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 0.05?

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

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA  

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

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 3: test statistic =   ; significant:  ---Select--- Yes No  
1 vs. 2: test statistic =   ; significant:  ---Select--- Yes No  

Answer 1

a) What is the appropriate test statistic?
one-way ANOVA
b) Obtain/compute the appropriate values to make a decision about H₀.
critical value = 3.555 ; test statistic = 13.213
Decision: Reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² = 0.595; medium effect

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 3: test statistic = -5.123 ; significant:  No  
1 vs. 2: test statistic = -2.934 ; significant: No