12.3 Notes Spearman Rank Correlation Tests

Spearman Rank Correlaiton Test – Used to determine if a monotone relation exists between two variables (as one increases the other increases - monotone increasing or as one increases the other decreases – monotone decreasing). Process 1.Establish H 0 and H 1. H0:H0: H1:H1: 2.Draw critical region and find the critical value using table 9 where n = number of pairs of data 3.Compute the sample statistic: where 4.Draw the conclusion.

Ex. 1 Hendricks College has a new faculty position. The faculty reserves the right to make the final hiring decision, however, they are interested in comparing faculty opinion with student opinion about the teaching ability of the candidates. A random sample of nine qualified candidates was asked to give a classroom presentation to a large class of students. Both faculty and students attended the lectures. At the end of each lecture, both faculty and students filled out a questionnaire about the teaching performance of the candidate. Based on these questionnaires, each candidate was given an overall rank from both the faculty and the students. The results are below. Higher ranks mean better performance. Candidate Faculty Rank Student Rank

Day 1 Assignment P. 687 #1-5

Ex. 2 Do people who drink more coffee tend to smoke more cigarettes? Test at 0.01 level of significance. Person Cigarettes per day Cups of Coffee per day Person Cigarettes Rank Coffee Rank Note: For cigarettes the three values of 15 comprise the rank of 3,4, and 5; therefore each receives the average of the ranks (4). For coffee the two values of 18 comprise the rank of 9 and 10; therefore each receives the average of the ranks (9.5).

Day 2 Assignment P. 688 #6-10