PAIRWISE t-TEST AND ANALYSIS OF VARIANCE

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Presentation transcript:

PAIRWISE t-TEST AND ANALYSIS OF VARIANCE Emese Vágó, Sándor Kemény Budapest University of Technology and Economics

Outline I. Summary of paired t-test and analysis of variance II. Similarities and differences in the two procedures III. Comparison of the models IV. Comment IV. Conclusions

Example The effect of a diet on weight was investigated using ten people. Results:

Paired t-test Pairs

Analysis of variance yij: weight of jth men before(i=1)/after(i=2) diet r: levels of A (2) Random effect (B) n: levels of B (10)

Similarities and differences Conditions of the two analysis differ in spite of the same statistics. Why is it so? ? ? Same statistic Same model

Assumptions - paired t-test Product moment correlation, can not be estimated Assumptions of independence for

Assumptions - analysis of variance   Assumptions of independence for - yij - levels of B 

Comparison of assumptions Paired t-test Analysis of variance If the models do not correspond If

Comparison of assumptions ANOVA method may be used with weaker assumptions about homogeneity of variances for: - one random, and - one fixed effect (number of levels is two) design - sample sizes are one - testing only the effect of fixed factor

Comment - distribution of the random effect

Comment - sample sizes larger then one Sample size: q

Consequence ANOVA method may be used with weaker assumptions about homogeneity of variances for testing the effect of a 2-level fixed factor, if the other factor is - random, or fixed and - sample sizes are one, or larger then one.

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