Module 11, two-way tables, 5 of 16. Exploring the relationship between two categorical variables. Exploring the relationship between two categorical variables, in this case body image and gender, amounts to comparing the distributions of the response variable. In this case, the response variable is body image.
for different values of the explanatory variable. In this case, the explanatory variable is gender. Example, is body image related to gender?
For each body image category, we compare females and males, so we need to know the total numbers of females and males. We no longer need to know the total number of students for each body image category. So we remove these totals from the table. Note that there are many more females than males in this sample. So when we compare females to males, it is misleading to compare raw counts in each body image category.
For example, it is misleading to say 560 females responded about right compared to only 295 males because the sample includes a lot more females than males. So we have a total of 760 females but we only have 440 males. So instead, we compare the percentages of females who responded about right to the percentage of males who responded about right. So we want to compare percentages instead of counts, right? And that is very important.
Of the 760 females, 560 responded about right. To get the percentage, we divide. So 560 divided by 760 will give me 73.7%.
Now of the males, 440 of them total that we have. 295 of them responded about right. So we do part divided by the total. In this case, the part is 295. The total is 440, and we get a percentage of 67%.
We can interpret the percentage as a number out of 100. So by converting to percentages, we are... reporting the results as though there are 100 females and 100 males. We can see that a higher percentage of females feel about right about their body image.
Note, it is important to identify the explanatory variable because we always use the totals for the explanatory variable to calculate the percentages. So you always want to be aware of what is your explanatory variable. So that's something that you want to figure out when you're reading a problem. We call this condition of percentages.
So what we just calculated right here, we call these conditional percentages. The percentages in the female row are the distribution of body image based on the condition that students are females. The percentage of the male row are the distribution of body image based on the condition that students are male. Thus, our two sets of conditional percentages Form two conditional distributions for body image.
So here we have the conditional distributions of females. For females, we have that 73.7% thought of their body weight as about right. Right, and again that is a conditional percentage.
Conditional percentage. So it's under the condition that the student is a female. So if we look at let's say this percentage right here, 16.4 percent, right, so this percent is under the assumption, right, that we have a male student. So 16.4 percent. male students thought of their body weight as overweight.
And here is a side-by-side display comparing the conditional body image distributions for females and males. So here we could clearly see right that females think of themselves as 73.7% of them think of their body weight as about right, versus males, only 67% thought of their body weight as about right.