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Eight elementary science teachers have been ranked by a judge according to their teaching ability, and all have taken a national teachers' examination. The data are as follows.
judge_rank <- c(2, 8, 3, 1, 4, 5, 6, 7)
exam_score <- c(72, 44, 80, 93, 82, 70, 69, 67)
We want to determine if the data suggest agreement between the judge's ranking and the examination score. The perfect agreement means the higher the judge's ranking, the higher the exam score. Higher ranking means smaller number in the judge's ranking, i.e. 1 = highest rank, 8 = lowest rank. So we should have the Spearman's rank-order correlation coefficient rs = -1 for perfect agreement.
Null hypothesis: There is no relation between the judge's ranking and the exam score (rs = 0).
Alternative hypothesis: There is a correlation between the judge's ranking and the exam score – a higher ranking (lower rank number) tends to have a higher score (rs < 0).
Use cor.test() function to perform a Spearman's correlation test to test the hypothesis. Make sure to set the 'alternative' parameter appropriately. Enter Spearman's correlation coefficient rs and the p-value to 3 significant figures.
a. Spearman's correlation coefficient rs =
b. P-value of the test =
Reject the null at α = 5%? yes no
