46. The following data were obtained from a two factor independent-measures expe

Question

46. The following data were obtained from a two factor independent-measures experiment with n = 5 participants in each treatment condition. B1B2 N 30 M=6 T=30 B3 M=9 T=45 A1 T= 15 (12a) (2,20) ss, = 43 11 T2= 5 | ss-2808 | ANNA Table SS = SS = 26 SS = 1 8 M=1 T=5 M=4 T 20 A2 Benn | ZX-13 SS=8 EX) = 25 SS = 20 SS = 20 . State the hypotheses for each of the three separate tests included in the two-factor ANOVA. b Calculate degrees of freedom and locate the critical region for each of the three tests. ) c. Calculate the three F-ratios. d. State a conclusion for each test.

Explanation / Answer

a) The null hypotheses for each of the sets are given below.

b) The degree of freedom for row test is 1 and for column test is 2. For the interaction the degree of freedom is 1*2=2.

c) The F ratio is given as if y=SS/df(degree of freedom of the particular test) then F=y/M. Aand thus it can be calculated for each variable as 28.283,12.393 and 1.973 and corresponding p values are 0, 0 and 0.12

d)For the first two tests, the conclusion is that null hypothesis is rejected since p <0.05 but for the last test p>0.05 and thus there the null hypothesis is not rejected and thus we cannot conclude that there doesn't exist any interaction effects among the factors.

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