 Dear students, up till now we have studied two tests for hypothesis testing. One of those tests was Pearson R correlation test and the second one was a partial correlation coefficient test. Now we will talk about independent sample T test. Independent sample T test is a part of the T test which we conduct for the hypothesis testing. The other types of testing include paired sample T test, one sample T test, and one independent sample extension which we call one-way ANOVA, that comes. If we talk about independent sample T test, then this test is conducted or performed when you want to see an effect on a dependent variable of a nominal variable or if we want to say that you want to see an effect on a dependent variable of a grouping variable. So when you perform this test, then you have to have a dependent variable that is a composite score or it is measured on a continuous level and our independent variable is a grouping variable, nominal dichotomous variable, which has two categories. If there are three categories of a variable, then we can perform this test with two categories. When we perform this test in SPSS, then I will tell you its procedure. Before performing the independent sample T test, let's talk about its assumptions. The first assumption is that there should be independence of observations, i.e. your respondents belong to a particular group, they do not fall into a group. For example, we want to see the effect on gender on the base of gender on the GPA, so there should be an independent observation that the men report will not be in the women's category. In some situations, there should be a clear dichotomous variable where your independence of observation is not there. Before performing this test, we have to see in the dependent variable for each group category that there is no outlier. i.e. if you want to see the effect on the GPA of gender, then you will check the GPA with reference to the men and GPA with reference to women, they are normally distributed and there is no outlier. The fourth assumption is that if we are going to compute a test of two dichotomous categories, then your dependent variable should have equal reports for both groups. If this is not an equal report, then we will use its alternate path to compute the T value. In the independent sample T test, if we talk about hypothesis, we write it in this way that there is no mean difference on the basis of grouping variable and the alternate hypothesis we will write that there is a statistically mean difference on the basis of a grouping variable. The procedure for performing this test in SPSS is that you will go to analyze and tick the compare means. After clicking here, you will select the independent sample T test option. If you select it, you will have this dialogue box open in which it will ask you what is your test variable and what is your grouping variable. So the test variable here is our dependent variable and the grouping variable is our independent variable. And you have to remember that the test variable should be continuous in nature and the grouping variable should be a dichotomous in nature with two categories. So here we have seen that we want to look at preventive behavior, effect of gender. When you select the grouping variable here, it will ask you how you have given the values of groups. So the coding you have done in your SPSS sheet is what you have to write here. For example, if you have coded the gender with 0,1 key, if you have coded it with 1,2 or 2,3, then you will write it here. We will check it with 95% confidence interval. So we will continue this and you will continue this too. So when you continue this and do OK, then you will have two tables in the output view. So this has multiple information for you and it is necessary to understand it. So the first information you have to check is that the assumption of independent sample T test is that the equal variance should be assumed. So if we look here, the seek value is bigger than 0.05. Our value is 0.188. It means that we are accepting our H0 that the equal variance between both groups is assumed. So now we will look at the T value. So the T value is actually the value of the T test statistic. Now we have to see if this T value is significant or not. So for this we will look at the seek to tell value. So we have 850 which is bigger than 0.05. So here we will accept H0. There is no difference in the means only basis of gender in preventive behavior of the respondents. So our alternate hypothesis is accepted. Alternate hypothesis is rejected and null hypothesis is accepted. Now this is our hypothesis test. But in these two tables there is a lot of information which is meaningful for you. For instance, here you can see that the mean of the male is 27.22 on preventive behavior. Female and male are 27.11. So on the score of preventive behavior, the score of the female is slightly more. It is not statistically significant. But the female score is slightly more as compared to the male. And the difference between the two is 0.104. And this difference is very minute. That is why our alternate hypothesis is rejected. You have given the standard error value. Now where is the standard error value computed? So this is actually the standard error value. Your standard deviation divided by n. That means your value is 6.209. If we divide it by the root of 208, then you will get this value, 0.430. So the standard error value is computed from here to you. With this, if we look at how t value is computed. So the t value is your mean difference. If we divide it by the standard error, then you will get t value. That means if we divide 0.104 by 0.430, then the score you will get is 0.190. So this is your t value computed from here. With this, you have 95% confidence interval of the difference. So how does this compute? So this value is actually, we compute. For example, if we look at the lawyer, then this is your value computed. Mean difference minus value of z, multiplied with value of standard error. With this, you get your value. If we look at the upper limit, then the mean difference plus z, multiplied with the value of standard error. So z has 95 confidence interval of 1.96. So with this value, you get these values. So the rule of thumb of t test is that if the interval difference is 95%, if it is 0, then your alternate hypothesis is rejected. In our case, there is 0 in the middle. That is why our hypothesis is rejected. Now let us look at another example of this. Here we have seen the effect of preventive behavior. What is the effect of age on this? We had two age groups, up to 25 years and 26 to 50. If we look here, then the equal variance of preventive behavior was not assumed. That is, the sig value is 0.01 is smaller than 0.05. Now we have accepted age 1. When age 1 is accepted in this situation, then the t value will not be assumed. If we look here, then we know that the t value here is 0.088 which is higher than 0.05. Our hypothesis is not accepted that the two age groups have a significant effect on the score of preventive behavior. Because t value is not significant in this case. I have told you with two examples how to conduct independent sample t test and how to interpret it. How to compute table and write up and when we start the reporting section, we will study it.