theorem? Anyone? Meron ba dito? Nakarinig na ng term? Ayan. Hindi pa. So, ang central limit theorem, okay, yung binanggit ko kanina ang mga rules, eto yung summary nun. So, ang sinasabi ng central limit theorem, or the CLT, for any population na merong specific mean and standard deviation, okay? Kapag kumuha tayo dyan ng mga different sample means with a specific size, so yung mabubuo nating sampling distribution will have a mean equals to the population mean. The standard deviation is equals to the standard deviation of the population over the square root of n. And it will approach a normal distribution. Specifically, kapag yung n natin, it approaches infinity. Or habang lumalaki yung n ninyo. Okay, so ibig sabihin, kapag tumataas po yung sample size natin, mas nag-a-approach yung shape ng distribution ng normality. Nakukuha? Or the sampling distribution, specifically, nag-a-approach siya ng normal curve. Kapag mataas yung n. Okay? Nakukuha? Press 0 ko hindi, press 1 ko nakukuha na yun. Kaya itong number 30, ilang sets po kaya of samples, sir, para maging approximately, normally distributed po yung curve? So since tinanong mo yan, so titinan natin ngayon dito sa Jamovie, kung ilang sets nga kaya ang kailangan para maging... Normally distributed. Or para makita natin. na nag-normally distributed yung data. O, paulit daw ang central limit theorem. So, sige. So, again, ang central limit theorem, ito ang assumption niyan. Ito ang basic concept niyan. Kung meron kang population na merong specific mean and standard deviation, kapag kumuha tayo ng mga different sets of samples dito at ginawa natin siya ng distribution of sample means. Okay? Yung mean nitong distribution of sample means na to na mabubuo natin. would be equal to the population mean, lalo kung makukuha natin lahat ng possible sets ng n. And yung standard deviation itong distribution of sample means would be equal to the standard deviation of the population over square root of n, and magiging normally distributed siya as the n approaches infinity. So habang tumataas yung n na nakukuha natin from the population, Nagiging normally distributed yung sampling distribution natin. Nakukuha ba nung nagtanong kanina? Naka-private eh. Hindi ko na kung pwede sabihin yung name. Ayan. Okay. So that's central limit theorem. So lalong-lalong kapag ang n natin is greater than or equal to 30. Kapag ganyan na ang size. So yung sampling distribution, it will approach the normal curve. Okay? So, now, so, ilang sets of samples daw kaya ang kailangan mo kuha para makabuo ng normal distribution. So, sige. I-open ko yung Jamovie ko. Kung gusto nyo, i-open nyo rin yung Jamovie nyo. And then, meron doong module ng central limit theorem. So, papakita ko sa inyo kaya. So, since this is recorded, ito yung isasend ko mamaya sa 1-1 din. So panoorin nyo na lang one-one, pag itong video na ito ang papanoorin ninyo, itong part na ito, kasi hindi ko siya nasama kanina doon sa lecture because of the time. Tsaka nag-log yung laptop. Pero ngayon itatrya natin. So open nyo yung Jamovie, and then sa modules, hanapin nyo yung central limit theorem. Kasi ito demonstrate ko sa inyo dyan, kung totoo ba yung sinasabi ni Sir Junar na nagiging normally distributed yung data. Lumalaki yung N. Ayan. So open nyo yung Jamovie. Share ko yung screen ko. Kita na ba? Kita nyo na yung Jamovie. Ayan. So click nyo yung modules. Jamovie library. And then hanapin nyo yung CLT or the Central Limit Theorem. So, meron dyang central limit theorem. Pang-demo lang naman ito. Ayan, CLT demonstrations. Install ninyo. Okay? So, pag na-install nyo na yung CLT demonstrations, lalabas yan dito sa taas. Pag wala, i-click nyo lang tong modules, eto siya. CLT. Okay? So gawin natin yung central limit theorem. Ayan. So pagka-click nyo yan, nilalabas ito. So tingnan natin ngayon kung totoo ba na kapag nilalakihan natin yung sample size, nagiging normally distributed. So alimbawa, n is equals to 2 lang. Ano kayo magiging shape ng distribution ng sample means natin? Ah, diba? 100 trials ito. na n equals to 2. Gawin natin one trial lang. Tapos n equals to 2. Ito yung itsura. Ito yung kanina. Halimbawa, kung isang set lang yung kukunin natin na sample. Gawin natin two. Two sets of samples. Diba? Wala pa rin siyang shape. 16, try natin yung kanina. 16 kasi yun eh. Ano napapansin ninyo dito sa demonstration natin? Habang lumalaki yung trials, nagiging approximately normally distributed na rin yan. So, ilagay natin doon sa 100 na default. 100 trials na puro tigtuto yung kuhunin natin sa sample natin. Puro tigtotoy yung kukunin natin sample from the population. So dito medyo hindi pakita na approximately normally distributed yung ating sampling distribution. Pero pag nilakihan ko yung sample size, tapos magsa-sampling with replacement tayo ng 100 times, tanda natin na 30. Okay, ano napansin ninyo? Pag habang lumalaki yung sample size, mas nagiging prominent yung Normal distribution. Gawin natin 1,000. Sobra na siya, sorry. Hanggang 200 lang pala. 200. Tapos gawin natin 10,000 trials. Or 10,000 na... Ba't ayaw niya mag-compute? 1,000. So medyo steep lang siya, pero nagiging normally distributed yan kapag ganyan. So ang source natin ng distribution, halimbawa, normal. Kung normal yung population, tapos halimbawa 100 trials lang na sampling with replacement, tapos 30 na sample size, ayan siya. Ganyan ang itsura. Magnonormal yan habang lumalaki yung sample size natin. Pero kung halimbawa, ibang shape ng distribution. Halimbawa, uniform yung pinanggalingan ng distribution. Ayan o. Kahit, pag sinabing uniform, rectangular. So, rectangular yung population, kumuha tayo ng sample size na 30. Tapos, 100 trials ang gagawin natin. So, kukuha tayo ng 130 paulit-ulit. Tapos, gagawa natin ng distribution. Ito yung naging itsura niya. Pag tinaasahan pa natin yung sample size, halimbawa, 60. Ayan. 100. Ayan. Ganun pa rin yung shape. Nasa range pa rin siya ng normal distribution. Diba? Nakikita nyo ba? O halimbawa, Wala kasi ditong skewed eh. Pero ito yung sinasabi ko kanina about uniform distribution. Pero pag normal, regardless of size niyan, so alimbawa 5 tayo, gawin natin 1,000 trials. So kukuha tayo ng 5 na individual from the population, tapos sampling with replacement tayo 1,000 times. Kita nyo? Nagiging normally distributed pa rin siya Nakukuha nyo ba yun? Press 0 o hindi press 1 kung nakukuha Ay sorry, nawala So yun So yung trials, yun yung number of Number of set of sample na kinukuha ninyo So yung kanina yung ginawa ko 16 diba? 16 yung nakukuha nating n So yun yung trials na ginawa ko dun sa Jamovi. So ito yun. So kung normally distributed yung population ninyo, regardless of size, ayan o, magiging normally distributed siya. Kapag nag-sampling with replacement kayo ng paulit-ulit. Tignan nyo, five lang ito. Normally distributed siya, di ba? Paano pa pag mas malaki? So, ano lang siya, nag-compress lang siya. Pero ano yan, normally distributed pa rin yan. Kasi ang daming trials eh. Pero pag uniform, halimbawa, rectangular yung distribution ng population, kumuha tayo halimbawa ng 5, tapos gawin natin 100 trials lang. Tignan natin kung ano yung tsura. So medyo mukha na siyang approximately normally distributed. Pero again, ang sinasabi kasi ng central limit theorem, dapat greater than or less than 30 kapag hindi normally distributed yung population. Para yung sampling distribution ninyo maging approximately normally distributed. So gawin natin 30 yung sample size. Ayan. Ayan, ito yung closer Medyo skewed pa siya, taasan pa natin Greater than 30, pwede natin i-assume na siguro 40 Ayan, so yan o, makikita nyo Habang tumataas, nagiging normally distributed siya Habang tumataas yung sample size O, 70 Closer look to ah Makikita nyo ba yung closer look? Ayan o, gawin natin 100 yung sample size. Ayan. So, this is the demonstration ng CLT. So, pag normal, tingnan natin yung closer. So, normally distributed kasi normally distributed din yung pinanggalingan niya. Regardless of size. Five lang ilalagay ko. Diba? still yung sampling distribution approaching normal distribution pa rin. Okay? Nakukuha ba ito, class? Press 0 kung hindi, press 1 kung nakukuha na inyo. Okay, maganda lang, hindi naman lalabas ang examinja movie. Dinemonstrate ko lang yung CLT. And then, pinakita ko rin naman kanina, di ba? Kung mapapansin ninyo, kung lahat ng possible means makukuha nyo from specific set of samples. Yan, talagang mag-normally distributed ang distribution ninyo. Okay? Tulad itong example natin. So, yung example natin kanina, diba itong apat na to, kapag ginawan mo ng distribution itong population, eto, iisang score lang naman to. 2, 4, 6, 8. Meron tayong uniform distribution. Ayan o. Pero, Nung ginawa natin ang sampling distribution, itong uniform distribution na ito, kumuha tayo ng 16 na set of samples, ito yung lahat ng pwedeng makuha natin. Anong nangyari sa distribution? Kahit uniform yung population, tinan nyo nangyari sa sampling distribution, naging normally distributed siya. Diba? Okay? So now, anong iniimply nitong central limit theorem na ito? Diba? Ano bang importance nito in statistics? So, itong central limit theorem, yung mga normal distribution na yan, yan kasi ay gagamitin natin mga assumptions sa mga susunod nating test. Yung normality. Lalo kapag halimbawa nag-T-test tayo, requirement din ng T-test na approximately normally distributed yung data, the ANOVA, ganun din, hanggang correlation, merong assumption ng normality. And another one, ito. Kakabit din kasi ng CLT is the law of large numbers. So, ang sinasabi sa law of large numbers, the larger your sample size, the more probable that the sample mean will be close to the population mean. Iyon yung sinasabi doon. So, ibig sabihin, kapag mas malaki yung sample size ninyo, kunyari kumuha kayo ng sample from the population, at malaki ang sample size ninyo, more likely yung mean ng sample na yun, approaching na siya sa population mean. Kaya very important po in quantitative research na malaki ang sample size. Nakukuha? Press 0 kung hindi, press 1 kung nakukuha. So, baka tanongin nyo ako, sir ano po ang considered na large enough na sample size? So, yan ang pinakamahirap sagutin. In statistics. Yung large enough. Iba-iba kasi ang sinasabi ng references. Kung ano yung large enough. Kung halimbawa, nandun na tayo sa discussion ng power analysis na tinatawag. Meron doon, halimbawa, 15 lang large enough na. Meron namang 26 large enough na. It depends. It depends. Kung ano yung large enough. Pero kung CLT, yung pagbabasihan natin kung ano ba yung appropriate sample size, halimbawa sa research, ang sasabihin ng CLT, 30 or more. Nakukuha? Press 0 kung hindi, press 1 kung nakukuha. Mahirap pong mag-determine ng large enough sample size. Pero kung gusto ninyo, yung tinuro ko last time, Rousev. Basta given yung population, pwede nyo kompitein yung large enough. Pero iba-iba rin kasi yung sinasabi ng different references. In power analysis, iba rin yung large enough nila. Although ituturo ko rin naman sa inyo yung susunod na topics natin. Sa CLT, ayan, 30 pwede na. Pwede nyo nang gawin yan kung quantitative research. Pwede na kayo mag-30. Sa regression, iba rin. Halimbawa, regression analysis, although sa mga dulong topic pa natin yun, meron din formula ng sample size. Iba-iba. Iba-iba ang definition ng... Large enough in statistics. Pero tandaan nyo lang, CLT. Ang sinasabi lang ng CLT, na kapag ang population ninyo ay normally distributed at kumuha ka ng set of samples at ginawan mo siya ng sampling distribution, yung mean ng sampling distribution equal sa mean ng population. And then yung standard deviation ng sampling distribution is equal to the standard deviation of the population over square root of n. And yung shape ng sampling distribution will be approximately normally distributed kung ang pinanggalingan na population is normally distributed, regardless of size ng samples ninyo. Pero kung ang population ninyo ay hindi normally distributed like uniform, skewed, kailangan nyo ng greater than 30 or equal to 30 na sample size. Para yung sampling distribution na mabubuo ninyo magiging approximately normally distributed. So wala po talagang pinaka-general na large enough numbers po Wala Kasi ito ay tinanong ko rin in training ng stats Sabi ko, dun sa nag-training sa akin ng statistics Ano po ba ang large enough na sample size? Or what is considered large? Or what is considered small sample size? Ang sabi lang sa akin dun ay depende Walang makakasagot Kasi it depends Depend sa limbawa sa research ninyo, it depends sa population size, it depends sa limbawa sa power ng research or power ng study ninyo. Madami yung kinoconsider. Huwag