Question

An education researcher is interested in students’ motivation to study local history. The researcher believes that if students experience a particular form of positive coaching, then they will be more likely to show interest in local history.

This researcher is testing two hypotheses. The first is that the coaching boosts self-efficacy and has an effect on students’ motivation. The second is that this treatment effect is moderated by year in school. Past research has suggested that there should not be a main effect for school year. However, to control for this possibility, a 2-way (2x2) factorial ANOVA is being conducted to account for any influence from school year, the treatment, and the interaction of the two main effects.

To test the hypotheses, the research has obtained 28 participants: 14 year-7 students and 14 year-10 students. 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’ interest in issues relating to local history. (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 Coaching	Treatment: Positive Coaching
Factor A: School Year	Year 7	64.5 66.3 71.2 79.8 43.2 58.5 49.6	74.3 74.6 85.6 82.5 72.3 72.4 87.9
	Year 10	69.9 65.4 62.9 68.4 69.7 81.8 66.8	83.2 82.8 76.0 80.5 79.1 76.2 84.3

( 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 interest in local history?

• yes
• no

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

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

( 2c ) Does this support the researcher's assumption that school-year does NOT have an effect on interest in local history?

• 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 school-year?

• yes
• no

( 4 ) Based on these findings, which group can you say had the higher average on the test?

• year-7 students
• year-10 students
• group with no coaching
• group with positive coaching
• year-7 students in the control group
• year-10 students in the control group
• year-7 students in the treatment group
• year-10 students in the treatment group

Answer 1

Anova: Two-Factor With Replication
SUMMARY	no coaching	positive coaching	Total
year 7
Count	7	7	14
Sum	433.1	549.6	982.7
Average	61.87143	78.51429	70.19286
Variance	157.5924	43.8781	167.5592
year 10
Count	7	7	14
Sum	484.9	562.1	1047
Average	69.27143	80.3	74.78571
Variance	36.66571	11.24	54.8567
Total
Count	14	14
Sum	918	1111.7
Average	65.57143	79.40714
Variance	104.4007	26.29764
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	147.6604	1	147.6604	2.368476	0.13689	6.210859
Columns	1339.989	1	1339.989	21.49345	0.000105	6.210859
Interaction	55.16036	1	55.16036	0.884773	0.356269	6.210859
Within	1496.257	24	62.34405
Total	3039.067	27

F value for trwatment = 21.19345

p value = 0.0001

p value<0.0001, result is significant

researcher's hypothesis that the treatment has an effect on interest in local history?

• yes

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

F VALUE for school year effect =2.368

p value =0.13689

p value>0.02, no significant

researcher's assumption that school-year does NOT have an effect on interest in local history?

yes

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

F stat for intercation = 0.8847

p avlue =0.356

p value < 0.02, not significanr

researcher's hypothesis that the treatment effect is moderated by school-year?

NO

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