Question

Answer the one-way ANOVA questions using the data below. Use α = 0.01.

1	2	3	4
53 49 47 45 51 34 44	44 25 36 34 39 30 12	46 42 49 37 36 34 47	25 37 30 27 33 28 31

a. Compute the preliminary statistics below.

SS_BG = ________ ;   df_BG = _________

SS_WG = ________ ;   df_WG = ________

SS_T = ___________ ; df_T = _________

b. Compute the appropriate test statistic(s) to make a decision about H₀.

critical value = ____________ ; test statistic = ____________

Decision:

c. Compute the corresponding effect size(s) and indicate magnitude(s).

η² = __________; ---Select---na, trivial effect, small effect, medium effect, large effect

d. Make an interpretation based on the results.

-At least one mean is different from another

-None of the means differed from one another.    

e. Regardless of the H₀ decision in b), conduct Tukey's post hoc test for the following comparisons:

1 vs. 3: difference = __________ ; significant: YES OR NO

1 vs. 4: difference = __________ ; significant: YES OR NO

f. Regardless of the H₀ decision in b), conduct Scheffe's post hoc test for the following comparisons:

1 vs. 3: test statistic = ___________ ; significant: ---Select---YesNo
3 vs. 4: test statistic = ____________; significant: ---Select---YesNo

Answer 1

a. Compute the preliminary statistics below.

SS_BG = 1,274.964 ;   df_BG = 3

SS_WG = 1,207.143 ;   df_WG = 24

SS_T = 2,482.107 ; df_T = 27

b. Compute the appropriate test statistic(s) to make a decision about H₀.

critical value = 4.718 ; test statistic = 8.449

Decision: Reject Ho

c. Compute the corresponding effect size(s) and indicate magnitude(s).

η² = 0.514; -medium effect

d. Make an interpretation based on the results.

-At least one mean is different from another

e. Regardless of the H₀ decision in b), conduct Tukey's post hoc test for the following comparisons:

1 vs. 3: difference = 4.571 ; significant: NO

1 vs. 4: difference = 16 ; significant: YES

f. Regardless of the H₀ decision in b), conduct Scheffe's post hoc test for the following comparisons:

1 vs. 3: test statistic = 4.571 ; significant: No
3 vs. 4: test statistic = 16; significant: Yes