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 large effect
Time: η² =   ;  ---Select--- na trivial effect small effect large effect
Interaction: η² =   ;  ---Select--- na trivial effect small effect large effect

Answer 1

Anova: Two-Factor With Replication
SUMMARY	one hr	two hrs	three hrs	Total
old
Count	3	3	3	9
Sum	18	20	27	65
Average	6	6.666667	9	7.222222
Variance	1	0.333333	1	2.444444
meaningful
Count	3	3	3	9
Sum	24	30	26	80
Average	8	10	8.666667	8.888889
Variance	7	1	2.333333	3.361111
Total
Count	6	6	6
Sum	42	50	53
Average	7	8.333333	8.833333
Variance	4.4	3.866667	1.366667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	12.5	1	12.5	5.921053	0.031541	9.330212
Columns	10.77778	2	5.388889	2.552632	0.119209	6.926608
Interaction	10.33333	2	5.166667	2.447368	0.128404	6.926608
Within	25.33333	12	2.111111
Total	58.94444	17

Train: η² =SS(train)/SS(ttoal) =12.50/58.9444 =0.2121 ,  medium effect

TIme: η² =10.7778/58.9444 =0.1828 medium effect

Interaction: η² = 10.3333/58.9444 =0.1753  medium effect  

d)

There is no training difference in learning factions.    

There is no time difference in learning fraction.    

.There is no training by time interaction in learning fractions