Question

Run the following analyses using R.

Thirty-six Midwestern junior high students were randomly selected to participate in a study about the effectiveness of six different math curricula. The researcher randomly assigned six students to each of the six conditions (n_j = 6 for all groups). At the end of a lesson on fractions, students were administered a 10-point quiz. Each student’s score is in the table below:

Student	Curriculum
	A	B	C	D	E	F
1	4	7	4	2	5	3
2	5	8	3	3	6	4
3	6	6	2	4	7	5
4	3	5	5	5	7	6
5	2	6	4	6	8	7
6	4	4	6	4	9	5
Sample Mean	4	6	4	4	7	5

1. Perform a one-way ANOVA of these data by completing the following table:

Table 1. ANOVA Summary Table

Source	Sum of Squares	df	Mean Square	F	p
Between
Within
Total

Is the omnibus F test statistically significant at the a = 0.05 level? How should the researcher interpret this result?

2. The researcher is interested in testing the differences among all of the pairs of means.
   1. How many such unique pairwise comparisons are possible?
   2. Conduct an t-test for each of these comparisons.
   3. Which t-tests from question are significant without doing any adjustments (based on an a level = 0.05 for each t test)?

3. The researcher worries about the possible Type I Error associated with doing this many tests, and therefore wants to make adjustments.
   1. Use Bonferroni adjustment
   2. Use Holm-Bonferroni adjustment
   3. Use Fisher’s LSD test
   4. Use Tukey’s HSD Test
   5. Which post hoc test will you choose to use and why?
   6. Based on the result of the post hoc test you chose, which group means were found to be significantly different?

Answer 1

Using Excel

data -> data analysis -> Anova: Single Factor

a)

There are 6C2 = 15 t-test possible

b)

Using Excel

data -> data analysis -> t-Test: Two-Sample Assuming Equal Variances

For comparing A and B

TS = -2.4495

p-value = 0.0343 < alpha

hence we conclude that difference are signficant ,

similarly, it can be done for all comparison