8. Two-way ANOVA without replication is equivalent to paired t test if comparing two population mean

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STAT 420 2GR, 2UG, 3GR, 3UG Examples for 10/11/2016 (2) Fall 2016 A. Stepanov (e) Compare the values of MSR from (b) and s D 2 from (a). For (a) and (d): Matched Pair Comparison: Pair Difference 1 X 1 Y 1 D 1 = X 1 – Y 1 2 X 2 Y 2 D 2 = X 2 – Y 2 n X n Y n D n = X n – Y n
Assume that the differences D i = X i – Y i are a random sample from normal distribution with mean δ and standard deviation σ D A confidence interval for δ is n s t D 2 D α ± . The number of degrees of freedom = n To test the hypothesis H 0 : δ = δ 0 , use the test statistic n s t D 0 D δ - = . n – 1 degrees of freedom a) . – 1.

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