19. Say we have an experimental design that contains one factor (independent var

Question

19. Say we have an experimental design that contains one factor (independent variable) with three levels. Why can't we just perform three t-tests to compare the different condition means? a. It would inflate the type I error rate of each test. b. It would increase the familywise error rate c. Both A and B. 20. With respect to Question #19, which would be a more appropriate way of comparing the three condition means? a. One-way ANOVA b. Tukey's HSD test c. Bonferroni-corrected t-tests d. All of the above 21. The difference between post-hoc tests that control the familywise error rate and tests that control the false discovery rate is: minimize the ceurence of amy a. Tests controlling the false discovery rate try to minimize the occurrence of any false positives, while tests controlling the familywise error rate attempt to ensure that only some small percentage of "positive" results are false positives. Tests controlling the false discovery rate attempt to ensure that only some small percentage of "positive" results are false positives, while tests controlling the familywise error rate try to minimize the occurrence of any false positives. Tests controlling the familywise error rate are typically more liberal than those controlling the false discovery rate. b. c.

Explanation / Answer

19)

Ans c) because the family-wise (FW) error rate is the probability of committing a Type1 error for an entire family of contrasts is

FW =(the number of families with at least one contrast declared falsely significant)/ number of familes

it will increase for each t test . For one-way ANOVA designs, there is only one family and so the probability of committing at least one type 1 error over an entire experiment are same.

20) answ d)

a) one way anova: here we compared group of means under Ho with the help of F global test. if Ho rejected we use Post-hoc test like tukey HSD , fisher LSD etc

b) when Ho is rejected we check which group of means difference significantly contributing in the response using tukey HSD.

c) Bonferroni correct t-test. in this method we control type 1 error simply alpha / #of test for each invidual test critical value.

hence all method are concerned with the inflation of type one error.

21)

ans b)

Test controlling the false discovery rate attempt to ensure that only some small percentage of positive results are false positives because in anova we accpet alternative to check which treatment group mean differe singnificantly among all pairs of combination using Post hoc test while test controlling the familywise error rate try to minimize the occurance of any false positives.

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