 Since we have done a two-way independent sample ANOVA and one-way independent sample ANOVA and then we did one-way repeated MANOVA, moving forward today we will be talking about repeated MANOVA with more than one independent variable. We know that between group design can be extended to incorporate multiple predictors more than one independent variables, same can be done and same could be true for the repeated MANOVA samples as well. Pictorial repeated MANOVA is used where the effect of two or more within-subject vectors on the dependent variable needs to be investigated simultaneously. Just like we have done in two-way independent sample ANOVA, just like we have done in repeated MANOVA, we can take more than one independent variable where individual variations of the subjects cannot be controlled. In those conditions where individual variation is too much and we want to control it, two-way repeated MANOVA is our best choice. What we do is that all subjects are tested in each level of both the factors. Like we have done in one-way repeated MANOVA, we have the same subjects and we use those same subjects across all levels of the independent variable. Here in two-way MANOVA, similarly, we will be using the same participants across each level of each independent variable. Mean difference between groups split on two-within-subject vectors are compared and then we compare them to groups that we have manipulated. For example, if we have factor A and it has two levels, like level one and level two and factor B, we have three levels, B1, B2 and B3, there will be six treatment conditions. Like we talk in factorial MANOVA, if it is a two-in-two, then two-in-two will be our four possible levels or conditions in which we have to take our participants. If our two-in-two-three factorial MANOVA means that our first independent variable has two levels and our second independent variable has three levels. So two-in-two-three means that we will have six possible conditions. Always remember that we are talking about one-way MANOVA, repeated or independent, and we are talking about two-way MANOVA, in which we have more than one independent variable, but our dependent variable will always be one. Because if we are increasing dependent variables, it means we are heading to the multivariate analysis, which we will not talk about multivariate in this BS level courses. So in factorial MANOVA, we can increase the number of independent variable and the number of independent variable within each variable, but our dependent variable will always be one. So the design investigates both the main effects of all factors and the interaction effect of the both factors, like we have done in the independent factorial MANOVA, where we calculate the main effects as well as the interaction effect. So this is similarly the two-way MANOVA factorial. Here is an example. We will do this in detail in the SPSS. There is a research evidence that attitudes towards stimuli can be changed using positive or negative imagery. We can change the attitudes by giving a positive or negative imagery. So as part of an initiative to look at which type of imagery could be used to make teenagers' attitudes towards alcohol more negative. So they wanted to make the attitude towards alcohol negative using different kind of imagery with each drink. The scientists compared the effects of three types of imagery that is positive, negative, and neutral imagery with the two different types of drinks, that is coffee and alcohol. So here we have two independent variables. Number one, drink, type of drink, where it has two levels, alcohol and coffee. So this is one independent variable and it has two levels. And secondly, our independent variable is type of imagery. And we have three levels in which we used positive imagery, negative imagery, and neutral imagery. So 2 into 3 means we have two-way MANOVA, where there are two independent variables. There are two levels of one, there are three levels of one. And if you're calling it a repeated MANOVA, it means that we are using the same participants in each one of these six conditions. So 3 into 2, 6 becomes 6. And 6 means that in all six conditions, we are only one participant. There would be like 1, 2, 3, 4, 5, 6, 7, 8. So eight participants across all six conditions will be used. So here I have explained that there are two predictor or independent variables, type of drink and type of imagery. The type of imagery used positive, negative, neutral, three levels, and the type of drink, two levels. So these two variables completely cross over, producing six experimental conditions. How do we make this hypothesis as we did in an independent MANOVA or one MANOVA? Similarly, we'll be using the same to construct our hypothesis. So main effect, main effect of drink, we'll make that there is no group main effect or at least one group mean is different or it differs. And similarly, main effect of imagery we'll make null hypothesis that there is no difference or alternative hypothesis that at least one group mean is different from the other two groups. Or is it that our interaction effect can be hypothesis? So if there are two independent variables, there will be three types of hypothesis, one for the main effect of first independent variables, second for the main effect of second independent variable, and third for the interaction of two variables so the null hypothesis would be there's no interaction between drink and imagery for alternative or that could there exist interaction between drink and imagery. In the next tutorial, we'll be using SPSS and conducting the same data in SPSS.