kayong mag-alala, tuturuan ko naman kayo ng power analysis sa next topic natin. It varies, that's correct. It varies, depende sa situation. Kung ano yung large or not. Pero ang maganda lang talaga in quanti, the more samples, the larger the sample size, better. Okay? Yun lang yung tatandaan ninyo. The more, the merrier in quantitative research. Kasi nga, naka-anchor tayo dito sa law of large numbers din. Nakapag mas malaki yung sample size ninyo or habang nag-reach ng infinity yung sample size ninyo, mas malapit na yung mean ng sample natin sa mean ng population. Okay? Nakukuha? Press 0 kung hindi, press 1 kung nakukuha ninyo. Tapos ko napakainit. Do you have questions pa ba about... CLT and law of large numbers? Question so far? Meron? Press 0 kung wala, press 1 kung meron? Or nalulugaw na sila sa CLT? Okay. So now let's proceed on using those rules na tinuro ko kanina about the CLT in determining the characteristics ng sampling distribution. So for example, suppose you have a distribution which is approximately normal with a mean of 200 and the standard deviation is 48 and then kumuha tayo halimbawa ng sample from that population na 64. So, what would be the characteristics of the sampling distribution? So, ito yung population natin. We have 200, standard deviation of 48. Now, halimbawa, kukuha tayo ng 64 na individuals from the population. So, ano kaya magiging characteristics ng sampling distribution natin? So, ngayon, apply lang natin yung rule. The mean of the distribution of means. is the same as the population mean. So, ano ang mean ng sampling distribution natin? Okay. Of course, 200 lang din yan. Okay? Ayan. Now, next one. The standard deviation daw, or the standard error, or the standard deviation of the sampling distribution is equals to the standard deviation of the population over the square root of n. Okay, so apply natin yung formula. We have 48 over square root of 64. So ano kaya ang ating standard error? Or the standard deviation of the sampling distribution? Ilan? So we have? Okay, that's correct. We have 6. So yun yung ating standard error. 6. Di lang kita. Asta na ba? Ayan. Eto, 6. Okay? So ganun lang po mag-determine ng characteristic ng sampling distribution. Now, i-apply natin ngayon itong natutunan ninyo about sampling distribution in this what we call the Z-test. So, ang Z-test, this is a hypothesis testing procedure na ginagamit natin siya kung meron tayong single sample with with unknown population variance or SD and known population mean. Okay, so gagamitin natin ito kung alam natin yung population na, alam natin yung population mean at saka variance ng population. Doon lang siya ginagamit. So sa tingin nyo, common itong gagamitin sa research. So very rare na makakakita kayo ng Z-test in research. Kasi in actual research, Wala po tayong idea about the population mean and variance ng population. Pero tuturo ko pa rin sa inyo ito kasi very important ang Z-test. So this is the formula for the Z-test. Z is equals to the mean of the sample minus the mean of the distribution of means over standard error or the standard deviation of the distribution of means or the standard deviation of sampling distribution. Ang dami lang tawag sa kanya. Pero standard error lang yun. So sulat nyo yung formula. Kasi gagamitin natin ito mamaya for the example. So press 1 na lang kung nasulat nyo na. So again, ginagamit lang po ang Z-test if you have information about the population. Specifically kung meron kayong mean ng population at variance ng population. Okay? Nasulat na? Okay. How about the others? Now, let's try muna mag-compute bago tayo mag-proceed with the specific research. So, for example, the mean of the sample is 18. The mean of the distribution of means is 10. And then the standard deviation of the distribution of means is 4. So, ano kaya yung z-score na makukuha natin dito? So, z is equals to m minus the mean of the distribution of means. over the standard error. So, ilan naman kukuha natin z? 18 minus 10 over 4. Okay, we have a z of 2.00. So, ganyan lang mag-compute ng z-test. Pero syempre, mas maganda kung mayroong research example. Balikan natin ngayon yung example natin kanina. Okay? So, babasahin ko na lang. Makinig na lang kayo. And then, we will try to test kung... I-reject ba natin or fail to reject yung null hypothesis? So, the social psychologist asked 64 randomly selected students. So, meron tayong N na 64. So, inote nyo na agad yung mga data na binibigay ko. So, again, the social psychologist asked 64 randomly selected students to rate the attractiveness of a particular person in a photograph. So, halimbawa, picture ko. Charot. Ayan. Prior to rating the attractiveness of the person nun nasa photograph, each student is told that the person has positive personality qualities. So, kindness, warmth, may sense of humor, tsaka intelligent daw. Nasa picture. Parang ako nga yun. Char. On a scale of zero, the lowest possible attractiveness, to 400. The highest possible attractiveness. The mean attractiveness rating given by the 64 students is 220. Is it the population mean or the sample mean? Ito naka-underline. The mean attractiveness rating given by the 64 students is 220. Is it the population mean or the sample mean? Okay, that's the sample mean. Now, from extensive previous research, The psychologist knows the distribution of attractiveness ratings of the person in the photograph when there has been no mention of person's personality qualities. So sa mga previous research daw, meron ng mga rating about a particular person without telling them, halimbawa, ng positive personality qualities. And sinasabi daw doon sa mga previous research na kapag wala tayong minention na positive qualities about the person, ang rating ng attractiveness is 200. From previous research ito, kapag walang binanggit na positive personality qualities, 200 daw ang mean. And ang standard deviation is 48. So ito ang ating population mean at ito ang ating population standard deviation. And it follows daw an approximately normal distribution. Now, we will test kung meron bang impact yung positive personality qualities. on attractiveness rating at 5% significance level. And tingnan natin ano kaya magiging conclusion nitong experiment na to. Okay, pakinoot lahat ng mga data and then press 1 sa ating chatbox kung okay na. Lahat ng mga sinulat ko tsaka binulugan ko. So, we have sample size 64. The mean of the sample is 220. The mean of the population is 200. The standard deviation of the population is 48. The significance level is 5%. Okay? Ready? Ready na ba? Just press 1 kung okay na. Kita ba yun? Ayan, 4. Okay, how about the others? So now let's proceed with the hypothesis testing. So what would be our null hypothesis? So ako na muna magbabanggit ngayon, mamaya kayo naman. So ang ating independent variable is the positive personality qualities. And titinan natin kung meron bang impact yun sa rating ng attractiveness. So pwede natin sabihin na the positive personality P. qualities has no significant effect on attractiveness rating. So this is the null. Tandaan nyo, null to ha, may no eh. No significant. Alternative, so positive. Personality qualities has a significant effect on attractiveness rating. Okay? Kuha? Nakukuha to? Press 1 kung goods. Next, anong next step natin? Anong next step natin in hypothesis testing? Step 2, we set, anong sinaset natin? The criteria for decision. So, ano ang ating alpha level? Alpha is, anong sinabi kanina? Ilan daw yung significance level? 5% or 0.05. Okay. Next, number three, the comparison distribution. So, alam natin na ito ay z-score lang naman. So, the mean of the comparison distribution is zero, standard deviation of one. So, anong gagamitin natin dito sa hypothesis test na ito? Is it... Two-tailed or one-tailed? That's the first question. Is it two-tailed or one-tailed? Basahin nyo maigi yung hypothesis kanina. Positive personality qualities has no significant effect on attractiveness rating. Okay, so sabi ni Richelle, two-tailed. Bakit two-tailed? Bakit kaya two-tailed? Tama naman two-tailed, pero bakit? Ano ba yung hypothesis natin? Nakastate siya in what form? Directional or non-directional? Sabi dun, has no significant effect. Okay, since wala siyang specific direction, non-directional yun. So basically, we will use two-tailed test. Okay, now, what is the cutoff score? Or the critical value? Or the critical values? Kasi dalawang tail yung gagamitin natin eh. At 0.05, two-tailed. Anong cutoff score natin? Based from previous discussion, eh 2.5 daw. Nanguhula ka ata riyan eh. At 0.05, two-tailed. Balikan ang previous lesson. Ako, kabisado ko. Kasi kabisado ko yung normal curve kapag 95% confidence interval eh. Okay? So negative and positive, 1.96. So ito ang ating critical value. Ito ang critical region. Okay? So, meron na tayong comparison distribution. Number four, collect the data and compute for sample statistics. So, try natin ngayon. So, meron tayong N na 64, mean na 220, mean ng population na 200, standard deviation na 48. Okay? Ang formula natin. is z equals to the mean of the sample. Pwede rin itong x-bar. Kung pure statistics tayo, x-bar yung ginagamit ng iba. Pero ako, m yung ginagamit ko. Yan. m minus the, haba, nawala. Mean of distribution of means over standard error. So, anong kailangan natin? The mean of the distribution of means. So, what is the mean of the distribution of means? First rule, what is the mean of the distribution of means? Of course, 200 lang din yun. Next, what is the standard deviation of the distribution of means or the standard error? So, kailangan natin compete din yan. We have standard deviation of the population over square root of n. So, nakuha na natin ito kanina, 48 over square root of 64 equals to 6. So, kumpleto na yung data natin, pwede na natin i-apply yung formula. So, we have 220 minus 200 over 6. So, what is our calculated Z? 3.33. Ayan, that's correct. Okay, now balik tayo doon sa comparison distribution. So nasaan ang 3.33? Siguro andito bandayon. So ang decision natin ngayon ay, ano ang decision? Okay, that's correct. We have to reject the null hypothesis. Okay. Dali lang, di ba? Abisin niyo, madali lang stats eh. Now, tingnan natin, balik tayo sa HO. So, i-reject daw natin ito. So, ibig sabihin, the alternative will be used. So, ang conclusion, positive personality qualities has a significant effect on attractiveness rating. So, dito, hindi pa natin alam kung anong effect. Tingnan natin ngayon yung distribution. Ano daw ang naging effect? Nasaan ang ating Z? Left side or right side? So, kung nasa right side, ibig sabihin, may increase. In the rating. Di ba? Nag-increase yung rating nung sinabi yung positive personality qualities. Totoo kaya to in the real world. Kapag halimbawa, may makikilala kang tao, tapos bago mo siya makilala, babanggitin yung friend mo, ay ano yan, matalino yan, may sense of humor, maraming pera, mabait. Pag kaya nakilala natin yung tao, tapos na-encounter na natin siya, tingin nyo ba, medyo tataas yung attractiveness rating sa kanya? or ma-attract kaya kayo. Patingin nyo Opo Oo mga to Kayo ah Ayan So yan yung result ng study So in this case Meron daw significant effect Yung pagsasabi ng positive personality qualities Sa attractiveness rating Specifically na i-increase niya Yung attractiveness rating Talaga ba? Ayan Okay Maraming na na-attract kay Sandro Kasi huwag tayong political masyado dito stats. Okay. So, malinaw to. Itong example na to. Press 0 kung hindi, press 1 kung malinaw. Dali lang yung computation. Ano? Question so far? Ayan. Sige, another example tayo. Gusto ko kayo naman yung mag-formulate ng hypothesis. This one. 214 pa lang naman. Okay. A psychologist is interested in the conditions that affect the number of dreams per month that people report in which they are alone. So gusto nilang malaman yung number of dreams per month ng mga tao dito sa example na to. Now, we will assume that based on extensive previous research, it is known that in the general population, the number of dreams per month follows a normal curve with a mean of 5 and a standard deviation of 4. So, pakinote na itong data. Mean is 5, standard deviation of 4. So, sa population daw, ang average number of dreams per month in the population is 5 and the standard deviation is 4. Now, the researchers or the researcher wants to test the prediction that the number of such dreams will be greater among people who have recently experienced traumatic event. So meron tayong independent variable or quasi-independent variable kasi hindi naman tayo pwede magmanipulate ng trauma. So hanap lang tayo na nakaranas ng traumatic events. So meron tayong