What you want to see is a significance value that is greater than .05. A significance value that is less than .05 would suggest that there are significant between the variances of the dependent variable across the groups in the study. In our example, none of the values for the Levene’s test is less than .05, so the homogeneity of variance assumption has been met. Our first independent variable (also known as a “factor”) is gender. SPSS Statistics generates quite a few tables in its output from a two-way ANOVA. It assesses whether the population variances of our dependent variable are equal over the levels of our factors.


Use a two-way ANOVA when you want to know how two independent variables, in combination, affect a dependent variable. This means that the effect of the intervention on the dependent variables is not the same for males and females. The two-way multivariate analysis of variance (two-way MANOVA) is often considered as an extension of the two-way ANOVA for situations where there is two or more dependent variables.


You should now be able to perform a two-way ANOVA in SPSS, check that the homogeneity of variance assumption has been met; interpret your result; and select appropriate follow up tests if applicable. The profile plot above suggests that there is nota significant interaction between gender and major and this is confirmed in theTests of Between-Subjects Effects table below . The p-value .795 is greater than .05, meaning that the interaction effect is not significant. It has three levels – Sociology, Political Science, and Economics. Last but not least, adjusted r squared tells us that 54.4% of the variance in weight loss is attributable to diet and exercise.

Frequently asked questions about two-way ANOVA

The two-way ANOVA is used to assess the effects of two independent categorical variables – both alone and in combination with each other – on a continuous dependent variable . In this tutorial we show you how to perform and interpret the results of a two-way ANOVA in SPSS. We also explain how to select follow up tests where these are appropriate. Finally, if you have a statistically significant interaction, you will also need to report simple main effects. Alternatively, if you do not have a statistically significant interaction, there are other procedures you will have to follow.

ANOVA tests for significance using the F test for statistical significance. The F test is a groupwise comparison test, which means it compares the variance in each group mean to the overall variance in the dependent variable. Consider an experiment where three teaching methods were being trialled in schools. The three teaching methods were called “Regular”, “Rote” and “Reasoning”.

Well, this will become clear if we understand what our interaction effect really means. The flowchart says we should now rerun our ANOVA with simple effects. For now, we’ll ignore the main effects -even if they’re statistically significant. According to the table below, our 2 main effects and our interaction are all statistically significant.

Simple Main Effects Tests for Two-Way ANOVA with Significant Interaction in SPSS

First, we set out the example we use to explain the two-way ANOVA procedure in SPSS Statistics. Run your SPSS two way ANOVA the right way in 5 simple steps. With downloadable data file, enhanced screenshots and annotated output. Levene’s test examines if 2+ populations have equal variances on some variable.

subjects effects table

Since each patient is measured on each of the four drugs, we will use a how to do two way anova in spss ANOVA to determine if the mean reaction time differs between drugs. This tutorial explains how to conduct a one-way repeated measures ANOVA in SPSS. Similarly, the 7.55% difference between the mean scores of Economics and Sociology students is significant. Again, this is denoted by the asterisk next to the mean difference value. The SPSS Output Viewer will pop up with the results of your two-way ANOVA and your post-hoc tests – Tukey’s HSD test in our example. You can even take photo of sum or record audio as question.


However, which within-subjects factor takes the role of the horizontal axis and which the separate lines for your study is up to you (i.e., whatever makes the most sense to you). Box the number of treatments (i.e., the number of levels of the within-subject factor). When you do not have a statistically significant interaction, we explain two options you have, as well as a procedure you can use in SPSS Statistics to deal with this issue. A basic ANOVA only tests the null hypothesis that all means are equal. If this is unlikely, then we’ll usually want to know exactly which means are not equal. The most common post hoc test for finding out is Tukey’s HSD .

