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Next, we will talk about the independent-samples t test. this is another inferential test that has a t distribution for its sampling distribution. Use this when you have two groups of participants and each person is in only one of those groups that is what it means by independent-samples. they are independent in the sense is that the two people is different groups aren't connected with each other in any way. they are independent of one another. You could have a caffeine condition and a decaffeinated condition, and you have different people on those two different groups. the people in those groups would be independent of one another. It is althe case that you only use this when you have a scale dependent variable. So, your outcome variable has to be interval or ratio scale a measure. You also, when you are using these, you don't know the population means or the population standard deviation. And you will be comparing two groups in this case. Really, you are making inferences about two population means.

The research hypothesis I will use as an example for the independent-samples t test is that men do better on statistics exams than women do. You might think this is the case because you think men are better at math or something like that.

The null hypothesis for this research hypothesis would be H-sub-nought (H-sub-0), colon, the population mean for men is the same as the population mean for women. If the null hypothesis is true, the research hypothesis is wrong. If the null hypothesis is true, there is no difference. Nothing interesting is happening in the population. Next, we will go through the steps for doing an independent-samples t test.

The first step is going to be to just write out what your null hypothesis is. Here, we are working with the research hypothesis that men do better on stats exams than women do, so the null hypothesis is going to say that they do exactly the same as each other. H-sub-nought, colon, the population mean for men (the average men's statistics score) is exactly the same as women's average statistics exam score.

The next thing we will do is draw the population distributions. Notice, there are two population distributions now. There is one for men, and one for women. These are going to be frequency distributions over here and like they have been in the past. This one being for men and one for women. This is the population distribution. These are our individuals up here. Individual men and women at the population level. Remember, this is if the null hypothesis is true. This is the null hypothesis population distribution of individuals. There is actually two distributions up here now. They are both normally distributed. One is men and the other one is women. I am trying to draw these so they are perfectly overlapping. For this, if we say black is men ... and the null hypothesis says that these two distributions have the exact same mean. There is more than one way to do these tests, but the one we are gonna do in this class, it is gonna assume that the standard deviation for women is the same as the population standard deviation for men. Notice we don't know what these population means are. We just know that they are the same as each other. And, we don't know what these standard deviations of these distributions are, but we are ultimately going to have two estimates, one from each of our samples, of what this exact same shared number is.
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