quasi-IV na trauma. traumatic experience. And gusto natin malaman kung may impact to sa number of dreams. And ang prediction natin, mas madami daw yung number of dreams ng mga nakaranas ng traumatic event. So is this a one-tailed test or two-tailed test? That's the first question. Is it a one-tailed test or two-tailed test? Based from the statement. Okay. So, since meron tayong specific direction ng prediction, we will be using a one-tailed test. Okay? Okay, now. Thus, the psychologist studies 36 individuals who have recently experienced a traumatic event. Okay? So, the mean of their dreams after recently experiencing traumatic event is 8. Okay? So the mean of the dreams daw ng mga nakaranas ng traumatic event is 8. Should we conclude that the people who have or that people who have recently had a traumatic experience have significantly different number of dreams? in which they are alone. So, I want you to carry a hypothesis testing at 0.05 significance level. One tail. Okay? So, gusto kong makita sa chat box what is our null hypothesis. Null hypothesis muna tayo. Nal-hypothesis natin. So, our quasi-independent variable would be traumatic experience. And then, the dependent variable would be the number of dreams. So, ano kayang pwede na nal-hypothesis? Chatbox tayo para may interaction. Malapit na yung nag-send dito Traumatic event has no significant impact to increase the number of dreams Charot lang sir Sige, ito yung mas magandang pagkakasulat niyan Traumatic event or pwede rin traumatic experience Does not significantly increase the number of dreams. So, pwede ganito. Okay? Malinaw? Iba ba? O, pwede rin yan. The traumatic experience. Kaso, frequency yung ginamit ng isa. Sabi dito sa chat, naka-private, traumatic experience does not increase the frequency of dreams being alone. Kaso, ang kinukuha natin yung mean eh. So, hindi pwede frequency. So, in general na lang, ayan, pwede ganito. Traumatic experience does not significantly increase the number of dreams. Or the average number of dreams. Pwede rin ganun. And then alternative, traumatic experience significantly increases the number of dreams. Ayan. So meron na tayong null and alternative. Alpha. What's our alpha? Alpha tayo. Ilan? Okay, that's correct. 0.05. Next, the comparison distribution. So since this is one-tailed, nasaan kaya ang ating rejection region? Is it left or right? 1 tilde. So based from the statement, increase. Okay, that's correct. We have, right. What is the cutoff sample score or the critical value? Positive 1.64. Okay, double check. 1.64 ata yun. Tama? 1.64? Okay, 1.64. Now, let's carry out the computation. Number 4. So, we have the mean of the sample 8. Population is 5. Standard deviation is 4. So, we need the mean of the distribution of means. So, since equal lang naman daw ang mean of distribution of means sa population mean, we have 8. And then the standard deviation of the distribution of means or standard error, ilan ang standard error natin? So we have ito yung formula, square root of n. So ang n natin is 36. Diba? Tama ba? Yeah, 36. So we have 0.67. So 4 over square root of 36. So, 4 over 6, that would be 0.67. Okay, now carry out the z-test. So, compute for the z. So, ilan ang z natin? z is equals to m minus the mean of the distribution of means over standard error. So, we have 8 minus 5 over 0.67. So, ilan? Ilan ang ating z? Ayan, nag-log na naman ako. Wait lang guys, mag-restart ako. So, what is our conclusion dun sa example kanina? So, number 4 na, no? So, we have z equals to the mean of... The sample, ilan yung minang sample? 8. Tapos, population is 5 over 0.67. So, ilan yung ating computed Z? 4 point? Okay, 4.48. Okay. So, yung comparison distribution, 1.64. So, what is our conclusion? Or decision muna tayo. Decision would be, are we going to reject or fail to reject the null? Ah, ito pala. Pala ko nawala. Ayan. So, this equals to 4.48. So, the decision is to reject the null hypothesis. Kasi nasaan ba yung 4.48? Buti na lang hindi sa kabilang side. Nandito siya banda. So reject the null. So ibig sabihin, kapag daw nakaranas ng traumatic event yung isang tao, nag-i-increase yung number of dreams niya. Tatingin niyo kaya totoo yun? Tatingin niyo? Is it true? Yes, that's true. Ito, matututunan niyo naman ito sa abpsych ninyo. So abnormal psychology. In PTSD One of the criteria ng PTSD si merong recurring ng mga dreams, ng mga traumatic events. So, common nangyayari yan sa mga may trauma na talagang tumataas yung number of dreams nila and yung content ng dreams related doon sa trauma na naranasan nila. Familiar kayo with Sherlock na series? Naalala nyo doon si Martin Freeman? si John Watson. Diba? Nung mga first episodes, merong part doon na napapanaginipan niya pa yung war. Diba? Kasi may PTSD. Post-traumatic stress disorder. So, yan. That's true naman. Na, yan. Traumatic events or traumatic experience can significantly increase the number of dreams. Diba? Psychosomatic pa nga siya doon, eh. Yung sa legs niya. Tapos nang wala pa si Sherlock M. Nag-fake that ano. Ayan. So that's Z-Test. Ayan. Nasaan na yung presentation ko? Ba't kaya? Siguro sa sobrang init kaya naglalag yung whiteboard ko. Ilan na ba yung temperature? Wait lang. Open ko lang yung presentation ko. Kasi patapos na naman tayo. Last part na. We have the advanced topic. Wait lang ah. Nahanap ko lang yung presentation. Ayan. Okay. Ayan. So, this is an example on how to report the results of a Z-test in research articles. So, kung mapapansin nyo dyan, so, ito yung conclusion natin. The study suggests, sabi ko sa inyo last time, huwag nyo gagamitin yung proves, magandang gamitin yung term na suggest, or this study provides evidence that Traumatic event has a significant effect on the number of dreams. With the calculated Z, italicize yung Z, it's equals to 4.48, the P value or the probability value is less than 0.05. Kaya natin na-reject yung null. Nandun siya sa low probability value, yung 4.48. Specifically, those subjects who experience traumatic events have greater number of dreams than those who did not experience traumatic events. Okay? Ayan. So now the last part ng ating topic, nasa section siya ng advanced topic in the reference material natin. We have here the confidence interval. The confidence interval. So ano ba ang confidence interval? So ginagamit natin itong CI or the confidence interval to estimate the population mean. Roughly speaking, this is the range of scores. kung saan natin makikita yung true population mean based from the sample mean. So, naalala nyo kanina, meron tayong mga given sample mean. And in actual research, wala naman tayong idea about population parameter. So, paano natin ma-estimate yung population mean kung meron lang tayong sample mean? So, pwede natin gamitin yung sample mean using confidence interval. So paano natin kinocompute yung confidence interval? So bago tayo mag-proceed with the computation, which is very easy lang naman yung computation niya, ito muna yung mga common na ginagamit natin confidence levels or confidence intervals. 95 and 99%. Kung ang alpha ninyo is 0.05, the confidence intervals nasa 95%. Or yung confidence level natin is 95%. Kung 0.01 ang alpha ninyo, 99% yung magiging confidence level natin. So paano ba iniinterpret yan? So halimbawa, kinumpit na natin yung range of scores kung saan natin makikita yung true population mean. So kung 95% yung confidence interval natin, pwede natin sabihin na yung true population mean is between the calculated range of scores. So mag-example tayo. So, paano ba mag-compute ng confidence interval? You need the standard error and then you need the cut-off sample scores or yung critical values doon sa comparison distribution. Okay? So, kung 95%, ang cut-off natin dyan, kailangan dito two-tailed eh. Ayan o. Ang cut-off natin dyan is the 1.96. So, kailangan nyo yung positive and negative 1.96 kung 95% confidence level. Pero kung... 99% confidence level, edo yung 2.58 yung gagamitin natin. Cut off. Okay? So, balik tayo dun sa example kanina. Yung traumatic event. Sa traumatic event. So, sabi doon, ang sample mean is 8. Diba? Now, imagine, wala tayong idea kung ano yung population mean ng mga dreams sa mga nasa population. Diba? Ang alam lang natin yung population nung hindi nakaranas ng traumatic event. Alam natin yung data nung mga individual na hindi nakaranas ng traumatic event. Ang mean niya is 5, standard deviation is 4. Now, wala tayong idea about the true population mean nung mga nakaranas naman ng traumatic event. Pero meron tayong sample mean. Meron tayong sample mean. Now, pwede natin i-estimate yung population mean using the sample mean. Gagamitin lang natin itong confidence interval. So, pakita ko sa inyo kung paano. Whiteboard. Ayan. So, gawin natin two-tailed halimbawa yung test kanina. So, ito ay 1.96 negative and positive. So, ito yung 95% na confidence level natin. At ito naman yung alpha level natin. So, since nireject natin yung null, So, alam natin na kapag nakaranas ng traumatic event, nag-increase significantly yung number of dreams. So, ang sample mean natin is 8. Gusto natin malaman, or gusto natin halimbawa magkaroon ng idea, ano kaya yung population mean naman ng itong mga individual na nakaranas ng traumatic event. Kasi itong population kanina, yun yung population nung hindi nakaranas ng traumatic event. Kinocompare natin yung nakaranas ng traumatic event at saka hindi nakaranas ng traumatic event. So now, paano naman yung mga nakaranas ng traumatic event in the population? Ano kaya yung mean ng population na yun? So gagamitin natin itong mean ng sample to estimate that. So ang gagawin nyo lang, apply nyo lang yung formula na tinuro ko last time sa z-score. So kukunin natin. yung range ng scores kung saan possibly nandun yung population mean natin. Okay, so ganito lang yan. So you have the mean of the sample plus minus. Kita nyo to. 1.96. Kung naka 95 confidence level kayo. Times the standard error. So ano ba yung standard error natin kanina? 0.67. So M plus minus eto yung Z na cut off. Z critical na lang. Times the standard error. Okay? So we have the mean of the sample is 8 plus minus 1.96 times 0.67. So, tingnan natin. Kunin natin yung lower limit. So, pag lower limit, ang gagawin nyo lang, ito muna, ima-minus nyo lang. So, imultiply nyo muna itong 1.96 sa 0.67, that would be 1.31. So, 8 minus 1.31, that would be 6.69. And then, 8... plus 1.31, yun naman yung upper limit. So that would be 9.31. So ibig sabihin, ayan, ibig sabihin, in the population, ang number of dreams in the population or the average number of dreams in the population naglalaro sa value ng 6.69 and 9.31. or the troop population mean lies between 6.69 and 9.31. And 95% confident tayo dyan na nandito yung true population mean. Nakukuha? Press 0 kung hindi, press 1 kung nakukuha na yun. Ayan. So, yung computation ng confidence interval, again, ginagamit natin siya to estimate the population mean. So, again, meron tayong data about the sample, about the traumatic event tsaka yung dreams nila. Pero gusto natin malaman or ma-estimate, paano kaya sa population? Ano kaya yung average number of dreams ng whole population? So, eto yung computation. So, in the population, in this particular example, we are 95% confident that the true population mean of the number of dreams in the population, in the population nito, lies between 6.69 and 9.31. Okay? Nakukuha? Press 0 o hindi, press 1 kung nakukuha ninyo. Ayan. Kuha tong confidence interval. Uy, huwag kayong mahiya magtanong. Confidence interval. So, again, pang-estimate po ito ng true population mean based from the sample mean. Ayan. So, na all confident. Ayan. So kung ano ang alpha level ninyo, 100 minus alpha level, yun yung confidence level natin. Ayan. Okay? So in this case, ayan, 95, for one, hindi, for two-tailed ito, hindi one-tailed. Kung napapansin mo kanina, ginawa kong two-tailed yung distribution. Ayan o. For two-tailed na ito. Oo. Kapag one-tailed, wala tayong ano dyan. Positive and negative. Kasi kailangan natin makuha yung lower limit sa left side at right side. Yung upper limit naman. So pag lower limit, ima-minus nyo lang yung product ng cutoff na z-score at standard error. Pag upper limit, i-add nyo yung product ng z na critical value at standard error sa mean ng sample. So kung ang mean ng sample natin is 8, ayan, 8 daw yung average number of dreams sa sample natin. So sa population, ang average number of dreams naglalaro sa 6.69 and 9.31. Ito yung mga nakaranas ng traumatic event. Dito naglalaro yung population mean natin. At 95% confident tayo dito. Ayan. Okay? So, stop ko na yung recording ko. Naku, pagdudugtongin ko na naman yung video.