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We now know that the average weight loss is not equal for all different diets and exercise levels. We can figure that out with post hoc tests, the most common of which is Tukey’s HSD, the output of which is shown below. You should now be able to perform pairwise comparisons in SPSS to determine which levels of your independent variable are significantly different from the other levels of the same variable. You may also be interested in our tutorial on exporting your SPSS output to another application such as Word, Excel, or PDF. Remember that you don’t need to move independent variables that have only two levels to the Post Hoc Tests box. As illustrated below, select your dependent variable and use the arrow button to move it to the Dependent Variable box.

Two Way ANOVA – Basic Idea

When reporting the results you should include the F statistic, degrees of freedom, and p value from your model output. Once you have your model output, you can report the results in the results section of your thesis, dissertation or research paper. The AIC model with the best fit will be listed first, with the second-best listed next, and so on. This comparison reveals that the two-way ANOVA without any interaction or blocking effects is the best fit for the data. AIC calculates the best-fit model by finding the model that explains the largest amount of variation in the response variable while using the fewest parameters.

  • There appears to be a significant interaction between gender and major, but we need to review the Tests of Between-Subjects Effects table to confirm this.
  • We show you these procedures in SPSS Statistics, as well as how to interpret and write up your results in our enhanced two-way ANOVA guide.
  • If your data don’t meet this assumption, you may be able to use a non-parametric alternative, like the Kruskal-Wallis test.
  • The mean Data Science exam score for female students in the Economics major is higher than that for male students in the same major.

The output may include post-hoc tests, effect sizes and power but not Levene’s test or any normality tests. Rebecca is working on her PhD in soil ecology and spends her free time writing. She’s very happy to be able to nerd out about statistics with all of you. Testing the effects of marital status , job status (employed, self-employed, unemployed, retired), and family history on the incidence of depression in a population. If the F statistic is higher than the critical value (the value of F that corresponds with your alpha value, usually 0.05), then the difference among groups is deemed statistically significant. Significant differences among group means are calculated using the F statistic, which is the ratio of the mean sum of squares to the mean square error .

Two-way ANOVAis used to determine whether or not there is a statistically significant difference between the means of three or more independent groups that have been split on two factors. If your data don’t meet this assumption (i.e. if you set up experimental treatments within blocks), you can include a blocking variable and/or use a repeated-measures ANOVA. Bushels per acre is a quantitative variable because it represents the amount of crop produced. It can be divided to find the average bushels per acre.A categorical variable represents types or categories of things.

Secondly, Categorical variables Gender and Marital status transfer into box Fixed Factor. There is a lot of statistical software out there, but SPSS is one of the most popular. If you’re a student who needs help with SPSS, there are a few different resources you can turn to. All contents can guide you through Step-by-step SPSS data analysis tutorials and you can see How to Run in Statistical Analysis in SPSS. Box the number of treatments (i.e., the number of levels of the within-subjects factor). In this case, enter “2”, which represents the control and intervention trials.

However, before we introduce you to this procedure, you need to understand the different assumptions that your data must meet in order for a two-way repeated measures ANOVA to give you a valid result. We don’t know which mean are different from other mean. In this scenario, we can follow up by conducting pairwise comparisonsto evaluate the differences between each pairing of the levels of the variable . Select one of your independent variables and use the arrow button to move it to the Separate Lines box. Then select the other independent variable and use the arrow button to move it to the Horizontal Axis box.

pairwise comparisons

We can obtain these plots by clicking “Plots” on the right. Move the other independent variable to theHorizontal Axis box. Although this graph is probably not of sufficient quality to present in your reports , it does tend to provide a good graphical illustration of your results. An interaction effect can usually be seen as a set of non-parallel lines. You can see from this graph that the lines do not appear to be parallel . You might expect there to be a statistically significant interaction, which we can confirm in the next section.

She plants 30 seeds and lets them grow for two months under different conditions for sunlight exposure and watering frequency. After two months, she records the height of each plant, in inches. Statology is a site that makes learning statistics easy by explaining topics in simple and straightforward ways. The only p-values below .05 are for drug 1 vs. drug 4 and drug 3 vs. drug 4. All of the other comparisons have p-values greater than .05. Drag the variabledruginto the box labelledHorizontal Axis.

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