Question

A study was conducted to see if students’ writing skills continue to improve as the academic year progresses. English 101 students were asked to write essays throughout the year in September, December, March and June. The scores were compared to see if there is any improvement in this one-year course. Was there a significant improvement?

The appropriate test for this problem is:

one-way ANOVA

repeated measurements

Student	September	December	March	June
1	17	23	21	24
2	25	21	21	24
3	24	16	21	29
4	18	18	25	27
5	25	21	24	24
6	25	25	16	25
7	24	15	23	22
8	24	21	19	23
9	20	17	16	28
10	24	22	21	22
11	16	24	25	29
12	18	24	23	24
13	15	16	22	27
14	23	24	22	22
15	21	24	20	25
16	22	16	25	26
17	16	16	20	23
18	24	22	22	27
19	19	23	23	27
20	19	17	25	25
21	20	17	19	22
22	22	19	25	24
23	15	24	22	26
24	22	21	15	26
25	25	16	24	22
26	15	22	25	23
27	15	17	25	29
28	18	18	19	23
29	17	17	21	29
30	19	17	15	26
31	19	16	18	26
32	22	21	16	29
33	16	19	19	29

The obtained statistic is:

F = 24.17

F = 12.71

F = 21.47

F = 17.42

The associated p value is:

< .05

< .01

< .001

< .0001

Decision is:

reject the null

retain the null

Conclusion is:

1) March scores are significantly lower than the rest of the months

2) December scores are significantly higher than September scores

3) March scores are significantly higher than September scores

4) June scores are significantly higher than the rest of the months

5 )no conclusion can be drawn

Answer 1

Following is the output of one way ANOVA:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
September	33	664	20.12121212	12.10984848
December	33	649	19.66666667	10.04166667
March	33	697	21.12121212	9.984848485
June	33	837	25.36363636	5.863636364
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	670.3863636	3	223.4621212	23.52232855	3.43E-12	2.675387
Within Groups	1216	128	9.5
Total	1886.386364	131

The F test statistics is:

F = 23.52

The p-value is less than 0.0001

p-value < 0.0001

Reject null hypothesis.

5 )no conclusion can be drawn