Kasi ang basic assumption natin, when we get a sample or acquire a sample from a population, the sample represents the population. So basically, there is no significant difference. Doon sa karakteristika.

ng sample and population. Now, if you will apply a particular treatment doon sa sample, and you are expecting na merong impact yung treatment at magbabago yung characteristics ng sample, now the goal here is to reject the null. And to conclude na dapat merong significant difference yung sample and population, or merong significant impact or effect yung treatment doon sa sample na kinuha natin from the population.

And then, of course, As we all know, we reject the null hypothesis kapag is it greater than or less than the significance level or alpha. Nag-i-in sa chatbox natin. Is it less than or greater than the significance level or the alpha level? So for example, nag-compute tayo ng z and then kinuha natin yung probability value. So ano ba dapat?

What is the value of the p? Is it less than or greater than the significance level? Greater than daw ang nagsabi sa chat. Ano ba sabi? When the P is...

Ano? When the P is... Okay. Diba sabi?

When the P is low, the hoe must go. So dapat, the P is less than the alpha or the significance level. So sa example natin last time, less than... 0.05 or less than 0.01.

So, depende kung anong isaset ninyong alpha level. Okay? So, now, ila-level up natin ng kaunti yung natutunan nyo last week about hypothesis testing.

So, we will be moving forward with the next topic. We have here the hypothesis test with means of samples. So, ano ba yung mga learning objectives natin in this particular topic?

So, the first one, of course, We will be defining the distribution of sample means. So later on, makikita ninyo kung ano ba yung ibig sabihin ko about the distribution of sample means or the sampling distribution. So meron tayong panibagong distribution na kailangan maintindihan bago tayo mag-proceed with the calculation or bago tayo mag-proceed with the formula ng Z-test.

And then we will explain or I will explain to you how the central limit theorem or the CLT na tinatawag in statistics, specifies the shape, the central tendency, and the variability for the distribution of sample means or the sampling distribution. And then you need to understand the basic logic behind hypothesis testing for means of samples or gagamitin natin yung formula ng Z-test. And then you need to show competency in calculating, analyzing, and interpreting the results of a Z-test.

and you will learn how to report Z-test results in research articles, specifically in APA format. Now, sa previous topic natin, when we are doing hypothesis testing, kung maaalala ninyo, meron tayong population, and then kumuha lang tayo ng isang individual from that population. And of course, alam naman natin in research, hindi naman isang individual lang. Yung ginagamit natin kapag nag-i-investigate tayo halimbawa ng particular phenomenon. Multiple individuals yung kinukuha natin in research.

Unless gagawa kayo ng qualitative research, konti lang talaga yung kailangan. Minsan isa kung case study. Pero kung quantitative research, hindi pwedeng isa lang.

Kadalasan, more than one yung individuals na kinukuha natin. from the population. Now, meron tayong malaking problema in that particular case.

So, share ko yung whiteboard ko. Ayan. So, sa mga previous topics natin, we have a population and meron tayong distribution of scores, di ba?

So, sa x-axis, nandito yung mga scores or yung x. And then, of course, kapag naka-normal curve siya, yung gitna niyan is the mean of the population and then we have The standard distance ng score from the mean, the standard deviation of the population. So, ang ginawa natin last time, kumuha tayo sa population ng isang score or isang individual, tapos ginawa yung score niya, tapos compare natin kung saan magpo-fall itong particular score na to. Sa high probability value ba or sa low probability value.

So, ito okay lang kasi isang score lang to, isang individual lang to. Okay lang i-compare natin itong isang score na to dito sa distribution ng scores. Pero may problem tayo dito sa actual research.

Kasi sa actual research, again, multiple individuals yung kinukuha natin from the population. Or malaki yung sample size na kinukuha natin. Halimbawa, n is equals to 64 yung kinuha natin. And ang ginagawa natin, from these 64 respondents, kukunin natin yung mean, halimbawa, ng dependent variable na minimesure. So for example, I want to conduct a study wherein meron akong ipapakitang picture sa inyo or photograph ng isang tao and then babanggitin ko dun bago ko imeasure yung dependent variable na gusto ko imeasure sa inyo babanggitin ko yung positive personality qualities nung nasa picture.

So this is our independent variable or kukwasa independent variable. Ah sige, independent variable to kasi this is an experiment. So babanggitin ko muna yung positive personality qualities nung nasa picture na ipapakita ko sa inyo.

And then, afterwards, i-rate nyo yung attractiveness ng taong nasa picture. So, halimbawa, sinabi ko na mabait siya, may sense of humor, matalino. Ayan.

And then, afterwards, may bigyan nyo ng rating sa attractiveness. So, dito, halimbawa, kumuha tayo ng 64 respondents. Kukunin natin yung attractiveness rating for each respondent, and then kukunin natin yung mean ng 64 respondents na yun from that particular questionnaire. Now, meron tayong problem kasi, unang-una, itong mean ng 64 respondents na to, hindi natin pwede i-compare sa distribution ng scores na to. Kasi again, puro ito individual scores.

X. Para kang nagko-compare ng apple sa orange. Diba? Magkaiba ang x sa m. So hindi natin pwedeng gamitin yung steps na ginawa natin last time wherein we will be comparing this particular sample dun sa population.

Kasi again, mean na yung kinukuha natin sa samples. X lang yung kinukuha natin noong nakaraan. Okay? So kailangan natin ng panibagong distribution kung saan natin i-co-compare itong mean ng sample na to. Does that make sense?

Nakakuha ba yun? Press 0 kung hindi, press 1 kung nakakuha ninyo. Ayan. So, wala nakakuha nun. Okay, so again, kapag multiple individuals na yung kinuha nyo from the population, kukunin nyo na yung mean ng sample na yun.

Okay, so yung last hypothesis testing kasi natin, isang individual lang yung kinuha natin. Tapos, compare natin doon sa individual scores. na naka-distribute sa normal curve. Pero ngayon, hindi na pwede kasi nga again, multiple individuals na ito. So sa multiple individuals na ito, yung mean, i-co-compare mo sa individual scores, sa x.

Magkaiba ang m at saka yung x. So hindi natin pwedeng gamitin yung distribution ng individual scores. So we need another distribution wherein doon natin i-co-compare ngayon yung mean ng sum.

Okay? Kasi yun yung last time, score ng sample yung compare natin sa individual scores na naka-plot sa normal curve or sa histogram. So okay lang yun.

Kasi puro x yun eh. Diba? Puro x-es yun nandito.

Tapos kumuha tayo ng isa, x yung score ng isang individual, kikocompare natin. Okay lang kasi puro x yung nasa x-axis natin. Puro scores yung nasa x-axis or individual scores. Pero ngayon, hindi na pwede. Kasi again, we will be dealing with multiple individuals.

Mean na to ng sample mismo, ng multiple individuals in a particular sample. So, hindi pwedeng i-compare ang mean sa x or sa individual score. Nakukuha?

Press 0 kung hindi, press 1 kung nakukuha ninyo. Ayan. So now, we need another distribution.

So in this topic, meron tayong another distribution na tinatawag nating distribution of sample means. Okay, so pag sinabi natin distribution of sample means This is a particular distribution or gagawa tayo halimbawa ng histogram or gagawa tayo ng distribution na puro mean ang nasa x-axis. Kasi nung last time, puro individual scores lang. Puro x or xs. Ngayon, puro means yung nasa x-axis natin instead of individual scores.

So another term for the distribution of sample means is the sampling distribution. So ito na yung gagamitin natin, comparison distribution, kapag nag-hypothesis testing tayo. Lalo kapag ang n natin is not 1. Kapag more than 1 yung n natin. So again, this is also called the sampling distribution. This is a particular distribution obtained by selecting all the possible samples of a specific size from a population.

So let me demonstrate kung ano bang ibig sabihin nung... sampling distribution na yan. So, paano ba yan ginagawa?

So, kunyari, meron tayong population na merong 1,000 individuals. So, syempre, meron niyang specified parameters. Alimbawa, meron niyang specific mean and meron niyang specific standard deviation. So, let's say ang mean nito ay nasa 55. itong population na ito. So, pag kumuha ako ng sample dito, halimbawa, kuha ako ng sample na 30, kukuha na natin ito ng mean and SD.

Tapos, pwede ulit akong kumuha ng another set of 30, na merong ibang mean and SD rin yun. Pwede rin akong kumuha ng another set of samples, 30 pa rin, meron niyang specified mean and SD. So napakadami kong pwedeng set of samples na makuha from 1,000 na population size.

And each sample, alam natin na may iba-ibang mean and SD yan. So for example, kumuha ko ng 30 samples dito sa 1,000 na population, pwedeng ang mean niyan around 53. Itong 30 na another kukunin ko, pwedeng 54. Ito pwedeng 55. Ito pwedeng 56. At alam natin na merong discrepancy. yung sample mean sa population mean because of, anong tawag doon, sa discrepancy na yun? Okay, because of sampling error.

So, ito yung sinasabi ko sa inyo. Kapag gumukuha tayo ng sample from the population, pwede tayo makakuha ng different means in different set of samples. So, yung different set of samples na yan, pwede natin i-plot yan into a histogram.

So, halimbawa, ito. So, kumuha ako ng apat na set ng samples. So, 53 yung mean nito, ito 54, ito 55, ito 56. So, gagawa ako ngayon ng distribution of sample means.

Wherein, ang nasa x-axis, puro mean ng bawat sample na to. So, for example, we have 53, 54, 55, 56. Tapos yun na sa y-axis, frequency pa rin. So, ito na yung tinatawag nating distribution of sample means.

So, ang distribution of sample means, yan ay parang collection ng mga different means from different samples na pwede nyong makuha from the population. So, kalimbawa dito, meron tayong isang 53, meron tayong isang 54, may 55, may 56. So, pwede yan. So, the more samples na kukuni natin from the population, merong mabubuong shape yan.

Yung distribution of sample means. Na mamaya ipapakita ko rin sa inyo. Okay?

So, nakukuha nyo ba yung concept ng distribution of sample means? Press 0 kung hindi, press 1 kung nakukuha ninyo. Ayan. Okay.

So, now, sige, i-level up pa natin yung sampling distribution. So imagine meron tayong population na merong size na 4. So apat lang yung nasa population. At ito yung mga scores na nasa population.

2, 4, 6, and 8. So now kunin natin ngayon yung population mean. Nung dataset na ito. Yung 2, 4, 6, and 8. So meron tayong size na population na 4. And then ito yung scores na nandun sa population.

2, 4. 6 and 8. So, ilan yung mean natin for the population? So, add nyo lang and then over n, that would be the mean. So, 2 plus 4 plus 6 plus 8 over 4, that would be ilan? We have 5. So, ito ang population mean natin. Now, halimbawa, mag-research ako.

Kukuha ko ng sample. Ang kailangan kong sample ay dalawa lang. Okay? So, napakadaming permutation yung pwede natin makuha from this population size of 4. Diba? Specifically, kapag ginamit natin yung sampling with replacement.

Naaalala nyo yung sampling with replacement? Kuha ka ng sample, ibabalik mo. So gagamitin natin yung sampling with replacement in this sample size of 2. So ano bang pwede nating permutation na makuha dito?

Kapag halimbawa, dalawa lang yung kukunin natin from 4 na population size. So kuha ko ng isa, halimbawa, randomly. Nakuha ko si 2. And then ibabalik ko si 2. Pagkakuha ko ulit, pwede ko makuha si 2 ulit.

