[Music] inferential statistics is often the part of research methods that students dread and there are a fair few complex terms that we're going to use in this video but the statistics questions in the exam are often the ones that give you the most points for the least amount of writing so definitely worth getting right if you completed the video series so far we're going to use many of the ideas we've discussed already these videos in particular go into depth on the knowledge we're going to apply to inferential statistics in this video when it comes to answering questions in your exam papers for AQA the only statistical test we need to calculate is the sign test and I'll show you how to do that in this video for the other seven tests we just need to know their names and when to use them so in this research methods video I'm going to show you a simple way of remembering when to use each statistical test and I'll tell you how to show this knowledge off to The Examiner psych boost.com over 170 videos to help you with your qualification and patreon supporters can access bonus resources tutorial videos and the Discord Channel what are inferential statistics so you'll likely saw on this video without much of an idea of what the term inferential means well in the previous video we covered descriptive statistics those techniques like measuring the central tendency or dispersion summarize and describe raw data that researchers collect from the sample inferential statistics go beyond the sample they generalize the results in other words they make inferences about the behavior of the entire Target population from the data collected from the sample the question the researcher needs to ask is this from the data collected from the sample how confident am I that this data is strong enough to support my inference that the same behavior is found in the Target population as we covered in the previous video the researcher makes that decision on the basis of probability if the likelihood of the results being due to Chance is less than 1 in 20 phrase formally is p is less than 0.05 this arrow symbol means less than by the way then the data collected from the sample is just to be significant and accepted the statistical tests are the tools that the researchers use to work out of the results are significant and they use different tools depending on how they've structured their research study deciding which statistical task to use in your exam when a stats question is asked before the question you're highly likely to see a scenario what we call a stem this stem will probably outline a piece of research and this demo will provide you of all the clues you need to figure out which statistical test is needed for the stats question you're asked you can see here I have an empty table you're going to want to grab some paper and fill this out with me because this table is how we're going to take all the clues given to you in the stem and come up with the right statistical test to use and be able to justify to The Examiner why we've chosen it first thing we want to figure out is if the study is a correlation or a test of difference a correlation is when the research just measures two covariables and looks for a relationship so you're looking for words like correlation relationship or Association in the stem a test of difference simply means an experiment the researchers testing for a difference in the dependent variable as a result of manipulating the independent variable if you think back to the experimental design video you should remember independent groups design the data we get from this design is known as independent data because the groups are measured independently you should also remember repeated measure design the data we get from this design is called related data as each data point in one condition has a related data point in the other condition there is also match pairs design now it's important to remember we treat data from matched pairs despite coming from separate groups as related data as each data point in one condition has a match data point in the other condition along the top of the table we have the levels of measurement nominal data dating categories or no data data that we can put in order and interval data where there's the same difference between each data point we also treat ratio data as interval data in this table the statistical test that we'll use depends on the dependent variable's level of measurement or in a correlation the covariable with the lowest level of measurement I'll fill a table with the names of each of the sysical tests as you can see each of the statical tests is only appropriate for a particular combination of data and it's your job to work out which one to use in an exam so at first this might be a little overwhelming with such a large number of unusually named statical tests but quite frankly we need to memorize this table and actually if you write it out a few times from memory it will go in a good strategy is to make a phrase with the first letter of each Cisco test so s w r c m u c s p and that for me is space weather really contains many UFOs chasing small pigs that works for me you might be able to think of one that works better for you but the point is to get the right letters into the correct part of the table then we can write in scientist wilcoxon related t-test Chi Squared man Whitney unrelated t-test chi-squared again spearman's row and Pearsons so to be clear on how this table works if the study in the stem is a correlational study the stats test to use be one of the ones in the bottom row it is an experiment also called a tested difference then the test we want the ones on the top two rows we can then narrow it down by figuring out the experimental design if it's