A researcher was interested in determining whether a six-week low- or high-intensity exercise-training program was best at reducing blood cholesterol concentrations in middle-aged men. Both exercise programs were designed so that the same number of calories was expended in the low- and high-intensity groups. As such, the duration of exercise differed between groups. The researcher expected that any reduction in cholesterol concentration elicited by the interventions would also depend on the participant's initial cholesterol concentration. As such, the researcher wanted to use pre-intervention cholesterol concentration as a covariate when comparing the post-intervention cholesterol concentrations between the interventions and a control group. Therefore, the researcher ran a one-way ANCOVA with: (a) post-intervention cholesterol concentration (post) as the dependent variable; (b) the control and two intervention groups as levels of the independent variable,group; and (c) the pre-intervention cholesterol concentrations as the covariate,pre.

Table 3.

Tests of Between-Subjects Effects

Dependent Variable: Post

Source	Type III Sum of Squares	df	Mean Square	F	Sig.	Partial Eta Squared
Corrected Model	17.687	3	5.896	475.503	.000	.972
Intercept	.001	1	.001	.120	.731	.003
pre	13.412	1	13.412	1081.692	.000	.963
group	2.616	2	1.308	105.512	.000	.837
Error	.508	41	.012
Total	1494.874	45
Corrected Total	18.196	44

1. R Squared = .972 (Adjusted R Squared = .970)

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Question:

Using Table 3, please respond to the following items:

1. Given our discussions about effect size in class, please explain why the value of R², provided as a footnote in the table below, the same value as the value of Partial Eta Squared in the table (Table 3)?
2. How was partial eta squared in Table 3 determined for both "group" and "pre"?Please show work.
3. Is partial eta squared in Table 3 for both "group" and "pre" the same thing as the effect size of both "group" and "pre"? If yes, how do you know? If no, how do you determine the effect size of each?