Question

An educational psychologist wants to know if length of time and type of training affect learning simple fractions. Fifth graders were randomly selected and assigned to different times (from 1 to 3 hours) and different teaching conditions (old method vs. meaningful method). All students were then tested on the "fractions" subtest of a standard arithmetic test. What can the psychologist conclude with α = 0.01?

	Time
Train	one hr	two hrs	three hrs
old	5 6 7	6 7 7	8 9 10
meaningful	6 7 11	9 10 11	7 9 10

Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
Train: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect
Time: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect

Answer 1

Applying ANOVA:

Source of Variation	SS	df	MS	F	P-value	F crit
train	12.5000	1	12.5000	5.9211	0.0315	9.3302
Time	10.7778	2	5.3889	2.5526	0.1192	6.9266
Interaction	10.3333	2	5.1667	2.4474	0.1284	6.9266
Within	25.3333	12	2.1111
Total	58.9444	17

Train: η² = 12.5/58.9444 =0.2120 ,  medium effect

Time: η² =10.7778/25.3333 =0.1828 , medium effect

Interaction: η² = 10.3333/58.9444 , medium effect