One- Way Repeated Measures ANOVA

 

The same group of subjects rated the following four brands of coffee. The order of tasting was counterbalanced. Are the mean ratings the same?

Data Set

 


 

 

Definitional Formula
 

Variance Due to Column Means (Brands of Coffee)

Compute the column means.

The variance due to different group means is equal to 6.637.

Variance Due to Row Means (Subjects)

The average rating of each judge gave over different brands of coffee (sum/4) can be computed as 

The variance due to different row means (subjects) is equal to 7.321. 


Variance Due to the Total Group

Ignore column and row information. Combine all the scores into one group. The overall mean is 8.5 and the total variance is equal to 14.607.

Residual Term

14.607 - 6.637 - 7.321 = .649

Using the repeated-measures design, the researcher reduces the residual term by subtracting the effect due to individual differences.
 

Divide each component by the total variance of the dependent variable Y.
 

Source of Variance True Variance Standard Variance
Columns 6.637 6.637 / 14.607 = .4543
Rows 7.321 7.321 / 14.607 = .5012
Residual .649 .649 / 14.607 = .044
Total 14.607 14.607 / 14.607 = 1


Approximately 45% of the variance in the dependent variable Y was accounted for by the brands of coffee. About 50% of the variance in the dependent variable Y was accounted for by subjects. About 5% of the variance in the dependent variable Y was not accounted for.

 


 


 

The observed significance level was less than .001. There were significant differences in the mean ratings among the four brands of coffee.
 

 

 

Computational Formula
 

Reading: Within-Subjects Analysis of Variance by Jason Newsom

 

 

SPSS or Windows


Input

 

1. Choose Analyze \ General Linear Model \ Repeated Measures.
 

Within-Subject Factor  Name: Type brand.

Numbers of Levels:  Type 4. Click Add.

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

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

Click Options. Move the variable "brand" to the Display Means for box. Click Descriptive statistics in the Display area.

Click Continue. Click OK.


Output

Descriptive Statistics

 

 
There were significant differences in the mean ratings among the four brands of coffee, F(3,18) = 61.465, p < .001.

 

Optional SPSS Lessons

 

 

Optional Reading