Two way ANOVA is the test used in SPSS for understanding how the changes in two groups of elements simultaneously affect the third element. Here, the initial two groups of elements are called ‘independent variables’ whereas the third element is the ‘dependent variable’. Such a comparison is possible when both variables have similar categories or classifications.
The first step of applying the two way ANOVA test
Click Analyze > General Linear Model > Univariate… on the top menu, as shown below.
The second step is to define the variables
Drag the response variable height into the box labelled Dependent variable. Drag the two-factor variables water and sun into the box labelled Fixed Factor, using relevant buttons, as shown below:
Next, click the Plots button. Drag water into the box labelled Horizontal axis and sun into the box labelled in separate lines. Then click Add. The words water*sun will appear in the box labelled Plots. Then click Continue.
Post Hoc multiple comparisons
Next, click the Post Hoc button. In the new window that pops up, drag the variable sun into the box labelled Post Hoc Tests. Then check the box next to Tukey. Then click Continue.
Calculating estimated marginal means
Next, click the EM Means button. Drag the following variables into the box labelled Display Means for. Then click Continue.
Lastly, click OK. The following output window pops up:
Interpreting two way ANOVA test results in SPSS
Taking a case of a study to find whether an individual’s IQ score is influenced by their level of education and gender. The study incorporated a random sample of participants and asked about their interest in politics. The participants scored from 0 to 100, with higher scores indicating a greater interest in politics. The participants were then divided on the basis of gender and their level of education.
Therefore, the dependent variable was “IQ score”, and the two independent variables were “gender” and “education”. The results of the case are presented below:
The above table shows the generic statistics of the case, i.e. mean and standard deviation. In our case, the descriptive statistics table shows that among the selected respondents:
- the average IQ of males is more than that of females at the University level
- the average IQ of males and females is the same at the College level.
However, as the standard deviation for college-going males is close to 4.5 this shows there is high variability in their data compared to females.
The between-subject effects table shows the significance value for interaction between the variables. The significance value should always be less than 0.05 or 0.10 in order to prove an effect. However, in the case of this example, the effect is 0.203 which is more than 0.05. Therefore we must conclude through the two way ANOVA test that gender and education do not affect the IQ score.