 # HOW TO RUN ONE WAY MANOVA TEST IN SPSS

## What is a One-Way MANOVA?

### Using the MANOVA test in Research

This easy tutorial will show you how to run the One Way MANOVA test in SPSS, and how to interpret the result.

Multivariate analysis of variance (MANOVA) is a statistical test for comparing multivariate means of several groups (Source). On the other hand, if you need more deep information about the formula of the test. Finally, if you need more information, please read this article (Source)

For instance, one-way MANOVA is a parametric test (data are normally distributed) and we use this test when we want to determine whether there are differences between groups (two or more) of the categorical variable on more than one continuous dependent variable. Therefore, we have one independent categorical variable and two or more continuous dependent variables.

### Assumptions of the MANOVA Test:

When performing a One-Way MANOVA procedure the following assumptions are required:

• independent categorical variable 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: One-Way MANOVA Test

This guide will explain, step by step, how to run a one-way MANOVA Test in SPSS statistical software by using an example.

We wanted to examine whether there is a difference between males and females on English test scores, Math test scores, and History test scores. Therefore, we have one independent categorical variable gender (male and female) and three continuous dependent variables (English test score, Math test score, and History test score).

Null hypothesis:

There is no difference between groups of the categorical independent variable on two or more continuous variables.

Alternative hypothesis:

There is a difference between groups of the categorical independent variable on two or more continuous variables.

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## How to Run One-Way MANOVA in SPSS: Explanation Step by Step

### Click the Options button, and a new window will open.

From the box Factor and Factor Interactions transfer, categorical variable into Display means for the box. In the Display box, choose Descriptive statistics, Homogeneity tests, and Estimates of effect size. Click Continue, and you will return to the previous window. Click OK.

## How to report a One-Way MANOVA results: Explanation Step by Step

### How to Report Between-Subjects Factors Table in SPSS Output?

Between-Subjects Factors table shows how categorical variable is coded and the number of observations in each group.

### How to Report Descriptive Statistics Table in SPSS Output?

The 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 is 66.57 (M=66.57; SD=19.88), while the average English test score for a female is 69.26 (M=69.26, SD=21.38).

### How to Report Box’s test of equality of Covariance Matrices Table SPSS Output?

The following table shows the results of the Box’s test of equality of covariance matrices. That is to say, the null hypothesis that the observed covariance matrices of the dependent variables are equal across groups.

If the p-value is greater than 0.05, then we may proceed to interpret the results of one-way MANOVA.

In our example, the p-value is 0.368, so we fail to reject the null hypothesis.

### How to Report Multivariate Tests in SPSS output?

Multivariate tests show the results of Wilk’s Lambda test. Therefore, we should look at the results of Wilk’s Lambda test in the row for our categorical variable gender.

If the p-value is lower than 0.05. That is to say, there is a statistically significant difference in test scores (English, Maths, History) between males and females.

In our example, the p-value is 0.740, so we fail to reject the null hypothesis and conclude that there is no statistically significant difference in test scores (English, Maths, History) between males and females.

### How to report Levene’s test of equality of error Variances in SPSS Output?

The following table shows Levene’s test of equality of error variances results. That is to say, If the p-value is lower 0.05, the error variances of the dependent variable is not equal across groups. In our example, for three dependent variables p > = 0.01, so we fail to reject the null hypothesis and conclude that the error variances of the dependent variable are equal across groups.

### How to report Tests of between-subjects in SPSS Output?

Tests of between-subjects effects shows how the dependent variables (English test score, Math test score, History test score) differ for the independent variable (Gender).

### How to report Categorical Variables in SPSS Output?

The last table shows mean, standard error, and 95% confidence interval for each variable across categorical variables.

## How to Interpret a One-Way MANOVA Test Results in APA Style?

One-way MANOVA was conducted to determine whether there is a difference between males and females on English test scores, Math test scores, and History test scores. There was non-significant difference in test scores (English, Maths and History) based on gender, F(3, 73) = 0.419, p = 0.740; Wilk’s lambda = 0.983, partial eta squared = 0.017.

Furthermore, there is no significant effect of gender on English test score, F(1, 75) = 0.325, p = 0.570, partial eta squared = 0.04. There is no significant effect of gender on Math test score, F(1, 75) = 0.195, p = 0.660, partial eta squared = 0.03. There is no significant effect of gender on History test score, F(1, 75) = 1.079, p = 0.302, partial eta squared = 0.014.

We fail to reject the null hypothesis and conclude that there is no difference between males and females on the English test score, Math test score, and History test score.

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