So ito yung dalawang individual in this sample size na 2. Pwede rin kuha ko ng 2, tapos binalik ko ulit. Ang nakuha ko naman si 4. So ito yung sample 1 natin, sample 2, sample 3, sample 4. Ano pang pwede? Pwede rin 2 at saka 6. Pwede rin 2 and 8. So meron tayong... Apat dito.

Pero pwede rin tayo makakuha ng another sample wherein 4 yung unang makukuha natin tapos 2. Pwede rin 4 and 4. Wait lang ha. Burahin ko lang to. Pwede rin 4 and 4. Pwede rin 4 and 6. Pwede rin 4 and 8. Ano pa?

Meron pa bang ibang combination? Pwede rin tayong makakuha ng another sample. Salimbawa, si 6 and 2, 6 and 4, 6 and 6, 6 and 8. Pwede rin 8 and 2, 8 and 4, 8 and 6, tsaka 8 and 8. So, meron tayong mabubuong how many samples? How many sets of samples? Meron tayong 16 sets of samples na pwede mabuo.

Dito sa population na size na 4, tapos ang kukunin lang natin na sample size is 2. So now, kukunin nyo yung mean ng bawat set ng sample. So kunin natin yung mean ng bawat set ng sample. Ayan.

So pakicompute. So ito demonstrate ko lang sa inyo yung sampling distribution. So 2 plus 2 divided by 2, that would be 4. 2 plus 4 is 6, divided by 2 is 3. 2, 3, 4 lang ito, and then ito 5. Ito ay 6 plus 2 is 8, over 2 is 4. So may pattern naman ito. So 4 plus 2 is 6, over 2 is 3. So 4, 5, and 6. Okay, itong kabila.

6 plus 2 is 8 over 2, that would be 4. 5, 6, and then 7. So, pasang ko na ko itong 5, 6, 7. Again, min lang ito nito. Itong mga bawat pairs. Ayan.

So, 8 plus 2 is 10 over 2, 5. So, 5, 6, 7, and then 8. Okay? So, pakidouble check kung pareho tayo na nakuha ang sagot. Press 1 na lang kung... nakuha ninyo.

So, each sample or each set of sample, kailangan nyo kunin yung mean. Okay na? Ayan.

Wait lang ah. Monitor lang natin temperature. 74 degrees Celsius.

Okay. How about the others? So, pakidouble check kung pareho tayo na nakuha ah. So, si sample 1, ang mean niya is 2. Sample 2, ang mean niya is 3, 4, 5, and so on. Pareho?

Ayan. So now, gagawa natin ngayon ng distribution itong mga sample means. Okay, so gagawa tayo ngayon ng distribution of sample means or the sampling distribution.

So ang pinakamataas natin ay 8, ano, na mean. Pinakamababa is 2. Okay, so gawa tayo ngayon dito sa baba For example, gagawa ako ngayon ng distribution of sample means. So we have 2, 3, 4, 5, 6, 7, and then 8. And nandito yung frequency. We have 1, 2, 3, 4, and then 5. So pakibilang kung ilan yung 2 na mean sa example natin.

So tinan natin kung ilan yung 2. na mean. So we have 1. Tama, 1 lang. Pakidouble check. 1 nga lang ba? Press 0 kung hindi, press 1 kung 1 lang.

Okay. So isa lang siya. So lagay tayo ngayon ng histogram. Ayan. So isa lang yung ating 2. How about yung 3?

Ilan yung 3 natin? Pakilagay sa chatbox para hindi ko natitignan sa taas. Cross-check na lang natin mamaya.

Ilan yung 3? Dalawa, no? So we have 1 and then we have 2. How about yung 4?

Tatlo. Okay, 1, 2, and then we have 3. Ang taas naman yung 3. Ayan, haya mo na. Okay, 5. Ilan yung 5 natin? Apat, no? Tama, apat?

Okay, apat. So, 1, 2, 3, and then, ang taas naman nun. And then, 4. Ayan. And then, yung 6. Tatlo rin. I think tatlo lang yung 6 dyan.

And then, dalawa yung 7. Isa yung 8. Tama? Tama ba? Ganito bang magiging itsura ng histogram natin? Anong napansin ninyo?

Anong napansin ninyo sa shape ng distribution? Symmetrical and unimodal? Anong piramid doon? Walang ganun shape ng distribution. Piramid.

Meron tayong normal curve. So, if you can acquire all the possible set of samples from a population, makakabuo kayo ng normal distribution. At tulad sa example natin, gumamit tayo ng sampling with replacement, kinuha natin yung all possible permutations or all possible samples or set of samples from the population, eto yung nakuha natin yung distribution.

N equals, we have an N is equals to 2, diba? Kumuha tayo ng tig to 2, kinuha natin yung mean, eto yung distribution of sample means. At normally distributed siya. Kapag nakuha nyo yung lahat ng possible set of samples or means of samples. Now, meron tayong characteristics ng sampling distribution.

So, the first characteristic na kailangan nyong malaman about this sampling distribution, pakita ko lang yung ano ko. presentation. So the first characteristic ng sampling distribution or the distribution of sample means is the mean of the distribution of means or the sampling distribution is the same as the mean of the population. Naniniwala ba kayo na yung mean ng sampling distribution kanina, the same lang yung mean ng population natin.

Itest natin ngayon. Kasi yun yung rule number one. Sabi, itong mean daw ng sampling distribution, yung mean daw ng sampling distribution, equal lang daw sa mean ng population. So, ang mean ng population natin kanina is 5. So, tingnan natin kung totoo ang sinasabi na ang mean ng sampling distribution is equal to the mean of the population. So, kunin natin yung mean netong distribution of means or the sampling distribution.

So, 2 plus 3 plus 4 plus 5 plus 3 plus 4 plus 5 plus 6, plus 4 plus 5 plus 6 plus 7, plus 5 plus 6 plus 7 plus 8, that would be 80. Pag pinag-add nyo lahat ng mean. Over 16, meron tayong 16 na sample, or samples, ilan ang nakuha ninyo? Okay, that would be 5. Okay?

So, ang mean nito is 5 din. So, that's the first rule. Nakukuha, press 0 kung hindi, press 1 kung nakukuha na niya. So, the mean of the sampling distribution or the mean of the distribution of means is the same with the population mean. Okay, next.

The next rule is... The variance naman ng sampling distribution. So the variance of the sampling distribution or the variance of the distribution of means is equal to the variance of the population over the sample size.

So inote nyo muna yung formula bago natin kunin mamay. So inote nyo muna ito ha. So yung variance daw ng sampling distribution is equal to the variance of the population over N or the sample size. And then press 1 na lang sa chat box kung nanote nyo na yung formula. So this is the variance of the distribution of means, kaya may sub M sa baba.

It's equals to the variance of the population over N. Now, paano natin kukunin yung standard deviation ng sampling distribution? So isquare root lang natin ito. So makakancel to. Makakancel to.

So yung standard deviation ng sampling distribution is equals to the standard deviation of the population over the square root of n. Okay? So yan. So inote nyo tong formula.

Okay? So that's rule 2b. The standard deviation of the sampling distribution or the... or the distribution of sample means is the square root of the variance of the distribution of means. Or, ganito na lang, para mas madali.

The standard deviation of the sampling distribution is equals to the standard deviation of the population over square root of n. Now, ang tawag natin dito, itong sigma sub m, or the standard deviation of the sampling distribution, yan po yung tinatawag natin, standard error of... of the mean or the SEM. Although meron pang another SEM in statistics, pero ngayon, ito lang muna tandaan ninyo. Standard error of the mean or standard error.

So ano ba ang standard error? Okay? So ang standard error, pagpalagay natin muna yung term na error lang. Okay?

So yung error, parang yun yung discrepancy, parang sa sampling error. Yun yung discrepancy. So yung standard error, in-estimate niya, Ina-estimate niya kung gaano ba kalaki yung deviation ng sampling distribution mean doon sa population mean.

So again, the standard error will tell us how much ba nagde-deviate yung mga mean from the distribution of sample means from the population mean. Yun yung sinasabi niya. So diba ang dami nating pinlat na means kanina.

sa sampling distribution natin. So, yung standard error, siya yung nagbibigay sa atin ng estimate kung gaano ba kalaki yung difference or distance, alimbawa, itong mga sample means na ito from the population mean. Nakukuha?

Press 0 kung hindi, press 1 kung nakukuha na ito. Okay? Ayan.

Now, The last rule in determining the characteristics of the sampling distribution or the distribution of means is the shape of the sampling distribution or the shape of the distribution of means is approximately normal if either each sample is of 30 or more individuals. So kapag daw, Ang sample size is greater than or equal to 30 in each sample na kinuha natin from the population. Kapag ginawa nyo ng sampling distribution, approximately normally distributed yung shape ng distribution.

So, pinakita ko sa inyo kanina. Although hindi yun n is equals to 30. Pero, kinuha kasi natin yung lahat ng... possible sample na pwedeng makuha sa population, yun po ang nagiging shape.

kapag pinlat natin yun sa distribution. So, sa example ko kanina, since nakuha natin lahat ng possible means from all possible sample or set of samples, normally distributed lagi ang lalabas dyan. Okay? Ayan. Another one, kung ang population ninyo ay skewed, Or halimbawa, uniform.

Kung sinabing uniform, walang mode. Pare-pareha sila ng frequency. O kaya halimbawa, meron pa isang exponential. Ang itsura na ay parang pa ganito. Hindi, parang baliktad.

Kalimutan ko itsura ng exponential distribution. So pagpalagay na lang natin ito muna ang tatlo. Kapag skewed ang distribution or uniform, halimbawa. Kapag daw kumuha tayo, halimbawa... From this particular population, basta ang ating n is greater than or equal to 30. So halimbawa, kumuha tayo dito sa skewed distribution ng isang sample set na 30 or above.

So kumuha tayo ng napakadaming set of samples na tig to 30 or above. Kapag daw ginawan nyo ng sampling distribution or distribution of means, still magiging normally distributed siya. Okay?

Nakakuha? So again, kahit anong shape ng distribution, kunyari skewed or uniform yung distribution natin, or rectangular, kapag kumuha ka dyan ng mga different sets of sample, basta raw greater than or equal to 30 yung kukunin ninyo. Kapag ginawan daw yan ng sampling distribution, or distribution of means, it will follow a normal curve. Okay?

Malinaw? Press 0 kung hindi, press 1 kung malinaw. Ayan.

Another one, paano naman po kung yung population na pinanggalingan ng samples ay normally distributed? So, kung ang population nyo ay normally distributed or normal curve yung shape niya, kahit anong size, ng sample ninyo, regardless of size, kahit hindi 30, kapag nag-plot kayo ngayon ng distribution of sample means, approximately normally distributed siya. Yun yung sinasabi ng concept na tinatawag na CLT or the Central Limit Theorem. Narinig nyo na ba yung term?

Yung Central Limit Theorem? Ayan. Narinig nyo na yung term na central limit theorem? Anyone?

Meron ba dito? Nakarinig na ng term? Ayan.

Hindi pa. So, ang central limit theorem, okay, yung binanggit ko kanina ang mga rules, eto yung summary nun. So, ang sinasabi ng central limit theorem, or the CLT, for any population na merong specific mean and standard deviation, okay? Kapag kumuha tayo dyan ng mga different sample means with a specific size, so yung mabubuo nating sampling distribution will have a mean equals to the population mean. The standard deviation is equals to the standard deviation of the population over the square root of n.

And it will approach a normal distribution. Specifically, kapag yung n natin, it approaches infinity. Or habang lumalaki yung n ninyo.

Okay, so ibig sabihin, kapag tumataas po yung sample size natin, mas nag-a-approach yung shape ng distribution ng normality. Nakukuha? Or the sampling distribution, specifically, nag-a-approach siya ng normal curve. Kapag mataas yung n.

Okay? Nakukuha? Press 0 ko hindi, press 1 ko nakukuha na yun. Kaya itong number 30, ilang sets po kaya of samples, sir, para maging approximately, normally distributed po yung curve? So since tinanong mo yan, so titinan natin ngayon dito sa Jamovie, kung ilang sets nga kaya ang kailangan para maging...