independent group so unrelated data it'll be one of the tests in the middle row if it's repeated measures or matched pairs the data is related data and the stats test used will be in the top row final decision we need to make is on the data collected if it's nominal the stats test we need we found in the First Column ordinal or second and interval the third now you need to be able to sketch this table up very quickly to remind yourself which test to use or Justify why a test was used both possible questions here's a quick sketch I made after a couple of practice goes it took me less than 30 seconds and in an exam situation when you're looking at a stats question that might be worth seven marks 30 seconds to draw this in the margin is a really good investment to make sure you're picking the correct test if we can figure out all of that from the stem we should now have our stats test selected using the stats test table so you should have your own stats test sketch to hand here are nine examples of studies pause the video and see if you can figure out which study goes with which statistical test think carefully about the language used in each example once you've done that unpause the video and I'll walk you through each example number one for this study the researcher will use at Pearson's R it's clearly a correlation and the date you use for each covariable is at the interval level of measurement two for this study the research will use a chi-squared the study is an experiment so a test of difference the researchers using embedding groups so unrelated data and the level of data used to match the DV is categories so nominal free for this study the researcher would use a spearman's row this again is a correlation and the data collected is at the ordinal level full this is an unrelated t-test a test of difference and unrelated data as independent groups are used as it has unrelated in the name the status is pretty easy to remember the data collected is at the interval level 5. wilcoxon this is a test of difference it uses repeated measures so is related data and it's collected at the ordinal level six a sign test a test of difference and again it uses repeated measure design so related data but the data collected is in categories so nominal data 7 a related t-test as an experiment it's a tested difference its related data as it's a match pairs design and the data collected is of course at the interval level eight a man Whitney it's a test of difference using an independent group's design so unrelated data the data collected is at the ordinal level finally nine for this study the research will again use a chi-squared this time for a correlation but the data again is at the nominal level so from that task you should now be able to identify the stats test that needs to be used based on the details you're given in the exam but you also need to be able to actually answer status question in a way that will maximize your marks in the exam let me show you how we can do that how to answer the stats question a common question to ask after this damn is name an appropriate cyclical test that could be used justify your choice for marks so using the skills we just developed we can take the clues given in the stem and identify the test as a man Whitney test now we've done the hard work but only got one point so far we have to justify why we've named the test so this is likely one point for saying it's a test of difference one point for saying it uses unrelated data and a final point for saying the data is at the ordinal level the question is sometimes phrased differently the question could say the name of the test used and asked to explain why this was a suitable test then we have to justify why the test was used in the same way keep in mind for these questions to get all of the marks it may not be enough just to save the test of difference you need to stay clearly the levels of independent variable if it's a correlation give both covariables and explain the researcher was looking for a relationship between them when stating that data is nominal or nor interval State exactly what scale was used in the study I've seen these questions scored as high as seven marks so it's well worth taking the time to contextualize your response to get them right a more complex stats test question will ask us to work out if the test is significant or not in this case we'll see a critical values table which again looks a little intimidating but really with a bit of practice they are fairly easy to use somewhere in the stem it will state the calculated value worked out by the researcher your job is to compare this calculated value to the correct critical value in the critical value table but how do you find it firstly we need to work out the number of participants in the study again this will be mentioned somewhere in the stem for some of the tasks something called degrees of freedom are used instead of participants but again it should give you this in the question or the stem now we know the row and we can ignore all of the other values in all of the other rows now we need to figure out the level significance used well if you remember from the probability video it's likely 0.05 0.01 is very occasionally used in replications or of the study is controversial if the question wants you to use a 0.01 level it should tell you in fact so far I've never seen a question that didn't use a 0.05 level of significance not saying it can't happen but I've not seen it so picking 0.05 we're now down to only two numbers 0.05 for a one-tailed test and 0.05 for a two-tailed test thinking back to the hypothesis videos You'll likely remember a one-tailed test is a direct hypothesis and a two-tailed test is non-directional in this case the hypothesis is