Please verify my answer: E, F, & G 1-5.

Also for Questions E & F (based on your answers), how and why would it be: F(2, 78)= 20.599, p= < .001, = 0.232???

Is my output wrong? Please explain where I can locate my errors

E. Reporting the ANOVA Result

My Answer:

F(2, 78)= 20.599, p= < .001, = 0.346

Correction: Based on the provided output:

F(2, 78)= 20.599, p= < .001, = 0.232

Reasoning: The correct partial eta squared is 0.232, not 0.346 as originally stated. This indicates that 23.2% of the variance in reading comprehension scores can be attributed to the grade levels.

This data set contains reading comprehension scores from a group of elementary school children who were in a special reading program. These children were tested when they entered the reading program at third grade, and then tested again at fourth grade, and finally tested as they leave the program at fifth grade. Ensure that your data values, labels, and measures are correct before proceeding.

Perform and interpret a one-way repeated-measures ANOVA.

To see if the reading program leads to significant improvement on reading comprehension, the researchers want to compare the three test scores at the three grade levels. Perform a one-way repeated-measured ANOVA to answer the following question:

Is reading comprehension significantly different across the three grade levels?

A. What is the null hypothesis?

Null Hypothesis (H0): Reading comprehension is not significantly different across the three grade levels.

3rd = 4th = 5th

B. What are the DV and IV?

DV: Reading comprehension

IV: Grade levels (3rd, 4th, 5th)

C. Run the ANOVA with the following options:Descriptives; Estimate of effect size (partial eta squared) -Paste the entire output for this analysis here.

D. Examine the Sphericity test result. Is the sphericity assumption met? How do you know?

The null hypothesis represents the assumption of Sphericity. p = .938, which is larger than the alpha of .05, so the null hypothesis has a high probability of being true. We can assume sphericity in the data. Thus, the null hypothesis is not rejected. Since the p-value for Mauchly's test of sphericity is greater than 0.05, we do not reject the null hypothesis that sphericity holds.

Sphericity Test Result: 2=0.128

p-value: 0.938 ( > 0.05)

E. Report the test result in APA forma (includingF statistic, p value,and partial ²).

F(2, 78)= 20.599, p= < .001, 2= 0.346

2= partial eta squared

F. What is the answer to the research question based on the test result?

Yes, the reading comprehension is significantly different across the three grade levels.

The ANOVA test result shows a significant effect of grade level on reading comprehension. The F statistic is 20.599 with a p-value less than .001. This means that the probability of getting a result as extreme as this, assuming there is no effect of grade level, is less than .001. Therefore, we reject the null hypothesis that there is no difference in reading comprehension across the three grade levels. The partial eta squared () is .346 = 34.6% of the variance is a large effect size, further supporting the conclusion that there is a significant difference in reading comprehension across the three grade levels.

G. 1. Run the same ANOVA again, but this time request "contrasts" to compare each level with every other level.

G. 2. Run the repeated-measures ANOVA, then requestsimple contrasts for the variable of "Grade", with "Last" level as the reference category. This will compare each level with the "last" level.Paste the table of "Tests of Within-Subjects Contrasts" below

G. 3. Run the repeated-measures ANOVA, then requestsimple contrasts for the variable of "Grade", with "First" level as the reference category. This will compare each level with the "first" level.Paste the table of "Tests of Within-Subjects Contrasts" below

G. 4. Report the result of each of the pair-wise contrasts, includingF statistics (with df's) andp value, in APA form.

Last Level as the Reference Category:

Level 3 vs. Level 1 result:F(1, 39) = 38.491, p = <.001, partial 2 = .497

Level 3 vs. Level 2 result:F(1, 39) = = 6.919, p= 0.012, partial 2= .151

First Level as the Reference Category:

Level 1 vs. Level 2 result:F(1, 39) = 14.761,p<.001, partial2=.275

Level 1 vs. Level 3 result:F(1, 39) = 38.491,p<.001, partial2=.497

G. 5. Determine whether there is a significant difference in reading comprehension in each contrast. What are all the pairs that have significant differences in reading comprehension.

All three pairs have p-values less than 0.05, indicating that the differences in reading comprehension between each pair are statistically significant. Therefore, all pairs (Level 1 vs. Level 2, Level 2 vs. Level 3, and Level 1 vs. Level 3) have significant differences in reading comprehension.

or

There is a significant difference in reading comprehension in Level 1 vs Level 2 and Level 1 vs Level 3 because the p value is less than the alpha value. There is not a significant difference in reading comprehension in Level 2 vs Level 3 because the p value is higher than the alpha value.

CODEBOOK for DATA SET

Variable Name	Description	Value
ReadG3	Reading comprehension at 3rd grade	Test score
ReadG4	Reading comprehension at 4th grade	Test score
ReadG5	Reading comprehension at 5th grade	Test score

DATA SET

Subject	ReadingG3	ReadingG4	ReadingG5
1	59.00	71.00	69.00
2	70.00	77.00	79.00
3	53.00	55.00	82.00
4	69.00	65.00	80.00
5	59.00	62.00	76.00
6	63.00	79.00	86.00
7	55.00	72.00	78.00
8	71.00	58.00	74.00
9	62.00	63.00	75.00
10	68.00	56.00	69.00
11	59.00	62.00	88.00
12	57.00	58.00	73.00
13	55.00	60.00	72.00
14	64.00	75.00	83.00
15	62.00	88.00	68.00
16	56.00	81.00	80.00
17	65.00	85.00	89.00
18	55.00	75.00	80.00
19	76.00	84.00	69.00
20	60.00	80.00	73.00
21	58.00	62.00	64.00
22	59.00	69.00	77.00
23	73.00	66.00	61.00
24	70.00	57.00	62.00
25	78.00	68.00	71.00
26	72.00	70.00	69.00
27	70.00	78.00	70.00
28	60.00	56.00	62.00
29	59.00	82.00	69.00
30	69.00	69.00	88.00
31	64.00	82.00	84.00
32	58.00	58.00	60.00
33	70.00	85.00	65.00
34	65.00	60.00	70.00
35	67.00	84.00	80.00
36	62.00	80.00	80.00
37	69.00	64.00	65.00
38	61.00	71.00	85.00
39	71.00	82.00	90.00
40	58.00	66.00	80.00