Statistical Analysis for Education and Psychology Researchers

principle of evaluating the degrees of freedom is important to grasp. The corrected total
degrees of freedom is simply, number of subjects −1=(24–1)=23.

Steps in Computation

To compute F-ratios the general procedure is 1) Identify the sources of variance and
compute sums of squares for each source; 2) apportion degrees of freedom to each source
of variance; 3) evaluate the mean squares; and 4) calculate F-statistics and determine
probabilities.

Step 1: Compute sums of squares

a) Sums of squares between groups (conditions or treatments) Computation of sums of
squares causes the most confusion in ANOVA calculations. It may help if you realize
that the denominator value in a sums of squares calculation is the number of
observations on which the total score in the numerator is based.
Sums of squares between groups, SS(bet), is given by,

Sums of

squares

subjects—8.23

where:

Tj=Total score for the jth subgroup (treatment group)

nj=Number in the jth subgroup (treatment group)

N=Total number of subjects

xi=Individual score

This equation is appropriate for both balanced and imbalanced designs.

b) Sums of squares within individuals (error sums of squares)
The error sums of squares, SS(error), is given by

Sums of

squares

error—

8.24

Where:

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