Introduction to Probability and Statistics for Engineers and Scientists

482 Chapter 10:Analysis of Variance

p. 178, 1970). Half of the rats in both groups had their spleens removed. The

fibrinogen levels on day 21 are reported below.

(a) Test the hypothesis that there are no interactions.

(b) Test the hypothesis that there is no effect due to altitude.

(c) Test the hypothesis that there is no effect due to spleen removal. In all cases,

use the 5 percent level of significance.

Suppose thatμ,α 1 ,...,αm,β 1 ,...,βnandμ′,α′ 1 ,...,α′m,β 1 ′,...,β′nare such

that

μ+αi+βj=μ′+αi′+βj′ for alli,j

∑

i

αi=

∑

i

αi′=

∑

j

βj=

∑

j

βj′= 0

Show that

μ=μ′,αi=α′i,βj=βj′

for alliandj. This shows that the parametersμ,α 1 ,...,αm,β 1 ,...,βnin our

representation of two factor ANOVA are uniquely determined.