Question

A researcher is interested in determining whether the new design of the training simulator and a new behavior modification program will affect a student’s learning behavior. Sixty-three (63) students are randomly selected for inclusion in this research project. The students are randomly divided into 9 groups of 7. The group assignments are as follows:

	Design A	Design B	Design C
No behavior modification	12	18	21
	10	16	22
	19	27	33
	19	23	35
	15	26	27
	18	22	34
	22	22	32
Behavior modification every other day	28	30	38
	15	15	20
	20	20	23
	12	14	20
	14	15	14
	14	20	21
	17	19	21
Behavior modification every day	3	7	13
	10	14	18
	11	11	12
	8	12	13
	11	17	19
	5	10	9
	17	15	13

After 10 weeks, students are tested on an examination of their learning behavior. The scores range from a low of 1 (low) to 45 (high) (See above table for detailed scores). Analyze the data and answer the following questions. (For any test, use α=0.050 )

1. Based on your judgment, will you consider a one way or two-way ANOVA test?
2. Please clearly state your hypotheses for this problem.
3. Present your detailed statistical analysis results.
4. Interpret your results: Will the behavior modification program affect the score? Will the new design of the training simulator affect the score? Is there an interaction effect between the behavior modification program and the new design? Please justify your answers

Answer 1

two-way ANOVA test

Anova: Two-Factor With Replication
SUMMARY	Design A	Design B	Design C	Total
No behavior modification
Count	7	7	7	21
Sum	115	154	204	473
Average	16.42857	22	29.14286	22.52381
Variance	18.28571	15.66667	33.80952	48.7619
Behavior modification every other day
Count	7	7	7	21
Sum	120	133	157	410
Average	17.14286	19	22.42857	19.52381
Variance	29.47619	30	54.95238	39.3619
Behavior modification every day
Count	7	7	7	21
Sum	65	86	97	248
Average	9.285714	12.28571	13.85714	11.80952
Variance	20.90476	11.2381	12.14286	17.0619
Total
Count	21	21	21
Sum	300	373	458
Average	14.28571	17.7619	21.80952
Variance	33.81429	34.39048	71.3619
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	1283.143	2	641.5714	25.49558	0.0000	3.168246
Columns	595.5238	2	297.7619	11.83284	0.0000	3.168246
Interaction	149.3333	4	37.33333	1.4836	0.220011	2.542918
Within	1358.857	54	25.16402
Total	3386.857	62

p value for  behavior modification program = 0.0000

p value < 0.05

so,

behavior modification program affect the score

.........

p value for new design of the training = 0.0000

p value < 0.05

new design of the training simulator affect the score

...............

p value for interaction = 0.2200

p avlue > 0.05

so,  there is no  interaction effect between the behavior modification program and the new design

.................

THANKS

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