 students, this is the multivariate analysis of variants using software. Manova, we have done previous, now here we are doing Manova with SPSS. We are checking the two mean testing, only two mean testing we have to see, so we use T test in the univariate test. We are testing the two mean vector, we use Hoteling T square. For more than two mean vector testing, we are using Manova. So here is the example of the multivariate analysis of variants. Now the example is a nomadical example of the multivariate analysis of variants. You can say that this is the Manova. Suppose we want to investigate the effect of three different teaching methods. So we have the three different teaching methods, method A, method B and the method C on student performance. A method A, suppose method A is the online teaching, method B is the on-campus teaching and method C may be is the presentation, quiz or assignment teaching method. On student performance in three subjects, so we have three subjects, maths, English and science. Now in three subjects method A, in three subjects we will check its effect. Method B, in three subjects we will check its effect on student performance. Method C, in three subjects we will check student performance. Now the test, the hypothesis that all three teaching methods have the same effect on subjects, basically what we have to test is that all three teaching methods have the same effect on their subjects or they have different effect on their subjects. So the hypothesis we have, the hypothesis that the teaching method have the same effect on the subjects. Our hypothetical data set with 30 students, 10 for each teaching method. Total we have 30 students and 10 we have set according to each teaching method. So this is the data. So we have 20, 30 students. Total we have 30 students, 1 to 15 and other is the 15 to 30, 16 to 30. Now this is the teaching method A, this is the teaching method B and this is the teaching method C or unkaan ne konsa score che ghi hai, maths, science and English. Similarly this is the teaching method of A, B and C and here is the score of maths, science and English. Now this data we will take from here on SPSS and SPSS further we will analyze it. So this is the student ID, teaching method, maths, science and English. Now how many students do you have? We have 30 students. Okay, teaching method. Here you will go to variable view, ID, teaching method. The teaching method you had, if we will keep A, B, C then instead of numeric you will give it a string. So it will take the according of A, B, C. But what have we done here? Basically we have coded here. I have called method A as 1, method B as 2, method C as 3. Again method A as 1, method 2, B and method C which is equal to 3. We have coded here. And same math, science and English. Now what we have to do next? Analyse, journal-linear model, multivariate. Okay, analyze, journal-linear model and multivariate. Where do you have coding in multivariate? Teaching method make coding here. Teaching method, I have called it a fixed factor. And what are the variables we have in dependent? Maths, science and English. Math, science and English. And I have not touched any model here. I have not touched any option or anyone. And just I have done okay here. Now this is the output. Intercept. 1, 2, 3. You have how many each in 10? So you have method 1, method 2 and method 3 in 10 values. This is the Wilkes-Lambda. Teaching method of Wilkes-Lambda, what are the values we have? Here we have Wilkes-Lambda. So 0.281 is its value. Hortling trace 0.27. Plystrace 0.294. So here you have a multivariate test. Now we are going further to the slide. Now here is the solution. We have the hypothesis H0 mu1 mu2 mu3 means all teaching methods are equal. This is all three. Methods are equal. Not all methods are equal. This is the alternative hypothesis. And the significance value is 0.05. And this is the test statistics. And this is the Wilkes-Lambda. So these are the degree of freedom. To perform the Manova, I have performed all the Manova. To perform the Manova, what did you have? Organize your data with one row per subject and column for subject ID, treatment groups and the value of the dependent variable math science and English. We have prepared the data. Define your variables. Define in the variable view. We have defined the variable math, English and science. Math, science and English. We have defined all the variables in the variable view. Next, this is the step three. Where did you go? Analyze. Journal-linear model. And from there we entered the data in the multivariate. And how did we enter the data? We have three dependent variables. We have moved them in the dependent variable. And we have moved the dependent variable which was our student ID in the fixed factor. Then click the option. If we want a post-hoc test, we want a tucky test, we want to check their significance, then we apply them. You know what condition they apply. If P value is less than, then we have a test applied. Post-hoc test. Then click Manova. And after clicking Manova, you had a result generated. And in the result, you have seen what is P value. We applied the multivariate test. We use the univariate test when we have single variable with different options. That is, we had to do only one comparison with three subjects. So, then we use the Anova test. Then, we have interpreted the significance level. We have interpreted it. We have used the Manova test. If you look at the values of Manova, then the values of Manova were insignificant. When we saw the values of Manova, the values of Wilks-Lemda, the values of Wilks-Lemda were basically insignificant. So, to get insignificant values, we have to interpret the reason for that. So, we conclude that. What are we doing? Hypothesis, we have all teaching methods have the same effect on students. Yes. All teaching methods have the same effect on subjects. We have the same hypothesis which we determined, which we constructed. We have the same hypothesis in the conclusion. So, we have accepted null hypothesis. What we have in acceptance? All teaching methods have the same effect on subjects. This is the conclusion of this example.