010+Correlation

Zhensykbaev correlation or ha 0 lower tailed test

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Unformatted text preview: rs : rs = √ SSuv , SSuu SSvv where SSuv , SSuu and SSvv was introduced early. For ranks we can use shortcut formula: 6 rs = 1 − n(n2 − 1) n (ui − vi )2 . i=1 The null hypothesis about a correlation coecient is H0 = {ρ = 0}. Alternative hypotheses for one-tailed tests are Ha = {ρ > 0} (upper-tailed test or positive correlation) 7 A. Zhensykbaev Correlation or Ha = {ρ < 0} (lower-tailed test or negative correlation). Rejection region is RR = {rs ≥ rsα }, (or RR = {rs ≤ −rsα }, where rsα is dened from the Table XVII (McClave and Benson) for n pairs of observations.. If H0 is not rejected we may conclude (only in the normal case) that random variables X and Y are independent with the probability P = 1 − α. Alternative hypothesis for two-tailed tests is Ha = {ρ = 0}. Rejection region is RR = {rs ≥ rsα/2 } ∪ {rs ≤ −rsα/2 }. Example 2. Suppose we would like to know with 95% condence level, is there any dependence between income and total borrowed for a sample of...
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