Bluman A.G. Elementary Statistics- A Step By Step Approach

706 Chapter 13 Nonparametric StatisticsProcedure TableThe Runs TestStep 1State the hypotheses and identify the claim.Step 2 Find the number of runs.Note: When the data are numerical, find the median. Then compare each datavalue with the median and classify it as above or below the median. Other methodssuch as odd-even can also be used. (Discard any value that is equal to the median.)Step 3 Find the critical value. Use Table M.Step 4 Make the decision. Compare the actual number of runs with the critical value.Step 5 Summarize the results.Applying the Concepts 13–6Tall TreesAs a biologist, you wish to see if there is a relationship between the heights of tall trees andtheir diameters. You find the following data for the diameter (in inches) of the tree at 4.5 feetfrom the ground and the corresponding heights (in feet).Diameter (in.) Height (ft)1024 261950 321451 219505 281761 159644 83707 191586 141442 232546 108Source: The World Almanac and Book of Facts.1. What question are you trying to answer?2. What type of nonparametric analysis could be used to answer the question?3. What would be the corresponding parametric test that could be used?4. Which test do you think would be better?5. Perform both tests and write a short statement comparing the results.See page 718 for the answer.Exercises 13–6For Exercises 1 through 4, find the critical value fromTable L for the rank correlation coefficient, given samplesize n and A. Assume that the test is two-tailed.1. n 14, a 0.01 0.7162. n 28, a 0.02 0.4883. n 10, a 0.05 0.6484. n 9, a 0.01 0.833For Exercises 5 through 14, perform these steps.a. Find the Spearman rank correlation coefficient.b. State the hypotheses.c. Find the critical value. Use a 0.05.d. Make the decision.e. Summarize the results.13–36