Normally distributed. Or para makita natin. na nag-normally distributed yung data. O, paulit daw ang central limit theorem.

So, sige. So, again, ang central limit theorem, ito ang assumption niyan. Ito ang basic concept niyan.

Kung meron kang population na merong specific mean and standard deviation, kapag kumuha tayo ng mga different sets of samples dito at ginawa natin siya ng distribution of sample means. Okay? Yung mean nitong distribution of sample means na to na mabubuo natin.

would be equal to the population mean, lalo kung makukuha natin lahat ng possible sets ng n. And yung standard deviation itong distribution of sample means would be equal to the standard deviation of the population over square root of n, and magiging normally distributed siya as the n approaches infinity. So habang tumataas yung n na nakukuha natin from the population, Nagiging normally distributed yung sampling distribution natin. Nakukuha ba nung nagtanong kanina?

Naka-private eh. Hindi ko na kung pwede sabihin yung name. Ayan.

Okay. So that's central limit theorem. So lalong-lalong kapag ang n natin is greater than or equal to 30. Kapag ganyan na ang size.

So yung sampling distribution, it will approach the normal curve. Okay? So, now, so, ilang sets of samples daw kaya ang kailangan mo kuha para makabuo ng normal distribution.

So, sige. I-open ko yung Jamovie ko. Kung gusto nyo, i-open nyo rin yung Jamovie nyo. And then, meron doong module ng central limit theorem. So, papakita ko sa inyo kaya.

So, since this is recorded, ito yung isasend ko mamaya sa 1-1 din. So panoorin nyo na lang one-one, pag itong video na ito ang papanoorin ninyo, itong part na ito, kasi hindi ko siya nasama kanina doon sa lecture because of the time. Tsaka nag-log yung laptop. Pero ngayon itatrya natin. So open nyo yung Jamovie, and then sa modules, hanapin nyo yung central limit theorem.

Kasi ito demonstrate ko sa inyo dyan, kung totoo ba yung sinasabi ni Sir Junar na nagiging normally distributed yung data. Lumalaki yung N. Ayan. So open nyo yung Jamovie. Share ko yung screen ko.

Kita na ba? Kita nyo na yung Jamovie. Ayan.

So click nyo yung modules. Jamovie library. And then hanapin nyo yung CLT or the Central Limit Theorem. So, meron dyang central limit theorem. Pang-demo lang naman ito.

Ayan, CLT demonstrations. Install ninyo. Okay? So, pag na-install nyo na yung CLT demonstrations, lalabas yan dito sa taas. Pag wala, i-click nyo lang tong modules, eto siya.

CLT. Okay? So gawin natin yung central limit theorem.

Ayan. So pagka-click nyo yan, nilalabas ito. So tingnan natin ngayon kung totoo ba na kapag nilalakihan natin yung sample size, nagiging normally distributed.

So alimbawa, n is equals to 2 lang. Ano kayo magiging shape ng distribution ng sample means natin? Ah, diba?

100 trials ito. na n equals to 2. Gawin natin one trial lang. Tapos n equals to 2. Ito yung itsura.

Ito yung kanina. Halimbawa, kung isang set lang yung kukunin natin na sample. Gawin natin two. Two sets of samples.

Diba? Wala pa rin siyang shape. 16, try natin yung kanina. 16 kasi yun eh.

Ano napapansin ninyo dito sa demonstration natin? Habang lumalaki yung trials, nagiging approximately normally distributed na rin yan. So, ilagay natin doon sa 100 na default. 100 trials na puro tigtuto yung kuhunin natin sa sample natin.

Puro tigtotoy yung kukunin natin sample from the population. So dito medyo hindi pakita na approximately normally distributed yung ating sampling distribution. Pero pag nilakihan ko yung sample size, tapos magsa-sampling with replacement tayo ng 100 times, tanda natin na 30. Okay, ano napansin ninyo? Pag habang lumalaki yung sample size, mas nagiging prominent yung Normal distribution. Gawin natin 1,000.

Sobra na siya, sorry. Hanggang 200 lang pala. 200. Tapos gawin natin 10,000 trials. Or 10,000 na...

Ba't ayaw niya mag-compute? 1,000. So medyo steep lang siya, pero nagiging normally distributed yan kapag ganyan.

So ang source natin ng distribution, halimbawa, normal. Kung normal yung population, tapos halimbawa 100 trials lang na sampling with replacement, tapos 30 na sample size, ayan siya. Ganyan ang itsura. Magnonormal yan habang lumalaki yung sample size natin. Pero kung halimbawa, ibang shape ng distribution.

Halimbawa, uniform yung pinanggalingan ng distribution. Ayan o. Kahit, pag sinabing uniform, rectangular. So, rectangular yung population, kumuha tayo ng sample size na 30. Tapos, 100 trials ang gagawin natin.

So, kukuha tayo ng 130 paulit-ulit. Tapos, gagawa natin ng distribution. Ito yung naging itsura niya.

Pag tinaasahan pa natin yung sample size, halimbawa, 60. Ayan. 100. Ayan. Ganun pa rin yung shape.

Nasa range pa rin siya ng normal distribution. Diba? Nakikita nyo ba?

O halimbawa, Wala kasi ditong skewed eh. Pero ito yung sinasabi ko kanina about uniform distribution. Pero pag normal, regardless of size niyan, so alimbawa 5 tayo, gawin natin 1,000 trials. So kukuha tayo ng 5 na individual from the population, tapos sampling with replacement tayo 1,000 times. Kita nyo?

Nagiging normally distributed pa rin siya Nakukuha nyo ba yun? Press 0 o hindi press 1 kung nakukuha Ay sorry, nawala So yun So yung trials, yun yung number of Number of set of sample na kinukuha ninyo So yung kanina yung ginawa ko 16 diba? 16 yung nakukuha nating n So yun yung trials na ginawa ko dun sa Jamovi.

So ito yun. So kung normally distributed yung population ninyo, regardless of size, ayan o, magiging normally distributed siya. Kapag nag-sampling with replacement kayo ng paulit-ulit. Tignan nyo, five lang ito.

Normally distributed siya, di ba? Paano pa pag mas malaki? So, ano lang siya, nag-compress lang siya.

Pero ano yan, normally distributed pa rin yan. Kasi ang daming trials eh. Pero pag uniform, halimbawa, rectangular yung distribution ng population, kumuha tayo halimbawa ng 5, tapos gawin natin 100 trials lang.

Tignan natin kung ano yung tsura. So medyo mukha na siyang approximately normally distributed. Pero again, ang sinasabi kasi ng central limit theorem, dapat greater than or less than 30 kapag hindi normally distributed yung population.

Para yung sampling distribution ninyo maging approximately normally distributed. So gawin natin 30 yung sample size. Ayan.

Ayan, ito yung closer Medyo skewed pa siya, taasan pa natin Greater than 30, pwede natin i-assume na siguro 40 Ayan, so yan o, makikita nyo Habang tumataas, nagiging normally distributed siya Habang tumataas yung sample size O, 70 Closer look to ah Makikita nyo ba yung closer look? Ayan o, gawin natin 100 yung sample size. Ayan.

So, this is the demonstration ng CLT. So, pag normal, tingnan natin yung closer. So, normally distributed kasi normally distributed din yung pinanggalingan niya. Regardless of size.

Five lang ilalagay ko. Diba? still yung sampling distribution approaching normal distribution pa rin. Okay?

Nakukuha ba ito, class? Press 0 kung hindi, press 1 kung nakukuha na inyo. Okay, maganda lang, hindi naman lalabas ang examinja movie.

Dinemonstrate ko lang yung CLT. And then, pinakita ko rin naman kanina, di ba? Kung mapapansin ninyo, kung lahat ng possible means makukuha nyo from specific set of samples.

Yan, talagang mag-normally distributed ang distribution ninyo. Okay? Tulad itong example natin.

So, yung example natin kanina, diba itong apat na to, kapag ginawan mo ng distribution itong population, eto, iisang score lang naman to. 2, 4, 6, 8. Meron tayong uniform distribution. Ayan o. Pero, Nung ginawa natin ang sampling distribution, itong uniform distribution na ito, kumuha tayo ng 16 na set of samples, ito yung lahat ng pwedeng makuha natin.

Anong nangyari sa distribution? Kahit uniform yung population, tinan nyo nangyari sa sampling distribution, naging normally distributed siya. Diba? Okay?

So now, anong iniimply nitong central limit theorem na ito? Diba? Ano bang importance nito in statistics? So, itong central limit theorem, yung mga normal distribution na yan, yan kasi ay gagamitin natin mga assumptions sa mga susunod nating test. Yung normality.

Lalo kapag halimbawa nag-T-test tayo, requirement din ng T-test na approximately normally distributed yung data, the ANOVA, ganun din, hanggang correlation, merong assumption ng normality. And another one, ito. Kakabit din kasi ng CLT is the law of large numbers.

So, ang sinasabi sa law of large numbers, the larger your sample size, the more probable that the sample mean will be close to the population mean. Iyon yung sinasabi doon. So, ibig sabihin, kapag mas malaki yung sample size ninyo, kunyari kumuha kayo ng sample from the population, at malaki ang sample size ninyo, more likely yung mean ng sample na yun, approaching na siya sa population mean. Kaya very important po in quantitative research na malaki ang sample size.

Nakukuha? Press 0 kung hindi, press 1 kung nakukuha. So, baka tanongin nyo ako, sir ano po ang considered na large enough na sample size?

So, yan ang pinakamahirap sagutin. In statistics. Yung large enough.

Iba-iba kasi ang sinasabi ng references. Kung ano yung large enough. Kung halimbawa, nandun na tayo sa discussion ng power analysis na tinatawag.

Meron doon, halimbawa, 15 lang large enough na. Meron namang 26 large enough na. It depends.

It depends. Kung ano yung large enough. Pero kung CLT, yung pagbabasihan natin kung ano ba yung appropriate sample size, halimbawa sa research, ang sasabihin ng CLT, 30 or more. Nakukuha?

Press 0 kung hindi, press 1 kung nakukuha. Mahirap pong mag-determine ng large enough sample size. Pero kung gusto ninyo, yung tinuro ko last time, Rousev. Basta given yung population, pwede nyo kompitein yung large enough.

Pero iba-iba rin kasi yung sinasabi ng different references. In power analysis, iba rin yung large enough nila. Although ituturo ko rin naman sa inyo yung susunod na topics natin.

Sa CLT, ayan, 30 pwede na. Pwede nyo nang gawin yan kung quantitative research. Pwede na kayo mag-30. Sa regression, iba rin.

Halimbawa, regression analysis, although sa mga dulong topic pa natin yun, meron din formula ng sample size. Iba-iba. Iba-iba ang definition ng... Large enough in statistics.

Pero tandaan nyo lang, CLT. Ang sinasabi lang ng CLT, na kapag ang population ninyo ay normally distributed at kumuha ka ng set of samples at ginawan mo siya ng sampling distribution, yung mean ng sampling distribution equal sa mean ng population. And then yung standard deviation ng sampling distribution is equal to the standard deviation of the population over square root of n. And yung shape ng sampling distribution will be approximately normally distributed kung ang pinanggalingan na population is normally distributed, regardless of size ng samples ninyo.

Pero kung ang population ninyo ay hindi normally distributed like uniform, skewed, kailangan nyo ng greater than 30 or equal to 30 na sample size. Para yung sampling distribution na mabubuo ninyo magiging approximately normally distributed. So wala po talagang pinaka-general na large enough numbers po Wala Kasi ito ay tinanong ko rin in training ng stats Sabi ko, dun sa nag-training sa akin ng statistics Ano po ba ang large enough na sample size? Or what is considered large?

Or what is considered small sample size? Ang sabi lang sa akin dun ay depende Walang makakasagot Kasi it depends Depend sa limbawa sa research ninyo, it depends sa population size, it depends sa limbawa sa power ng research or power ng study ninyo. Madami yung kinoconsider. Huwag kayong mag-alala, tuturuan ko naman kayo ng power analysis sa next topic natin. It varies, that's correct.

It varies, depende sa situation. Kung ano yung large or not. Pero ang maganda lang talaga in quanti, the more samples, the larger the sample size, better. Okay?

