This tutorial shows the steps of how you can do two-way ANOVA in SPSS. A two-way ANOVA is used to estimate how a quantitative variable (i.e., Y) changes according to the levels of two categorical variables (X_{1} and X_{2}).

This tutorial uses hypothetical data of brand (X_{1}) and City (X_{2}) and sales as Y. You can download the data using this link.

## Steps of two-way ANOVA in SPSS

## Step 1: Select “Univariate”

“Analyze”, then “General Linear Model”, then “Univariate.”

## Step 2: Drag variables

Drag variables of City and Brand as Fixed Factor(s) and sales as Dependent Variable.

## Step 3: Click “Descriptive statistics”

Click “Options” then “Descriptive statistics.” Then, click “Continue” and “OK.”

## Step 4: Interpret the output

The following is the output. The interaction effect is F(1, 19) = 6.34, p = 0.023. Thus, the interaction of Brand * City is significant.

However, what does it mean by saying that the interaction effect is significant? We need to put the 4 means into a table to better understand it. These 4 means are from the table of “Descriptive Statistics.” We can use the following table to better summarize the results.

City 1 | City 2 | |

Brand 1 | 48.0 | 7.0 |

Brand 2 | 6.8 | 6.6 |

Difference between Brand 1 and Brand 2 | 48.0-6.8=41.2 | 7.0-6.6=0.4 |

For City 1, the sales difference between Brand 1 and Brand 2 is 41.2. For City 2, the difference is 0.4. Therefore, a significant interaction means that 41.2 and 0.4 are statistically significant.

## Step 5: Plot Interaction for two-way ANOVA

We can further plot the interaction for two-way ANOVA in SPSS. Such a plot can better help us understand the nature of the interaction. The following is the plot. Regarding how to plot it, please refer to another tutorial here.

## Further Reading

The following tutorials are in SPSS: