Statistical Analysis for Education and Psychology Researchers

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

ni=Number in the jth subgroup (treatment group)

xi=Individual score

c) Corrected total sums of squares
The corrected total sums of squares, SS(ct) is given in the usual way

Corrected total

sums of

squares—8.25

Where:

xi=Individual score

N=Total of all subjects

SS(error)=7224−7083.25=140.750

The reader should note that an easier computation for SS(error) is given by:

SS(error)=SS(ct)−SS(bet)=151.333−10.5833=140.750

Step 2: Evaluate degrees of freedom (for explanation see above)

The df for SS(bet) is 2, the df for SS(error) is 21 and the df(ct) is 23.

Step 3: Evaluate mean squares

The mean square for between groups MS(bet) is SS(bet)/df(bet)=10.5833/2= 5.2917. Mean
square error is calculated in exactly the same way, MS(error)=
SS(error)/df(error)=140.750/21=6.7024.

Step 4: Calculate F-ratios

In this example there is only one F-ratio to calculate which is a test of the hypothesis that
subgroup mean attribution scores are equal. The F-statistic is given as
MS(bet)/MS(error)=5.2917/6.7024=0.7895 with 2 and 21 degrees of freedom. The degrees of
freedom of 2 relates the numerator mean square (MS(bet)) and degrees of freedom of 21
corresponds to the denominator df (MS(error)).

Inferences involving continuous data 319