Yun lang yung tatandaan ninyo. The more, the merrier in quantitative research. Kasi nga, naka-anchor tayo dito sa law of large numbers din. Nakapag mas malaki yung sample size ninyo or habang nag-reach ng infinity yung sample size ninyo, mas malapit na yung mean ng sample natin sa mean ng population. Okay?

Nakukuha? Press 0 kung hindi, press 1 kung nakukuha ninyo. Tapos ko napakainit.

Do you have questions pa ba about... CLT and law of large numbers? Question so far?

Meron? Press 0 kung wala, press 1 kung meron? Or nalulugaw na sila sa CLT? Okay.

So now let's proceed on using those rules na tinuro ko kanina about the CLT in determining the characteristics ng sampling distribution. So for example, suppose you have a distribution which is approximately normal with a mean of 200 and the standard deviation is 48 and then kumuha tayo halimbawa ng sample from that population na 64. So, what would be the characteristics of the sampling distribution? So, ito yung population natin. We have 200, standard deviation of 48. Now, halimbawa, kukuha tayo ng 64 na individuals from the population.

So, ano kaya magiging characteristics ng sampling distribution natin? So, ngayon, apply lang natin yung rule. The mean of the distribution of means. is the same as the population mean.

So, ano ang mean ng sampling distribution natin? Okay. Of course, 200 lang din yan.

Okay? Ayan. Now, next one. The standard deviation daw, or the standard error, or the standard deviation of the sampling distribution is equals to the standard deviation of the population over the square root of n.

Okay, so apply natin yung formula. We have 48 over square root of 64. So ano kaya ang ating standard error? Or the standard deviation of the sampling distribution?

Ilan? So we have? Okay, that's correct. We have 6. So yun yung ating standard error. 6. Di lang kita.

Asta na ba? Ayan. Eto, 6. Okay? So ganun lang po mag-determine ng characteristic ng sampling distribution.

Now, i-apply natin ngayon itong natutunan ninyo about sampling distribution in this what we call the Z-test. So, ang Z-test, this is a hypothesis testing procedure na ginagamit natin siya kung meron tayong single sample with with unknown population variance or SD and known population mean. Okay, so gagamitin natin ito kung alam natin yung population na, alam natin yung population mean at saka variance ng population.

Doon lang siya ginagamit. So sa tingin nyo, common itong gagamitin sa research. So very rare na makakakita kayo ng Z-test in research.

Kasi in actual research, Wala po tayong idea about the population mean and variance ng population. Pero tuturo ko pa rin sa inyo ito kasi very important ang Z-test. So this is the formula for the Z-test. Z is equals to the mean of the sample minus the mean of the distribution of means over standard error or the standard deviation of the distribution of means or the standard deviation of sampling distribution.

Ang dami lang tawag sa kanya. Pero standard error lang yun. So sulat nyo yung formula.

Kasi gagamitin natin ito mamaya for the example. So press 1 na lang kung nasulat nyo na. So again, ginagamit lang po ang Z-test if you have information about the population.

Specifically kung meron kayong mean ng population at variance ng population. Okay? Nasulat na? Okay. How about the others?

Now, let's try muna mag-compute bago tayo mag-proceed with the specific research. So, for example, the mean of the sample is 18. The mean of the distribution of means is 10. And then the standard deviation of the distribution of means is 4. So, ano kaya yung z-score na makukuha natin dito? So, z is equals to m minus the mean of the distribution of means. over the standard error.

So, ilan naman kukuha natin z? 18 minus 10 over 4. Okay, we have a z of 2.00. So, ganyan lang mag-compute ng z-test.

Pero syempre, mas maganda kung mayroong research example. Balikan natin ngayon yung example natin kanina. Okay? So, babasahin ko na lang. Makinig na lang kayo.

And then, we will try to test kung... I-reject ba natin or fail to reject yung null hypothesis? So, the social psychologist asked 64 randomly selected students. So, meron tayong N na 64. So, inote nyo na agad yung mga data na binibigay ko.

So, again, the social psychologist asked 64 randomly selected students to rate the attractiveness of a particular person in a photograph. So, halimbawa, picture ko. Charot.

Ayan. Prior to rating the attractiveness of the person nun nasa photograph, each student is told that the person has positive personality qualities. So, kindness, warmth, may sense of humor, tsaka intelligent daw.

Nasa picture. Parang ako nga yun. Char. On a scale of zero, the lowest possible attractiveness, to 400. The highest possible attractiveness. The mean attractiveness rating given by the 64 students is 220. Is it the population mean or the sample mean?

Ito naka-underline. The mean attractiveness rating given by the 64 students is 220. Is it the population mean or the sample mean? Okay, that's the sample mean.

Now, from extensive previous research, The psychologist knows the distribution of attractiveness ratings of the person in the photograph when there has been no mention of person's personality qualities. So sa mga previous research daw, meron ng mga rating about a particular person without telling them, halimbawa, ng positive personality qualities. And sinasabi daw doon sa mga previous research na kapag wala tayong minention na positive qualities about the person, ang rating ng attractiveness is 200. From previous research ito, kapag walang binanggit na positive personality qualities, 200 daw ang mean.

And ang standard deviation is 48. So ito ang ating population mean at ito ang ating population standard deviation. And it follows daw an approximately normal distribution. Now, we will test kung meron bang impact yung positive personality qualities. on attractiveness rating at 5% significance level.

And tingnan natin ano kaya magiging conclusion nitong experiment na to. Okay, pakinoot lahat ng mga data and then press 1 sa ating chatbox kung okay na. Lahat ng mga sinulat ko tsaka binulugan ko.

So, we have sample size 64. The mean of the sample is 220. The mean of the population is 200. The standard deviation of the population is 48. The significance level is 5%. Okay? Ready? Ready na ba?

Just press 1 kung okay na. Kita ba yun? Ayan, 4. Okay, how about the others?

So now let's proceed with the hypothesis testing. So what would be our null hypothesis? So ako na muna magbabanggit ngayon, mamaya kayo naman.

So ang ating independent variable is the positive personality qualities. And titinan natin kung meron bang impact yun sa rating ng attractiveness. So pwede natin sabihin na the positive personality P. qualities has no significant effect on attractiveness rating.

So this is the null. Tandaan nyo, null to ha, may no eh. No significant. Alternative, so positive.

Personality qualities has a significant effect on attractiveness rating. Okay? Kuha?

Nakukuha to? Press 1 kung goods. Next, anong next step natin?

Anong next step natin in hypothesis testing? Step 2, we set, anong sinaset natin? The criteria for decision. So, ano ang ating alpha level?

Alpha is, anong sinabi kanina? Ilan daw yung significance level? 5% or 0.05.

Okay. Next, number three, the comparison distribution. So, alam natin na ito ay z-score lang naman. So, the mean of the comparison distribution is zero, standard deviation of one. So, anong gagamitin natin dito sa hypothesis test na ito?

Is it... Two-tailed or one-tailed? That's the first question.

Is it two-tailed or one-tailed? Basahin nyo maigi yung hypothesis kanina. Positive personality qualities has no significant effect on attractiveness rating. Okay, so sabi ni Richelle, two-tailed.

Bakit two-tailed? Bakit kaya two-tailed? Tama naman two-tailed, pero bakit? Ano ba yung hypothesis natin? Nakastate siya in what form?

Directional or non-directional? Sabi dun, has no significant effect. Okay, since wala siyang specific direction, non-directional yun.

So basically, we will use two-tailed test. Okay, now, what is the cutoff score? Or the critical value?

Or the critical values? Kasi dalawang tail yung gagamitin natin eh. At 0.05, two-tailed. Anong cutoff score natin? Based from previous discussion, eh 2.5 daw.

Nanguhula ka ata riyan eh. At 0.05, two-tailed. Balikan ang previous lesson.

Ako, kabisado ko. Kasi kabisado ko yung normal curve kapag 95% confidence interval eh. Okay? So negative and positive, 1.96.

So ito ang ating critical value. Ito ang critical region. Okay? So, meron na tayong comparison distribution.

Number four, collect the data and compute for sample statistics. So, try natin ngayon. So, meron tayong N na 64, mean na 220, mean ng population na 200, standard deviation na 48. Okay? Ang formula natin. is z equals to the mean of the sample.

Pwede rin itong x-bar. Kung pure statistics tayo, x-bar yung ginagamit ng iba. Pero ako, m yung ginagamit ko. Yan. m minus the, haba, nawala.

Mean of distribution of means over standard error. So, anong kailangan natin? The mean of the distribution of means. So, what is the mean of the distribution of means?

First rule, what is the mean of the distribution of means? Of course, 200 lang din yun. Next, what is the standard deviation of the distribution of means or the standard error? So, kailangan natin compete din yan.

We have standard deviation of the population over square root of n. So, nakuha na natin ito kanina, 48 over square root of 64 equals to 6. So, kumpleto na yung data natin, pwede na natin i-apply yung formula. So, we have 220 minus 200 over 6. So, what is our calculated Z?

3.33. Ayan, that's correct. Okay, now balik tayo doon sa comparison distribution. So nasaan ang 3.33?

Siguro andito bandayon. So ang decision natin ngayon ay, ano ang decision? Okay, that's correct. We have to reject the null hypothesis. Okay.

Dali lang, di ba? Abisin niyo, madali lang stats eh. Now, tingnan natin, balik tayo sa HO.

So, i-reject daw natin ito. So, ibig sabihin, the alternative will be used. So, ang conclusion, positive personality qualities has a significant effect on attractiveness rating.

So, dito, hindi pa natin alam kung anong effect. Tingnan natin ngayon yung distribution. Ano daw ang naging effect? Nasaan ang ating Z? Left side or right side?

So, kung nasa right side, ibig sabihin, may increase. In the rating. Di ba? Nag-increase yung rating nung sinabi yung positive personality qualities. Totoo kaya to in the real world.

Kapag halimbawa, may makikilala kang tao, tapos bago mo siya makilala, babanggitin yung friend mo, ay ano yan, matalino yan, may sense of humor, maraming pera, mabait. Pag kaya nakilala natin yung tao, tapos na-encounter na natin siya, tingin nyo ba, medyo tataas yung attractiveness rating sa kanya? or ma-attract kaya kayo.

Patingin nyo Opo Oo mga to Kayo ah Ayan So yan yung result ng study So in this case Meron daw significant effect Yung pagsasabi ng positive personality qualities Sa attractiveness rating Specifically na i-increase niya Yung attractiveness rating Talaga ba? Ayan Okay Maraming na na-attract kay Sandro Kasi huwag tayong political masyado dito stats. Okay. So, malinaw to.

Itong example na to. Press 0 kung hindi, press 1 kung malinaw. Dali lang yung computation.

Ano? Question so far? Ayan.

Sige, another example tayo. Gusto ko kayo naman yung mag-formulate ng hypothesis. This one. 214 pa lang naman. Okay.

A psychologist is interested in the conditions that affect the number of dreams per month that people report in which they are alone. So gusto nilang malaman yung number of dreams per month ng mga tao dito sa example na to. Now, we will assume that based on extensive previous research, it is known that in the general population, the number of dreams per month follows a normal curve with a mean of 5 and a standard deviation of 4. So, pakinote na itong data.

Mean is 5, standard deviation of 4. So, sa population daw, ang average number of dreams per month in the population is 5 and the standard deviation is 4. Now, the researchers or the researcher wants to test the prediction that the number of such dreams will be greater among people who have recently experienced traumatic event. So meron tayong independent variable or quasi-independent variable kasi hindi naman tayo pwede magmanipulate ng trauma. So hanap lang tayo na nakaranas ng traumatic events.

So meron tayong quasi-IV na trauma. traumatic experience. And gusto natin malaman kung may impact to sa number of dreams. And ang prediction natin, mas madami daw yung number of dreams ng mga nakaranas ng traumatic event.

So is this a one-tailed test or two-tailed test? That's the first question. Is it a one-tailed test or two-tailed test? Based from the statement.

Okay. So, since meron tayong specific direction ng prediction, we will be using a one-tailed test. Okay?

Okay, now. Thus, the psychologist studies 36 individuals who have recently experienced a traumatic event. Okay?

