How to run a between-subjects ANOVA in SPSS

Overview:

The between-subjects ANOVA (Analysis of Variance) is a very common statistical method used to look at independent variables with more than 2 groups (levels).

When to use an ANOVA

A continuous dependent (Y) variable and 1 or more categorical unpaired, independent, (X) variables. If you’re dealing with 1 X variable with only 2 levels, you would be better suited to run a t-test. If you’re dealing with paired data, you would want to look at a within-subjects or a mixed-model ANOVA.

ANOVA assumptions

1. the dependent variable is continuous (interval or ratio).
2. the independent variables are not related to each other. For example, the independent variables are not before- and after- measures for the same person. Such a test would instead by a repeated-measures (within-subject) ANOVA.
3. the dependent variable (Y) should be normally distributed on each independent variable (X). For example, if you wanted to see if there were differences in scores on a math test based on whether participants identified their gender as male/female/non-binary, then males, females, and those who identify as non-binary should all have a relatively normally distributed math test scores.
4. homogeneous variance between the groups of your X variables. Using the same example above, that you have about the same amount of spread in the male distribution of math scores as you do in the female distribution of math scores. This assumption can be relatively easily tested (and corrected for) in SPSS.

Running an ANOVA in SPSS

We will again use the HSB data file for this example, which is publicly available data. Suppose we’re interested in looking at the outcome of mathematical achievement based on gender (male / female), minority status (coded minority / non-minority), and an interaction between gender and minority status (for example, that female minorities differ than female non-minorities). This is a between subjects (not a within-subjects or repeated measures) design because anyone who identified as male is not also coded as female (and anyone who is coded as minority is not coded as non-minority). Thus, each individual’s is only represented once in each category.

From the main toolbar click Analyze General Linear Model Univariate 
This produces the window show below:
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​Move the dependent variable mathach into the Dependent Variable slot
Move the independent variables minority and female into the Fixed Factor(s) slot

We don’t need to concern ourselves with Random Factors(s) or Covariates(s). Random factors are used with the assumption that we have only selected (at random) several levels of the IV from all possible levels, instead of investigating every possible level of IV. This would be the case if instead of 2-3 classifications of gender, we lived on a strange planet with 20 or 30 but for our study only had managed to recruit 2 of them. The Covariate(s) field is used to select continuously variables we suspect are varying simultaneously with the dependent variable, variable that we would like to control for or hold constant.

Click Plots
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Since these are both between subjects factors, it’s really a matter of personal preference which you would like to have as a separate line and which you would like aligned on the horizontal axis. In this case, let’s look at genders as separate lines, and minority status on the horizontal axis.

Move the minority into the Horizontal Axis slot
Move  female into the Separate Lines slot
Click Add (the option becomes available)
Click Continue to return to the previous menu
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Click Options
Move OVERALL and female*minority to the window to the right
Click the boxes corresponding to Descriptive statistics and Homogeneity tests
Click Continue
Click Paste (this will be explained below)

​There are a couple work-arounds for this. One thing you could do is split the file and run separate t-tests to get the desired cell-by-cell comparisons. That sounds tedious. A more simple way to go about doing this is to actually directly manipulate the syntax for this analysis, as show below. Notice that only text in the blue is being changed, but you’ll need to copy that line to create the second just below it. Copying this line and adding the “compare(minority)” and “compare(female)” options will give us the simple effects from two different perspectives: comparing minority vs. non-minority within each gender, and comparing male vs. female within minority status. ​

Once this is complete, select the newly created syntax command (the one on the left above) and click Run.  A new window (the output) will appear, and it’s time to sift through the results.
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Interpreting the ANOVA output

A lot of output will be produced from the code about, but the first thing we’re concerned about is the Tests of Between-Subjects Effects table. The variables of our analysis are indicated by the Source column, where we’re mostly concerned with the values that corresponds to each of our variables : minority, female, and the minority*female interaction we specified. There are also different statistics for the intercept and the corrected model, but we don’t usually worry about these. The intercept is sort of like the “b” in old-school “y = m*x + b” equations (also known as regression), and the Corrected Model is an overall significance measure of the entire model.

• • Sig. – The statistical significance (the p value) of the variables. Remember that we want these Sig. values (the p values) to be lower than .05 in order to indicate statistical significance. In simple terms, the p value merely indicates the probably that any differences seen between groups is due to chance. As scientists, when we make claims that one group is “different” than another, we want to be relatively certain of that claim. We would conclude from this data that female, and minority status make a difference, but there is no significant minority*female interaction.
  • Partial Eta Squared – This is an effect size estimate that is similar to the proportion of variance accounted for by the indicated variable. Minority status accounts for 7.2% of all the variance in match achievement, while female accounts for 1.1% of all the variance.

​Yet notice that this table doesn’t actually indicate which groups are greater or smaller than the other; it merely tells us whether the significant difference is at all present. In order to determine which group scored higher than other, there will be several tables in the output you could look at, but I find it most intuitive to look at the Descriptive Statistics table, which is given below: