Tukey's Quick Tost. In this exercise, we examine an alternative method, conceived by the late Professor John Tukey, for
performing a two-tailed hypothesis test for two population
Step 1 Count the number of observations in the high group that are greater than or equal to the largest observation in the low group. Count ties as 1/2.
Step 2 Count the number of observations in the low group that are less than or equal to the smallest observation in the high group. Count ties as 1/2.
Step 3 Add the two counts obtained in Steps 1 and 2, and denote the sum c.
Step 4 Reject the null hypothesis at the 5% significance level if and only if c ≥ 7; reject it at the 1% significance level if and only if c ≥ 10; and reject it at the 0.1% significance level if and only if c ≥ 13.
- a. Can Tukey’s quick test be applied to Exercise 10.48 on page 456? Explain your answer.
- b. If your answer to pan (a) was yes, apply Tukey’s quick test and compare your result to that found in Exercise 10.48, where a t-test was used.
- c. Can Tukey’s quick test be applied to Exercise 10.84? Explain your answer.
- d. If your answer to pan (c) was yes, apply Tukey’s quick test and compare your result to that found in Exercise 10.84, where a t-test was used.
- e. For more details about Tukey's quick test, see J. Tukey, “A Quick, Compact, Two-Sample Test to Duckworth’s Specifications” (Technometrics, Vol. 1, No. 1. pp. 31-48).
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Introductory Statistics (10th Edition)
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