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 an α of 0.05?

	Time
Train	one hr	two hrs	three hrs
old	5 2 7	6 7 7	8 9 10
meaningful	6 7 8	9 10 11	7 9 10

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Input the appropriate value(s) to make a decision about H₀.
Train: p-value = ___________ ; Decision:  ---Select--- Reject H0 Fail to reject H0
Time: p-value =___________   ; Decision:  ---Select--- Reject H0 Fail to reject H0
Interaction: p-value =___________   ; Decision:  ---Select--- Reject H0 Fail to reject H0


c) 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


d) Make an interpretation based on the results.

1)There is a training difference in learning fractions.

2)There is no training difference in learning factions.    

1)There is a time difference in learning fractions.

2)There is no time difference in learning fraction.    

1)There is a training by time interaction in learning fractions.

2)There is no training by time interaction in learning fractions.   

Answer 1

a) What is the appropriate test statistic?
two-way ANOVA

b) Input the appropriate value(s) to make a decision about H₀.
Train: p-value = 0.0205 ; Decision: Reject H0
Time: p-value = 0.0069 ; Decision:  Reject H0
Interaction: p-value = 0.1080 ; Decision: Fail to reject H0


c) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
Train: η² =0.178   ; small effect
Time: η² =  0.388 ; medium effect
Interaction: η² = 0.135 ; small effect


d) Make an interpretation based on the results.

1)There is a training difference in learning fractions.

1)There is a time difference in learning fractions.

2)There is no training by time interaction in learning fractions.   

Source	SS	df	MS	F	p-value	n²
Train	14.22	1	14.222	7.11	.0205	0.178
Time	31.00	2	15.500	7.75	.0069	0.388
Interaction	10.78	2	5.389	2.69	.1080	0.135
Error	24.00	12	2.000
Total	80.00	17