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Unformatted text preview: Statistics: Nonparametric methods summary Spearman rank correlation • Spearman’s rank correlation coefficient, r s , measures the correlation between the ranking of a population according to two measures. Suppose that a sample of items (individuals) is taken from some population and labelled i = 1 , 2 ,...n . Suppose that x i is the rank of item i with respect to a measure on one variable, and that y i is the rank of item i with respect to a measure on another variable. Then Spearman’s rank correlation between the two variables is given by r s = 1- 6 ∑ n i =1 d 2 i n ( n 2- 1) where d i = x i- y i is the difference between the ranks. • In the case of tied ranks, we award the average of the tied ranks as the rank. For example, suppose that two items are in equal third to fourth place. We assign a rank of 3 1 2 to each. Provided that there aren’t too many ties, our procedure remains acceptable. • We rank from low to high in both sets, or from high to low in both sets. It doesn’t matter which. If we rank the first set from low to high, and the other from high to low, the sign of the correlation is changed. • As with other correlations,- 1 ≤ r s ≤ 1, with r s = 0 meaning no correlation, r s =- 1 meaning perfect negative correlation, and so forth. Under the assumption that the two rankings are independent, E ( r s ) = 0 and V ar ( r s ) = 1 n- 1 . For large n , say n > 200, r s has approximately a Normal distribution which can be used as the basis of a test of independence of rankings. Otherwise, approximately T = r s √ n- 2 p 1- r 2 s has a t distribution with n- 2 degrees of freedom....
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- Spring '10
- Normal Distribution, Non-parametric statistics, Spearman's rank correlation coefficient, sample sizes