An experiment was conducted to compare the effectiveness of five treatments. Subjects were matched with respect to a relevant variable and assigned randomly to the treatments. Seven sets of matched subjects, i.e., blocks, with five subjects in each matched set were obtained. The subjects in each set were assigned randomly to the treatments. After a given period, scores on an outcome measure were obtained. The ANOVA table is given below.
Dependent Variable: score
|
Source
|
Type III Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
Corrected Model
|
93.543(a)
|
10
|
9.354
|
3.271
|
.008
|
|
Intercept
|
2036.829
|
1
|
2036.829
|
712.296
|
.000
|
|
Treat
|
38.171
|
4
|
9.543
|
3.337
|
.026
|
|
Block
|
55.371
|
6
|
9.229
|
3.227
|
.018
|
|
Error
|
68.629
|
24
|
2.860
|
|
|
|
Total
|
2199.000
|
35
|
|
|
|
|
Corrected Total
|
162.171
|
34
|
|
|
|
a R Squared = .577 (Adjusted R Squared = .400)
(a) What type of design was used in this analysis?
(b) State the hypothesis of interest. Using the results shown above, state your conclusions.
(c) Reconstruct the ANOVA table as if you had ignored the matching variable, i.e., Block, and carried out a one-way ANOVA.
(b) Based on your table in (b), what would you conclude about the relative effectiveness of the treatments? Explain.
(c) Given your findings in (b) and (c), was matching effective? Explain.