 # HOW TO RUN TWO WAY ANOVA TEST IN SPSS

## What is the Two Way ANOVA Test?

### Using the Two-Way ANOVA test in Research

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

The two-way ANOVA is a parametric test. In other words, We use two-way ANOVA, if we want to determine whether there is an interaction effect between two independent variables (factors) on the dependent variable. However, we may also determine whether there is the main effect of each factor on the dependent variable.

Moreover, the two-way analysis of variance is an extension of the one-way analysis of variance. However, because implementing the two-way ANOVA is relatively complicated, some clinical researchers prefer to apply the one-way ANOVA for one factor on each level of the other factor, repeatedly. (Source)

### Assumptions of the Two-Way ANOVA Test

When performing a Two-Way ANOVA procedure the following assumptions are required

• The populations from which the samples were obtained must be normally or approximately normally distributed.
• The samples must be independent.
• The variances of the populations must be equal.
• The groups must have the same sample size.
• One continuous dependent variable
• two categorical independent variables with two or more groups

### An Example: Two-Way ANOVA Test

This guide will explain, step by step, how to run the Two way ANOVA test in SPSS statistical software by using an example.

We collected data on gender, marital status, and level of happiness from 94 participants. Moreover, we want to determine whether there is an interaction effect between gender and marital status on the level of happiness. Therefore, we have one continuous dependent variable and two independent categorical variables:

gender with two groups (male, female) and marital status with five groups (single, married, divorced, separated, widowed).

Null hypothesis:
There is not an interaction effect between two independent variables (factors) on the dependent variable.

Alternative hypothesis:
There is an interaction effect between two independent variables (factors) on the dependent variable.

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## How to Run the Two Way ANOVA Test in SPSS: Explanation Step by Step

### A new window will open.

Firstly, From the left box, continuous dependent variable Happiness transfer to Dependent variable box. Secondly, Categorical variables Gender and Marital status transfer into box Fixed Factor(s).

### Click the Options Button

Firstly, you should choose Descriptive statistics, Homogeneity tests, and Estimates of effect size in the display box. Finally, click continue and you will return to the previous window.

### Click on the Post-Hoc button

Primarily, From the Factor(s) box transfer variable with three or more groups into Post Hoc Tests for box and in Equal Variances Assumed box choose Tukey and click Continue.

### Click on Plots button

Firstly, From the factors box transfer variable with three or more groups into Horizontal Axis box (in our example Marital status) and in Separate lines box transfer the second variable (in our example Gender).

Secondly, Click Add, and variables will appear in the Plots box (maritalstatus*gender).

Finally, Click Continue and click OK.

## How to report the Two Way ANOVA Test results: Explanation Step by Step

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

The table Between-Subjects Factors shows how categorical variables are coded and the number of observations in each group. For example, we have 41 males and 53 females.

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

The table shows mean, standard deviation, and number of observations of the dependent variable split by groups of categorical variables.

For example, the average level of happiness for single males is 5.56 (M=5.56, SD=3.00). On the other hand, the average level of happiness for single females is 5.61 (M=5.61, SD=2.81).

### How to Report Levene’s test Table SPSS Output?

The next table shows the results of Levene’s test of equality of error variances test. So, this test tests the bull hypothesis that the error variance of the dependent variable is equal across groups.

Our example p-value is 0.341, Therefore, we fail to reject the null hypothesis and may proceed to the Two-way ANOVA results.

### How to Report Between-Subjects Table in SPSS output?

The table effects show whether independent categorical variables or their interaction are statistically significant.

We should look at the Sig. column for the gender, marital status, and gender*marital status.

Firstly, the p-value is 0.877  for gender. So, there is no difference in the level of happiness between males and females.

Secondly, For marital status, p is 0.955. Therefore, we fail to reject the null hypothesis and conclude that there is no difference in the level of happiness between single, separated, divorced, married, and widowed.

Finally, P-value is 0.669 for interaction between gender and marital status, p = 0.669. Therefore, There was no statistically significant interaction between gender and marital status on the level of happiness.

### How to report Multiple Comparisons Table in SPSS Output?

The table shows the results of the Post hoc test (Tukey). So, If we find a statistically significant effect of marital status on the level of happiness than we would interpret the Post hoc test results.

### How to show the Line Chart in SPSS Output?

It shows the mean of the level of happiness for each combination of groups of gender and marital status.

## How to Interpret the Two Way ANOVA Test Results in APA Style?

The two-way ANOVA was conducted to determine the effects of gender and marital status on the level of happiness.

Firstly, the main effect of gender was not significant, F(1, 84) = 0.024, p = 0.877, partial eta squared = 0.000. Therefore, We, fail to reject the null hypothesis that there is no effect of gender on the level of happiness.

Secondly, the main effect of marital status was not significant, F(4, 84) = 0.167,  p = 0.955, partial eta-squared = 0.008. Therefore, we must fail to reject the null hypothesis that there is no effect of marital status on the level of happiness.

Finally, the interaction of gender and marital status was not significant, F(4, 84) = 0.593, p = 0.669, partial eta squared = 0.027. Consequently, we fail to reject the null hypothesis that the effect of gender on the level of happiness is the same across all levels of marital status.

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