One-Way Repeated Measures Analysis of Variance

 

Seven subjects were given a scale which measures attitudes toward four minority groups (a, b, c, and d). Higher scores indicate greater acceptance. Evaluate the differences in means among these four subscales. Use a .05 significant level.

SPSS for Windows

Enter data

Each subject had four scores. 

 

1. Data Visualization

Boxplot

Choose Graphs \ Boxplot. By default, Simple is selected. In the Data in Chart Are area, click Summaries of separate variables. Click Define as shown below.

Next, move the variables (a, b, c, and d) to the Boxes Represent area. Click OK.

Examine the boxplot

A boxplot plots the median, the 25th percentile, the 75th percentile, and values that far from the rest.

Length of the Box

The length of the box is the difference between the 75th and 25th percentiles. From the length of the box, you can determine the variability. The larger the box, the greater the spread of the data. Note that group B had largest variability and group C has smallest variability.

The horizontal line inside the box represents the median.

Values of the median across four groups

Note that group D has the lowest median score.

Skewness

If the median is not in the center of the box, the distribution might be skewed.

Whiskers

Lines are drawn from the ends of the box to the largest and smallest values which are not outliers. These lines are called whiskers. 

Error Bars

Choose Graphs \ error Bart. By default, Simple is selected. In the Data in Chart Are area, click Summaries of separate variables. Click Define. Next, move the variables (a, b, c, and d) to the Error Bars text box. Bars Represent: Confidence interval for mean is the default. Level: 95% is he default. Click OK.

The following error bars show the 95% confidence intervals for mean acceptance score by minority group.

 

 

Compare the confidence intervals across four minority groups. Was there much overlap? 

There was little overlap between the minority group D and the other three groups. However, the confidence intervals for minority groups A, B, and C were overlapped.

 

2. Repeated Measures Designs

Choose Analyze \ General Linear Model \ Repeated Measures.

Within-Subjects Factor  Name: group.

A repeated measures factor is also called as a within-subjects factor. For our example, "attitudes toward minority groups" is the within-subjects factor.

Numbers of Levels:  4. Click Add.

Click Define. Move the variables a, b, c, and d to the Within-Subjects Variables box.

A dependent variable, acceptance score,  is measured for all subjects across four minority groups (a, b, c, and d).

Click the Help button to know more about this procedure. Close the help window when you are done.

Click Options. Move the variable `group` to the Display Means for box. Click Descriptive statistics and Estimates of effect size in the Display box.

Click Continue. Click OK.

 

SPSS Output

Descriptive Statistics

Examine the four mean scores. Minority group B had the highest mean score and group D had the lowest mean score. Group A and group B had similar mean scores. 


Sphericity Assumption

The effects of the experimental conditions should be consistent among the subjects. Refer to Assumptions of the one-way ANOVA for correlated samples By Richard Lowry 


  

a. The hypothesis of sphericity was not rejected (p > .05). The sphericity assumption was met.

b. If the assumption of sphericity is not met, adjustments will be made.

Optional Reading: Assumptions for Within-subjects ANOVA by Jason Newsom


Tests of Within-Subjects Effects

Do average acceptance scores differ for different minority groups? (Are the four population means equal?)

Use a .05 significant level.

 

The F Test
 

F = 61.465, p < .05

What do you conclude?

Population means on the Acceptance scale varied with different minority groups, F(3,18) = 61.465, p < .05. 

These tests yields the same F value. However, the degrees of freedom are corrected for any violations of the sphericity assumption. 

 


Thus, (185.857)/(185.857+18.143) = .911

 

Advanced Topic (Optional): The Multivariate Test 

The multivariate test does not require the sphericity assumption.

Please refer to The Multivariate Approach to the One-Way Repeated Measures ANOVA by Karl Wuensch

What can you conclude?

Different degrees of acceptance were associated with different minority groups, Wilks' = .005, F(3, 4) = 282.273, p < .05.

(Wilk’s lambda is an inverse criterion. The smaller the value of the larger the treatment effects.) 

   

 

 Optional Reading
 


Optional SPSS Lessons