directional you should be able to work this out from the question it's either going to tell you if it's directional or not or it'll tell you it was based on previous research which means the researcher is using a directional hypothesis one final step under the critical value table it will tell you if the calculated value has to be equal or greater than or equal and less than the critical value to be significant in this case our calculated value is greater than the critical value so our data is not significant now to complete the question we need to write our answer in a way which shows to The Examiner we've used all the steps required to reach our conclusion and here's a template sentence that will help you structure your answer as The observed calculated value insert calculated value given here is greater or less select one of those than the critical value insert the critical value you found here we must accept or reject the alternate hypothesis at P equals 0.05 or really unusually 0.01 for a and then a one or a two-tailed test this sentence will likely be worth a large number of points as you're effectively explained to The Examiner why you came to a conclusion on the significance or not of the data working out degrees of freedom now it is possible if we're using a chi-square test AQA will ask you to work out the degrees of freedom DF before using that to read the critical value of the table I've only seen this once so far and the question gave you the formula but I'm going to quickly show you how to do it and it's pretty simple this is a formula and this is the table we're going to use it on so degrees of freedom is simply the number of rows minus one times the number of columns minus one we can now use this to find our critical value and complete the question calculating the sign test the one and only statistical tasks that we can be expected to calculate is a sign test fortunately once you know how to do it it is super simple and won't require Maps more complex than addition and subtraction in an exam you might be asked to complete the scientist from start to finish I'm going to show you how to do that but it's more likely you'll be asked to do part of the process like identifying n or s hopefully you remember from the grid the researcher uses a scientists when they conduct a test of different so an experiment not a correlation the experimental design is either repeated measures or match pairs so related data and the level of measurement is at the nominal level here's a set of scores I've made up for repeated measures experiment still participants have completed both condition a and condition B here are the raw scores for each condition the first step is to subtract the score and condition B from condition a it actually doesn't matter which way around I do this I could subtract condition a from B and the sine test would still work so in the first row it's nice to track 11 that's -2 and I'm going to do exactly the same for each row I now need to record the sign positive or negative for each of those calculations the first row is negative the second no sign so I'm going to leave that blank another third positive and so on now I can work out two really important numbers n and S N is the number of participants where there's a difference between the conditions so that is simply counting up all the positives and negatives in this data set n is seven and that's because there are five negatives and two positives we can ignore the three participants who score the same in each condition s is the least frequent sign so there are five negatives and two positives so s is two if you think about it s is all the people in the study who didn't behave in the way expected by the hypothesis and as you can probably guess for the data in a study to be significant this needs to be as few people as possible with n and S we can now find out if the data is significant or not using a critical value table we do this using the process I showed you earlier in the video let's say from the question in the exam paper I know this is a directional study and we're using a 0.05 level significance I'm looking down the First Column as that has a 0.05 for a one-tailed test I'm looking across an N of 7. and the point where these intersect is my critical value for the sign test the critical value has to be equal to or less than the calculated value to be significant because my calculated value of s is 2 which is more than the critical value of zero this means the data is not significant the alternate hypothesis is rejected and the null is accepted as you can see with such a small sample with only seven participants showing a difference between the conditions s would have had to be zero to be significant and as you can see as I include more people in the sample the non-participants behavior going against the hypothesis can increase while keeping my results significant I have eight tutorial videos coming the As and a level research method sections from 2017 to 2020. these videos have worked example to every question are full of exam tips patrons at the neural level and above can access these and many many more hours of exam tutorial videos as well as over a hundred printable resources from across the a level over on siteboost.com I do want to thank all the students and teachers who've supported site boost over on patreon during the development of the research methods unit it's their support that allows me to teach part-time so I can make psych boost on YouTube for everyone I also want to give a special shout out to the patrons who support me at the developer level so thanks to them and I would say see you in the next research methods video uh but this uh over one year epic of of prep is done hope you enjoyed it thank you very much right