So, the mean of their dreams after recently experiencing traumatic event is 8. Okay? So the mean of the dreams daw ng mga nakaranas ng traumatic event is 8. Should we conclude that the people who have or that people who have recently had a traumatic experience have significantly different number of dreams? in which they are alone.

So, I want you to carry a hypothesis testing at 0.05 significance level. One tail. Okay? So, gusto kong makita sa chat box what is our null hypothesis. Null hypothesis muna tayo.

Nal-hypothesis natin. So, our quasi-independent variable would be traumatic experience. And then, the dependent variable would be the number of dreams.

So, ano kayang pwede na nal-hypothesis? Chatbox tayo para may interaction. Malapit na yung nag-send dito Traumatic event has no significant impact to increase the number of dreams Charot lang sir Sige, ito yung mas magandang pagkakasulat niyan Traumatic event or pwede rin traumatic experience Does not significantly increase the number of dreams.

So, pwede ganito. Okay? Malinaw?

Iba ba? O, pwede rin yan. The traumatic experience.

Kaso, frequency yung ginamit ng isa. Sabi dito sa chat, naka-private, traumatic experience does not increase the frequency of dreams being alone. Kaso, ang kinukuha natin yung mean eh. So, hindi pwede frequency.

So, in general na lang, ayan, pwede ganito. Traumatic experience does not significantly increase the number of dreams. Or the average number of dreams.

Pwede rin ganun. And then alternative, traumatic experience significantly increases the number of dreams. Ayan.

So meron na tayong null and alternative. Alpha. What's our alpha? Alpha tayo. Ilan?

Okay, that's correct. 0.05. Next, the comparison distribution.

So since this is one-tailed, nasaan kaya ang ating rejection region? Is it left or right? 1 tilde. So based from the statement, increase. Okay, that's correct.

We have, right. What is the cutoff sample score or the critical value? Positive 1.64. Okay, double check. 1.64 ata yun.

Tama? 1.64? Okay, 1.64. Now, let's carry out the computation. Number 4. So, we have the mean of the sample 8. Population is 5. Standard deviation is 4. So, we need the mean of the distribution of means.

So, since equal lang naman daw ang mean of distribution of means sa population mean, we have 8. And then the standard deviation of the distribution of means or standard error, ilan ang standard error natin? So we have ito yung formula, square root of n. So ang n natin is 36. Diba?

Tama ba? Yeah, 36. So we have 0.67. So 4 over square root of 36. So, 4 over 6, that would be 0.67. Okay, now carry out the z-test. So, compute for the z.

So, ilan ang z natin? z is equals to m minus the mean of the distribution of means over standard error. So, we have 8 minus 5 over 0.67.

So, ilan? Ilan ang ating z? Ayan, nag-log na naman ako. Wait lang guys, mag-restart ako. So, what is our conclusion dun sa example kanina?

So, number 4 na, no? So, we have z equals to the mean of... The sample, ilan yung minang sample?

8. Tapos, population is 5 over 0.67. So, ilan yung ating computed Z? 4 point? Okay, 4.48. Okay.

So, yung comparison distribution, 1.64. So, what is our conclusion? Or decision muna tayo. Decision would be, are we going to reject or fail to reject the null? Ah, ito pala.

Pala ko nawala. Ayan. So, this equals to 4.48.

So, the decision is to reject the null hypothesis. Kasi nasaan ba yung 4.48? Buti na lang hindi sa kabilang side.

Nandito siya banda. So reject the null. So ibig sabihin, kapag daw nakaranas ng traumatic event yung isang tao, nag-i-increase yung number of dreams niya. Tatingin niyo kaya totoo yun?

Tatingin niyo? Is it true? Yes, that's true.

Ito, matututunan niyo naman ito sa abpsych ninyo. So abnormal psychology. In PTSD One of the criteria ng PTSD si merong recurring ng mga dreams, ng mga traumatic events.

So, common nangyayari yan sa mga may trauma na talagang tumataas yung number of dreams nila and yung content ng dreams related doon sa trauma na naranasan nila. Familiar kayo with Sherlock na series? Naalala nyo doon si Martin Freeman? si John Watson. Diba?

Nung mga first episodes, merong part doon na napapanaginipan niya pa yung war. Diba? Kasi may PTSD. Post-traumatic stress disorder.

So, yan. That's true naman. Na, yan. Traumatic events or traumatic experience can significantly increase the number of dreams.

Diba? Psychosomatic pa nga siya doon, eh. Yung sa legs niya.

Tapos nang wala pa si Sherlock M. Nag-fake that ano. Ayan. So that's Z-Test. Ayan. Nasaan na yung presentation ko?

Ba't kaya? Siguro sa sobrang init kaya naglalag yung whiteboard ko. Ilan na ba yung temperature?

Wait lang. Open ko lang yung presentation ko. Kasi patapos na naman tayo. Last part na. We have the advanced topic.

Wait lang ah. Nahanap ko lang yung presentation. Ayan. Okay. Ayan.

So, this is an example on how to report the results of a Z-test in research articles. So, kung mapapansin nyo dyan, so, ito yung conclusion natin. The study suggests, sabi ko sa inyo last time, huwag nyo gagamitin yung proves, magandang gamitin yung term na suggest, or this study provides evidence that Traumatic event has a significant effect on the number of dreams.

With the calculated Z, italicize yung Z, it's equals to 4.48, the P value or the probability value is less than 0.05. Kaya natin na-reject yung null. Nandun siya sa low probability value, yung 4.48.

Specifically, those subjects who experience traumatic events have greater number of dreams than those who did not experience traumatic events. Okay? Ayan.

So now the last part ng ating topic, nasa section siya ng advanced topic in the reference material natin. We have here the confidence interval. The confidence interval. So ano ba ang confidence interval? So ginagamit natin itong CI or the confidence interval to estimate the population mean.

Roughly speaking, this is the range of scores. kung saan natin makikita yung true population mean based from the sample mean. So, naalala nyo kanina, meron tayong mga given sample mean.

And in actual research, wala naman tayong idea about population parameter. So, paano natin ma-estimate yung population mean kung meron lang tayong sample mean? So, pwede natin gamitin yung sample mean using confidence interval. So paano natin kinocompute yung confidence interval? So bago tayo mag-proceed with the computation, which is very easy lang naman yung computation niya, ito muna yung mga common na ginagamit natin confidence levels or confidence intervals.

95 and 99%. Kung ang alpha ninyo is 0.05, the confidence intervals nasa 95%. Or yung confidence level natin is 95%. Kung 0.01 ang alpha ninyo, 99% yung magiging confidence level natin.

So paano ba iniinterpret yan? So halimbawa, kinumpit na natin yung range of scores kung saan natin makikita yung true population mean. So kung 95% yung confidence interval natin, pwede natin sabihin na yung true population mean is between the calculated range of scores. So mag-example tayo.

So, paano ba mag-compute ng confidence interval? You need the standard error and then you need the cut-off sample scores or yung critical values doon sa comparison distribution. Okay?

So, kung 95%, ang cut-off natin dyan, kailangan dito two-tailed eh. Ayan o. Ang cut-off natin dyan is the 1.96. So, kailangan nyo yung positive and negative 1.96 kung 95% confidence level. Pero kung...

99% confidence level, edo yung 2.58 yung gagamitin natin. Cut off. Okay? So, balik tayo dun sa example kanina.

Yung traumatic event. Sa traumatic event. So, sabi doon, ang sample mean is 8. Diba?

Now, imagine, wala tayong idea kung ano yung population mean ng mga dreams sa mga nasa population. Diba? Ang alam lang natin yung population nung hindi nakaranas ng traumatic event. Alam natin yung data nung mga individual na hindi nakaranas ng traumatic event. Ang mean niya is 5, standard deviation is 4. Now, wala tayong idea about the true population mean nung mga nakaranas naman ng traumatic event.

Pero meron tayong sample mean. Meron tayong sample mean. Now, pwede natin i-estimate yung population mean using the sample mean. Gagamitin lang natin itong confidence interval.

So, pakita ko sa inyo kung paano. Whiteboard. Ayan.

So, gawin natin two-tailed halimbawa yung test kanina. So, ito ay 1.96 negative and positive. So, ito yung 95% na confidence level natin.

At ito naman yung alpha level natin. So, since nireject natin yung null, So, alam natin na kapag nakaranas ng traumatic event, nag-increase significantly yung number of dreams. So, ang sample mean natin is 8. Gusto natin malaman, or gusto natin halimbawa magkaroon ng idea, ano kaya yung population mean naman ng itong mga individual na nakaranas ng traumatic event. Kasi itong population kanina, yun yung population nung hindi nakaranas ng traumatic event.

Kinocompare natin yung nakaranas ng traumatic event at saka hindi nakaranas ng traumatic event. So now, paano naman yung mga nakaranas ng traumatic event in the population? Ano kaya yung mean ng population na yun?

So gagamitin natin itong mean ng sample to estimate that. So ang gagawin nyo lang, apply nyo lang yung formula na tinuro ko last time sa z-score. So kukunin natin. yung range ng scores kung saan possibly nandun yung population mean natin.

Okay, so ganito lang yan. So you have the mean of the sample plus minus. Kita nyo to. 1.96.

Kung naka 95 confidence level kayo. Times the standard error. So ano ba yung standard error natin kanina?

0.67. So M plus minus eto yung Z na cut off. Z critical na lang. Times the standard error.

Okay? So we have the mean of the sample is 8 plus minus 1.96 times 0.67. So, tingnan natin.

Kunin natin yung lower limit. So, pag lower limit, ang gagawin nyo lang, ito muna, ima-minus nyo lang. So, imultiply nyo muna itong 1.96 sa 0.67, that would be 1.31.

So, 8 minus 1.31, that would be 6.69. And then, 8... plus 1.31, yun naman yung upper limit. So that would be 9.31.

So ibig sabihin, ayan, ibig sabihin, in the population, ang number of dreams in the population or the average number of dreams in the population naglalaro sa value ng 6.69 and 9.31. or the troop population mean lies between 6.69 and 9.31. And 95% confident tayo dyan na nandito yung true population mean.

Nakukuha? Press 0 kung hindi, press 1 kung nakukuha na yun. Ayan. So, yung computation ng confidence interval, again, ginagamit natin siya to estimate the population mean. So, again, meron tayong data about the sample, about the traumatic event tsaka yung dreams nila.

Pero gusto natin malaman or ma-estimate, paano kaya sa population? Ano kaya yung average number of dreams ng whole population? So, eto yung computation. So, in the population, in this particular example, we are 95% confident that the true population mean of the number of dreams in the population, in the population nito, lies between 6.69 and 9.31.

Okay? Nakukuha? Press 0 o hindi, press 1 kung nakukuha ninyo.

Ayan. Kuha tong confidence interval. Uy, huwag kayong mahiya magtanong.

Confidence interval. So, again, pang-estimate po ito ng true population mean based from the sample mean. Ayan.

So, na all confident. Ayan. So kung ano ang alpha level ninyo, 100 minus alpha level, yun yung confidence level natin.

Ayan. Okay? So in this case, ayan, 95, for one, hindi, for two-tailed ito, hindi one-tailed.

Kung napapansin mo kanina, ginawa kong two-tailed yung distribution. Ayan o. For two-tailed na ito.

Oo. Kapag one-tailed, wala tayong ano dyan. Positive and negative.

Kasi kailangan natin makuha yung lower limit sa left side at right side. Yung upper limit naman. So pag lower limit, ima-minus nyo lang yung product ng cutoff na z-score at standard error. Pag upper limit, i-add nyo yung product ng z na critical value at standard error sa mean ng sample. So kung ang mean ng sample natin is 8, ayan, 8 daw yung average number of dreams sa sample natin.

So sa population, ang average number of dreams naglalaro sa 6.69 and 9.31. Ito yung mga nakaranas ng traumatic event. Dito naglalaro yung population mean natin. At 95% confident tayo dito.

Ayan. Okay? So, stop ko na yung recording ko. Naku, pagdudugtongin ko na naman yung video.

Transcript for:Study on Sampling and CLT

Transcript for:
Study on Sampling and CLT