 We have done one sample t-test and independent sample t-test. Now the third kind is repeated mayor t-test or match group t-test which we call within subject. So repeated mayor t-test may or repeated mayor designs may which is a within subject design is one in which the dependent variable is mayor two or more times for each individual in a single sample meaning abhaja a group one or group two lehneke we ek sample ko at time one time two assess karte hain aur phir uski hain. Dekne ke significant difference aah. Psychology me jab hum experimental studies run karte hain. So usually hain pre-testing karte hain aur phir post-testing karte hain. It's not therapeutic intervention me bhi koi bhi therapy de ne se pehle we do pre-testing and then post-testing. So there are many kind of situations where we have to test the same participants at time one and time two. Je se mai usually apni class ke andar students ka motivation level check karte hain jab wo enter hote hain semester me aur phir by end of the semester unka motivation check karte hain ke wo kahaan ge hai. Isitaraan boh se variables ko time one time two ke upar mayor kar kya assess kar sakte hain ke kisi bhi intervention technique ya phir kisi bhi treatment ka kya effect aah waal. So in repeated mayor design aur in within subject design, we may hear the same participants two or more times. Repeted mayor design, this approach is also used when you have matched pairs of participants ya se aap groups ko match bhi kar lethne ya se for with age aapka gender aapka any specific criteria masan aap IQ ke upar aap kisi bhi ek variable ke upar subjects ko match kar ke phir bhi aap unko use kar sakte hain to hain to hain to hain to hain to hain to hain to hain to maach group design bhi kya dein. One of the pair is exposed to intervention and the other pair is exposed to intervention to jesa agar maach group design hain aur main aalready students bhir kool aegi taran ke IQ ke aur aegi gender ke aegi age ke bachhe liye hain taakke main baaki extraneous variables ko control kar sakute unko main aekko treatment one di hain aur aekko treatment two di hain and I want to see what is the difference. The T statistics for our repeated main design is structurally similar for other T statistics. So structurally it is the same as we used to do the mean one minus mean two as we have now compared boys and girls in an independent repeated main, we do time one and time two. But instead of taking raw scores in it, we take the difference that the score above time one and the score above time two actually have a difference. So the first step of repeated mayor or match group design is to calculate the difference between time one and time two on the dependent variable. Typically the difference scores are obtained by subtracting the first score, i.e. before treatment from the score, second time score after treatment for each person, and we calculate it as mean two minus mean one. Hypothesis for repeated mayor T-test is that null hypothesis would state that the difference in time one and time two is equal to zero. So time one minus time two difference is the mean difference which we denote in this way. Just like we do the independent sample that mu one would be equal to mu two. Similarly for repeated mayor we will claim the mean difference is zero. The alternative hypothesis states that there is a treatment effect that causes the scores in one treatment condition to be systematically higher or lower than the scores in the other conditions. So the alternative hypothesis would be that mean difference is not equal to zero, i.e. the scores after treatment would be greater as compared to one. And in this also, just like we calculated for the sample, we do the same for the mode less. Like we said, this is the difference of the population. Usually we don't have it. So by ignoring it, we just report the mean difference in both the groups, time one and time two. And then we divide it with the standard error of the mean difference. To calculate the estimated standard error, the first step is to calculate the standard deviation or you can calculate the variance and then you put it in its formula. So if you have calculated s, then usually you will get the standard error. But if you have calculated s square, which is equal to ss over n minus one, then you will use this formula for the standard error. We have already done it manually. And then we run it in SPSS. So here's an example. Please note that I have used all the examples and materials here. That is your textbook, which I have recommended to you on day one. All the examples, most of the content and the outline we have followed, we have followed your same textbook. I am sure that you have the copy. I will also leave a soft copy for you people here. So here's an example. A major oil company would like to improve. It's a tarnished image following a large oil spill. Its marketing department develops a short television commercial and test it on a sample of N7. So what information do we have in size? The other participants, seven participants, people's attitude about the company are made with a short questionnaire, both before and after viewing the commercial. So the data gives a mean difference of three. So they already calculate the mean difference. Time one, how was their company image? And after watching the commercial company image, its mean difference is three. And the ss, the sum of squares is equal to 74. The sum of squares means that you have x minus mean square, this value is given. That is, every x has a mean difference minus. So that is your 74. Was there a significant change? So first, let's do it manually and calculate it here. We have n size given, we have ss given, n we have six, and we have your ss given, which is 74. And you have a mean difference given, which is equal to three. So our degrees of freedom is given, n minus, sorry, is seven given, n is our seven, degrees of freedom will be six. n minus one is equal to six. After that, we have to see the critical value of t. Your critical value of t at six degrees of freedom and alpha point zero five, two-tailed test, your value in the table, if you look at two-tailed test, alpha point zero five, six degrees of freedom, that is plus minus 2.447. You can go back and consult the table, which we told you earlier. So this is actually the critical value. And with this, we have to compare the calculated value. So for the calculated value, first of all, you calculate the variance, and variance is equal to s square. So the variance we'll calculate, which is equal to ss over n minus one, ss is your given, 74, n minus one is six, it is equal to 12.33. So this is actually variance, right? So if we take this under root, then it will become standard deviation. Now we have to calculate the standard error. So to calculate the standard error, what you have to do is that you have to do variance divided by n. Now here, we don't have to do n minus one, because we have already done it. So variance divided by n, you have to put values. We have taken variance 12.33, n is our seven. We'll take this under root, please get your calculator, solve it, answer will be 1.33. I have already solved it. After that, we have to take out the calculated value of t. For the calculated value of t, we will do mean difference, which we can denote with md. And divide, we will do standard error of mean difference, mean difference is given to us. And the standard error, we have already calculated 1.33. Now when you calculate, the value will be 2.26. So this is calculated value. I'm sure that now you can compare 2.26 with 2.47. So our t at degrees of freedom 6 is equal to 2.26, which is smaller than t calculated, which is 2.447. So if our value is smaller, then our null hypothesis, our result is not significant, not significant, but if the result is not significant, then we fail to reject null hypothesis. Fail to reject null hypothesis. Okay, so what was our null hypothesis? Now we have told you that your null hypothesis, the mean difference will be 0, and our alternative hypothesis is that the mean difference will not be equal to 0. So in this case, when the calculated value is smaller than the table value, our results will be insignificant. Why? Because our results will be in our acceptance region. So our value 2.447 was critical here. If it was bigger than that, then it would fall in this critical region. But now our value is coming in this region, so results are not significant. This is how we'll calculate repeated mayor design.