mont4e_sm_ch13_mind

# mont4e_sm_ch13_mind - Mind Expanding Exercises 13-47 MS E =...

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Mind Expanding Exercises 13-47. ) 1 ( ) ( 11 2 = ∑∑ == n a y y MS a i n j i ij E and ij i ij a y ε μ + + = . Then . i ij i ij y y = and 1 ) ( 1 . = n n j i ij εε is recognized to be the sample variance of the independent random variables in i i , , , 2 1 . Therefore, 2 1 2 . 1 ) ( σ = = = n E n j i ij and 2 1 2 ) ( = = = a i E a MS E . The development would not change if the random effects model had been specified because . i ij i ij y y = for this model also. 13-48. The two sample t-test rejects equality of means if the statistic t y y s y y s p nn p n = + = || is too large. The ANOVA F-test rejects equality of means if 12 2 E 2 .. . i 2 1 i MS ) y y ( n F = = is too large. Now, n 2 E 2 . 2 . 1 E 2 . 2 . 1 2 n MS ) y y ( MS ) y y ( F = = and . 2 p E s MS = Consequently, . Also, the distribution of the square of a t random variable with a(n - 1) degrees of freedom is an F distribution with 1 and a(n - 1) degrees of freedom. Therefore, if the tabulated t value for a two-sided t-test of size , then the tabulated F value for the F test above is t Therefore, t > whenever F = and the two tests are identical. 2 t F = 0 t is α 0 2 . 0 t 2 0 2 t t > 13-49. ) 1 ( 2 ) ( 2 . 1 2 1 = = = n y y MS i ij n j i E and 1 ) ( 2 . 1 = n y y i ij n j is recognized as the sample standard deviation calculated from the data from population i. Then, 2 2 2 2 1 s s MS E + = which is the pooled variance estimate used in the t-test. 13-50. from the independence of YY ) ( ) ( . 2 1 . 1 i i a i i i a i Y V c Y c V = = = Y a ..

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mont4e_sm_ch13_mind - Mind Expanding Exercises 13-47 MS E =...

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