Example 5: Calculating Spearman's Rank Correlation Coefficient for Qualitative Data In a study of the relation between students' grades in mathematies and science, the following results were found for six students. \begin{tabular}{|c|l|l|l|l|l|l|} \hline Mathematics & D & B & A & B & D & D \\ \hline Science & C & C & B & A & C & F \\ \hline \end{tabular} Find the Spearman's correlation coefficient. Round your answer to three decimal places.
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Assume A = 1, B = 2, C = 3, D = 4, F = 5. Mathematics Grades: D, B, A, B, D, D Ranks: 4, 2, 1, 2, 4, 4 Science Grades: C, C, B, A, C, F Ranks: 3, 3, 2, 1, 3, 5 Show moreā¦
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Perform these steps. a. Find the Spearman rank correlation coefficient. b. State the hypotheses. c. Find the critical value. Use $\alpha=0.05$. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Textbook Ranking After reviewing 7 potential textbooks, an instructor ranked them from 1 to 7 , with 7 being the highest ranking. The instructor selected one of his previous students and had the student rank the potential textbooks. The rankings are shown. At $\alpha=0.05$, is there a relationship between the rankings? $$ \begin{array}{l|ccccccc} \text { Textbook } & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \mathrm{E} & \mathrm{F} & \mathrm{G} \\ \hline \text { Instructor } & 1 & 4 & 6 & 7 & 5 & 2 & 3 \\ \hline \text { Student } & 2 & 6 & 7 & 5 & 4 & 3 & 1 \end{array} $$
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