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An educational psychologist wants to know if length of time and type of training affect learning...

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Basic Math

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

Time
Trainone hrtwo hrsthree hrs
old5
6
7		6
7
7		8
9
10
meaningful6
7
11		9
10
11		7
9
10



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

b) Compute the appropriate test statistic(s) tomake 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 & Explanation Solved by verified expert
4.5 Ratings (827 Votes)

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
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