Two-Way ANOVA in SPSS

• Plan your analysis ahead of time

• Select the same dependent variable– Select two factors– Each factor is a nominal (grouping) variable– If both factors have many levels (values), your

analysis will be complex

• SPSS will generate a lot of output.

• Knowing which parts to use is important

Set options to show Variable Names in Alphabetical Order

Edit → Options

Use a boxplot to preview data

Dependent variable

Factor A

Factor B

Edited boxplot. Background changed to white.Text changed to white on outliers (doesn’t show)

Notice that the labels for the variable names cut off in mid-sentence. If you edit the labels in Variable View, you can generate useful labels.

Factorial ANOVAAnalyze→General Linear Model→Univariate

Several steps to prepare:First: choose the variables

DEPENDENT

FACTOR A

FACTOR B

Notice that the buttons for options are vertically

arranged along the side.

Second, choose Options

In the Options box …

• Request Means for Factors

•Request Means for Interaction

•Request descriptive statistics

•Request estimates of effect size (This will generate an estimate of η2)

•Click CONTINUE

•In main box, Click PLOTS

Get a Plot of the Means of Groups•Put Factor with the fewest categories into the box titled “Separate Lines”

•Put other Factor into “Horizontal Axis”

•Click on ADD to move variable names into the Plots listing box.

•Click CONTINUE to return to main dialogue box.

•Click POST HOC

Choose Post-Hoc Tests•Post-hoc tests are only needed if a Factor has a significant effect. You can request them now and decide later whether to use them.

•Post-hoc tests are only needed if a factor has a significant effect AND if it has 3 or more groups

•In this data, pricegas has 3 levels.Move pricegas to “Post hoc tests for”

•Choose Scheffé test because groups are not equal size.

•Note that Bonferroni (conservative) is also available.

•Click CONTINUE for main dialogue box

Click OK in the lower left corner

Means of all groupsTotal = row or column means

Descriptive Statistics

Dependent Variable: econgood On another subject, would you describe the state of the nation'seconomy these days as excellent, good, not so good or p

3.10 .718 195

3.14 .739 109

3.12 .724 304

2.81 .751 206

2.83 .830 107

2.82 .778 313

2.47 .713 249

2.57 .762 133

2.51 .731 382

2.77 .771 650

2.83 .809 349

2.79 .785 999

employed Are youyourself employedoutside the home, or not?1 Yes

2 No

Total

1 Yes

2 No

Total

1 Yes

2 No

Total

1 Yes

2 No

Total

pricegas Have recentprice increases ingasoline caused anyfinancial hardship foryou or others in yourhousehold, or not? [If y

1 Yes, serious

2 Yes, not serious

3 No

Total

Mean Std. Deviation N

Hypothesis Test Results

Tests of Between-Subjects Effects

Dependent Variable: econgood On another subject, would you describe the state of the nation's economythese days as excellent, good, not so good or p

64.366a 5 12.873 23.239 .000 .105

7153.781 1 7153.781 12914.219 .000 .929

55.839 2 27.920 50.402 .000 .092

.621 1 .621 1.121 .290 .001

.296 2 .148 .267 .765 .001

550.068 993 .554

8384.000 999

614.434 998

SourceCorrected Model

Intercept

pricegas

employed

pricegas * employed

Error

Total

Corrected Total

Type III Sumof Squares df Mean Square F Sig.

Partial EtaSquared

R Squared = .105 (Adjusted R Squared = .100)a.

Factor A

Factor B

Interaction

p-value η2

Post-hoc TestsAll groups of pricegas differ from each other significantly

Multiple Comparisons

Dependent Variable: econgood On another subject, would you describe the state of the nation's economy these days asexcellent, good, not so good or p

Scheffe

.30* .060 .000 .15 .44

.61* .057 .000 .47 .75

-.30* .060 .000 -.44 -.15

.31* .057 .000 .17 .45

-.61* .057 .000 -.75 -.47

-.31* .057 .000 -.45 -.17

(J) Have recent priceincreases in gasolinecaused any financialhardship for you orothers in yourhousehold, or not? [If y2 Yes, not serious

3 No

1 Yes, serious

3 No

1 Yes, serious

2 Yes, not serious

(I) Have recent priceincreases in gasolinecaused any financialhardship for you orothers in yourhousehold, or not? [If y1 Yes, serious

2 Yes, not serious

3 No

MeanDifference

(I-J) Std. Error Sig. Lower Bound Upper Bound

95% Confidence Interval

Based on observed means.

The mean difference is significant at the .05 level.*.

Means Plot, Edited

•Background made white

•Title on horizontal axis edited for clarity

•Chart title deleted (APA format has Figure title below the chart)

•Legend moved inside the box for clarity

Write-up• Sandwich format• Report three hypothesis tests with F and p-value

for each:– Factor A– Factor B– Interaction

• For any significant element, report means and effect size

• For any significant element with 3 or more groups, report post-hoc tests

• Close with a summary statement• Refer to boxplot or means plot as Figure 3 (or

whichever number) in the write-up.