Question

   An education researcher is interested in students’ performance on a mathematics test for a novel---and generally unfamiliar---concept. The researcher believes that if students participate in an extracurricular training session, then they will be more likely to perform better on the mathematics test.

This researcher is testing two hypotheses. The first is that the training session provides specific instruction and has an effect on students’ mathematics test scores. The second is that this treatment effect is moderated by gender. Past research has suggested that there should not be a main effect for gender. However, to control for this possibility, a 2-way (2x2) factorial ANOVA is being conducted to account for any influence from gender, the treatment, and the interaction of the two main effects.

To test the hypotheses, the research has obtained 28 participants: 14 boys and 14 girls. From each group of 14, 7 students were randomly chosen for the treatment group. After the treatment, all students were given the same test. This test has been used in previous research, has a range of 0 to 100, and measures students’ ability to correctly perform the novel mathematics exercise. (The higher the test score, the more positive the result.)

Use a 2x2 ANOVA with α=0.02α=0.02 to test the the data and evaluate the hypotheses. Results are provided below for each group of students.

		Factor B: Treatment
		Control: No Training	Treatment: Attend Training
Factor A: Gender	Male	67.6 60.0 65.4 67.3 57.6 43.1 61.3	61.6 69.3 70.5 56.6 64.2 60.5 62.6
	Female	52.8 51.5 66.5 62.7 55.8 48.1 58.6	71.0 73.6 76.4 62.4 74.4 86.9 71.2

( 1a ) What is the F value for the treatment effect?  
(Report answer accurate to 2 decimal place.)

( 1b ) What is the p-value for the F value for the treatment effect?  
(Report answer accurate to 4 decimal places.)

( 1c ) Does this support the researcher's hypothesis that the treatment has an effect on ability to solve the mathematics exercise?

• yes
• no

( 2a ) What is the F value for the gender effect?  
(Report answer accurate to 2 decimal place.)

( 2b ) What is the p-value for the F value for the gender effect?  
(Report answer accurate to 4 decimal places.)

( 2c ) Does this support the researcher's assumption that gender does NOT have an effect on ability to solve the mathematics exercise?

• yes
• no

( 3a ) What is the F value for the interaction effect?  
(Report answer accurate to 2 decimal place.)

( 3b ) What is the p-value for the F value for the interaction effect?  
(Report answer accurate to 4 decimal places.)

( 3c ) Does this support the researcher's hypothesis that the treatment effect is moderated by gender?

• yes
• no

Answer 1

Anova: Two-Factor With Replication
SUMMARY	NO TRANING	ATTEND TRANING	Total
MALE
Count	7	7	14
Sum	422.3	445.3	867.6
Average	60.32857	63.61429	61.97143
Variance	72.08571	24.01143	47.25912
FEMALE
Count	7	7	14
Sum	396	515.9	911.9
Average	56.57143	73.7	65.13571
Variance	42.09238	53.87667	123.2825
Total
Count	14	14
Sum	818.3	961.2
Average	58.45	68.65714
Variance	56.49808	63.33495
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	70.08893	1	70.08893	1.459683	0.238751	6.210859
Columns	729.3004	1	729.3004	15.18852	0.000683	6.210859
Interaction	335.3432	1	335.3432	6.983909	0.014255	6.210859
Within	1152.397	24	48.01655
Total	2287.13	27

F value for treatment = 15.188

p value = 0.000683

p value < 0.02 , significant

researcher's hypothesis that the treatment has an effect on ability to solve the mathematics exercise?

yes

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

F stat for gender effect = 1.4596

p value = 0.2387

p value > 0.02 , not significant

( 2c ) Does this support the researcher's assumption that gender does NOT have an effect on ability to solve the mathematics exercise?

YES

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

F stat for interaction = 6.983909

p value = 0.014255

p value < 0.02 , significant

Does this support the researcher's hypothesis that the treatment effect is moderated by gender?

yes

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

Please revert back in case of any doubt.

Please upvote. Thanks in advance.