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

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

b) Compute the appropriate test statistic(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:

Answer 1

a) Appropriate test statistic: Two-way ANOVA

Output using excel:

Anova: Two-Factor With Replication
SUMMARY	One hour	Two hour	Three hour	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

b) Train:

p-value = 0.0315

Decision:

As p-value > 0.01, we fail to reject Ho

------------------

Time:

p-value = 0.1192

Decision:  

As p-value > 0.01, we fail to reject Ho

-------------------

Interaction:

p-value = 0.1284

Decision:  

As p-value > 0.01, we fail to reject Ho