Question

A sample of soy bean plots were divided into three equal groups in a completely randomized design, and each group received a different formulation of a selective weed killer (wk). The researchers measured the area of crop damage inflicted by each formulation. The aim is to choose the weed killer formulation that inflicts the least amount of crop damage. What can the researchers conclude with an α of 0.01?

wk 1	wk 2	wk 3
11 10 13 10 15 17 10	24 26 20 29 19 14 21	27 38 37 22 18 30 24

b) Obtain/compute the appropriate values to make a decision about H₀.
critical value = ____________ ; test statistic = _______________
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² = ______________ ;  ---Select--- na trivial effect small effect medium effect large effect
.    

e) Regardless of the H₀ decision in b), conduct Tukey's post hoc test for the following comparisons:
2 vs. 3: difference = ______________ ; significant:  ---Select--- Yes No
1 vs. 2: difference =  ______________ ; significant:  ---Select--- Yes 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--- Yes No
2 vs. 3: test statistic =______________   ; significant:  ---Select--- Yes No

Answer 1

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	878.000	2	439.000	14.845	0.0002	6.01
Within Groups	532.286	18	29.571
Total	1410.286	20

B) CRITICAL VALUE = 6.01

test stat = 14.845

decision: reject Ho

c) eta square ,effect size = SSbet/SST=   0.6226 (large)

d)

2 vs. 3: difference = _____6.14_________ ; significant:  No
1 vs. 2: difference =  ______9.57________ ; significant: YES

e)

Test statistic, F'=   (X̅I - X̅j)²/(MSE*√(1ni+1/nj))

1 vs. 3: test statistic = ____45.93__________ ; significant: YES
2 vs. 3: test statistic =________7.018______   ; significant: YES