TWO WAY MANOVA
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Using the Two-Way MANOVA test in Research
This easy tutorial will show you how to run the Two Way MANOVA test in SPSS, and how to interpret the result.
Two-way multivariate analysis of variance (MANOVA) deals with testing the effects of the two grouping variables, usually called factors, on the measured observations as well as interaction effects between the factors. In addition, It is the direct multivariate analog of two-way univariate ANOVA and is able to deal with possible correlations between the variables under consideration. (Source)
On the other hand, two-way MANOVA is a parametric test. So, we use two-way MANOVA when we want to determine whether there is an interaction between the two independent categorical variables on the two or more continuous dependent variables. Therefore, we have two independent categorical variable and two or more continuous dependent variables.
Assumptions of the Two-Way MANOVA Test
When performing a Two-Way MANOVA procedure the following assumptions are required
- two independent categorical variables with two or more groups
- two or more dependent continuous variables
- data are normally distributed
- independence of observations
- sample size (more cases in each group than the number of dependent variables)
- no univariate or multivariate outliers
- homogeneity of variance-covariance matrices
- no multicollinearity
- a linear relationship between each pair of continuous dependent variables for each group of the independent categorical variable
- multivariate normality
An Example: Two-Way MANOVA Test
This guide will explain, step by step, how to run the Two-way MANOVA test in SPSS statistical software by using an example.
We want to examine whether there is an interaction effect of gender and training on English test scores, Math test scores, and History test scores. Therefore, we have two independent categorical variables: Gender (male and female) and training (1 or 2 or 3 months) and three continuous dependent variables (English test score, Math test score, and History test score).
Null hypothesis:
There is no effect of interaction between the two independent categorical variables on the two or more continuous dependent variables.
Alternative hypothesis:
There is an effect of interaction between the two independent categorical variables on the two or more continuous dependent variables.
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How to Run Two Way MANOVA Test in SPSS: Explanation Step by Step
From the SPSS menu, choose Analyze – General Linear Models – Multivariate
A new window will open.
Firstly, from the left box transfer continuous dependent variables into the Dependent Variables box. Secondly, categorical independent variables Gender and Training into Fixed Factor(s) box.
Click the Model button,
Firstly, choose Full factorial in the Specify Model box and Type III in Sum of squares box. Secondly, Click the Options button. In the Display box, choose Descriptive statistics.
The two-way MANOVA results will appear in the output window.
How to report Two Way MANOVA test results: Explanation Step by Step
How to Report Between-Subjects Factors Table in SPSS Output?
Between-Subjects Factors table shows how we coded the categorical variables and the number of observations in each group.
How to Report Descriptive statistics Table in SPSS Output?
The descriptive statistics table shows the number of observations, the mean and standard deviation in each group, and total. For example, the average English test score for a male who had one-month training is 69.55 (M=69.55; SD=22.69).
How to Report Multivariate Tests Table SPSS Output?
Multivariate Tests show the results of Wilk’s Lambda test. So, we should look at the results of Wilk’s Lambda test in the row for the interaction between Gender and Training.
Firstly, If our p-value is greater than 0.05. Therefore, there is no statistically significant effect of the interaction of gender and training on test scores (English, Maths, History).
Secondly, if our p-value is lower than 0.05. Therefore, there is a statistically significant effect of the interaction of gender and training on test scores (English, Maths, History).
For example, our p-value is 0.512. So, we fail to reject the null hypothesis and conclude that there is no statistically significant effect of the interaction of gender and training on test scores (English, Maths, History).
In addition, If we look at the p-value for Wilks’ Lambda in Gender row (p = 0.636), we fail to reject the null hypothesis and conclude that there is no effect of gender on test scores (English, Maths, History).
Finally, If we look p-value for Wilks’ Lambda in Training row (p = 0.010), we must reject the null hypothesis and conclude that there is the effect of training on test scores (English, Maths, History).
How to Report CTests of between-subjects Table in SPSS output?
Tests of between-subjects effects show how the dependent variables (English test score, Math test score, History test score) differ for the interaction between Gender and Training.
Moreover, we should look at the p-value in row Gender*Training. If p < 0.05, the interaction between gender and training has a statistically significant effect on a test score.
English test score:
Firstly, the p-value is 0.592 for the English test scores. So, we fail to reject the null hypothesis and conclude that interaction between gender and training does not have a statistically significant effect on English test scores.
Math test score:
Secondly, The P-value of the Math variable is 0.682. So, we fail to reject the null hypothesis and conclude that the interaction between gender and training does not have a statistically significant effect on Math test scores.
History test score:
Finally, The p-value is 0.201 for the History test. Therefore, we fail to reject the null hypothesis and conclude that interaction between does not have a statistically significant effect on the History test score.
Two-way MANOVA was conducted to determine whether there is an interaction effect between gender and training on English test scores, Math test scores, and History test scores.
Firstly, there is a non-significant effect of an interaction effect between gender and training on English test scores, F(2, 103) = 0.527, p = 0.592.
Secondly, there is a non-significant effect of an interaction effect between gender and training on Math test scores, F(2, 103) = 0.384, p = 0.682.
Finally, there is a non-significant effect of an interaction effect between gender and training on History test score, F(2, 103) = 1.632, p = 0.201. Therefore, we fail to reject the null hypothesis. There is no interaction effect between gender and training on English, Math, and History test scores.
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