MANOVA in SPSS
MANOVA in SPSS is similar to ANOVA, but it involves two or more dependent variables instead of one. It is concerned with examining the differences between groups. It also examines the group differences across multiple dependent variables simultaneously.
Use MANOVA in SPSS when you have two or more correlated dependent variables. If multiple dependent variables are uncorrelated or orthogonal, ANOVA on each variable is more appropriate than MANOVA in SPSS.
Let us take an example in MANOVA in SPSS. Four groups, each consisting of 100 randomly selected individuals, watch four different detergent commercials. After watching the commercial, each individual rated their preference for the product, the manufacturing company, and the commercial itself. Since these variables correlate, conduct a MANOVA in SPSS to find which commercial received the highest preference.
To conduct a MANOVA in SPSS, select “Analyze,” then “General Linear Model,” and choose “Multivariate” from the menus.
As in ANOVA, the first step is to identify the dependent and independent variables. It involves two or more metric dependent variables. Metric variables are those measured using an interval or ratio scale. They generally denote the dependent variable by Y and the independent variable by X.
In MANOVA in SPSS, the null hypothesis states that the mean vectors of multiple dependent variables are equal across groups.
Like in ANOVA, MANOVA in SPSS also decomposes the total variation and observes it across all the dependent variables simultaneously. In MANOVA in SPSS, SSy represents the total variation in Y, divided into model variation (SSM) and error variation (SSE).
SSy = SSbetween + SSwithin
Here the subscripts ‘between’ and ‘within’ refer to the categories of X in it. SSbetween is the portion of the sum of squares in Y related to the independent variable or factor X. Thus, it is generally referred to as the sum of squares of X. SSwithin is the variation in Y which is related to the variation within each category of X. It is generally referred to as the sum of squares for errors in it.
Researchers decompose the total variation for all the dependent variables (such as Y1, Y2, and so on) simultaneously.
The next task in MANOVA in SPSS is to the measure the effects of X on Y1,Y2 (and so on). This is generally done by the sum of squares of X. The relative magnitude of the sum of squares of X in MANOVA in SPSS increases as the difference among the means of Y1,Y2 (and so on) in categories of X increases. The relative magnitude of the sum of squares of X in MANOVA in SPSS increases as the variation in Y1,Y2 (and so on) within the categories of X decreases.
In MANOVA in SPSS, researchers measure the strength of the effects of X on Y1, Y2, and so on using η². The value of η2 varies between 0 and 1. η2 assumes a value of 0 in MANOVA in SPSS when all the category means are equal, indicating that X has no effect on Y1,Y2 (and so on). η2 assumes a value of 1, when there is no variability within each category of X, while there is some variability between the categories.
In MANOVA in SPSS, the final step is to calculate the mean square by dividing the sum of squares by the corresponding degrees of freedom. They test the null hypothesis of equal vectors of means using an F statistic, which is the ratio of the mean square related to the independent variable to the mean square related to error.
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