 We were doing testing hypothesis and we were discussing about what kind of statistical test we can use to test any assumption or hypothesis. So, remember we are in the inferential statistics where we want to test any assumption, any hypothesis that we make about the population. We take a sample, we test it and then we make an inference about the larger population. In our last module we did the t-test which is very simple and easy and we did one sample t-test. In one sample t-test usually one standard value is given and we compare this sample mean with that standard value. For example, just if someone claims that the average IQ of this class is this much, we will take a sample of that class and we will test whether the claimed average IQ is that much, whether the hypothesis is right or not. In most cases, the standard value is not given especially in psychology when you are conducting research, when you are doing group research or you are doing your thesis, manuscripts, dissertations, usually what you are doing you are comparing two groups. In clinical psychology or even psychology mostly what we are doing we are comparing male and female, we are comparing treatment one versus treatment two, we are comparing therapy one versus therapy two. So it's an experimental design, maybe we are comparing two groups or social sciences maybe even. As we say working women's stress level as compared to non-working women or how boys are different in their achievements as compared to girls. So when we have to compare two independent groups, we will be testing those assumptions or hypothesis through independent sample t-test. Independent sample t-test is a name that says that samples are independent, so the two groups that we are comparing actually are independent means that we have different people in group one and we have different people in group two. The two sets of data could come from two completely separate groups of the participants. So that's why it's called independent sample t-test or it's called independent male design or between subject design because between subject means that your two groups are independent. They are different people in group one, they are different people in group two, they could be entirely different populations like boys and girls, unmarried, then you are comparing them. So it's called independent or between subject design. In contrast to between subject design, we have a within subject design as well, which we also call repeated mayor. So repeated mayor is totally in contrast with the independent sample t-test. In repeated mayor, we measure the same subjects on time one and on time two. For example, you are running an experimental study and you are kind of looking at that you have given any therapeutic intervention, you have given some therapy, for example depression therapy, so what is the improvement, so you will be taking pre-test and then the post-test and in between you have the treatment, which means that the same subjects that you have assessed on time one, then you give treatment and the same subjects study the same sample on time two. So repeated mayor or within subject design means that we are using the same sample, same participants, same subjects at time one and then time two and we will be comparing those two groups. We are using, we have to make certain assumptions. You will be ending up with the misleading results or maybe you cannot use those results to kind of make inference. So t-test's assumptions is that observation within each sample must be independent. The two top populations from which the sample is selected must be normal. We have done sampling distribution and we said that if everyone takes sample from the same population and report a value, that will be normal or in other words, if our sample size is greater than 30, then naturally its distribution shape will be normal. So our second assumption is that our underlying population, with which we have drawn the sample, that should be normal or the second assumption is that the two populations from which the samples are selected must have equal variance also referred to as homogeneity. This is very important for t-test, particularly for independent sample t-test because you have to compare two groups. First, you are saying that boys and girls are comparing achievements, but if you have already recorded the sample in sample one, then they are really intelligent already or you have recorded them from your top school and you have done the sample of the girls, so if there are already differences in the group, then maybe you cannot conclude that boys are more intelligent as compared to girls. So homogeneity of variance means that the variance or variability in both groups should be equal. This is called homogeneity of variance and we can do it through SPSS test as well. So all these three assumptions we need to meet before we go ahead and run independent sample t-test.