Question

In: Statistics and Probability

An education researcher is interested in students’ performance on a standardised reading test.

An education researcher is interested in students’ performance on a standardised reading test. The researcher believes that if students experience a particular form of positive coaching, then they will be more likely to perform better on the reading test.

This researcher is testing two hypotheses. The first is that the coaching boosts self-efficacy and has an effect on students’ reading test scores. 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’ reading comprehension. (The higher the test score, the more positive the result.)

Use a 2x2 ANOVA with α=0.01α=0.01 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	37.2 43.0 29.4 34.8 13.1 38.4 36.7	44.3 37.1 42.7 59.9 61.1 53.9 41.1
Factor A: School Year	Year 10	48.1 43.7 32.6 40.2 43.3 42.7 38.4	50.6 48.9 53.2 51.6 46.4 34.2 58.7

( 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 reading comprehension?

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 reading comprehension?

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

Expert Solution

data -> data analysis -> Anova: Two-Factor With Replication

Treatment effect is in columns
a) F = 12.3962
b) p-value = 0.0034
c) yes, as p-value < alpha

school-year is in sample
a) F = 0.1765
b) p-value = 0.9788
c) yes, p-value > alpha

Interaction
a) F = 1.5506
b) p-value = 0.2332
c) No, as p-value > alpha

orchestra answered 2 years ago

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