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 onetailed tests are Ha = {ρ > 0} (uppertailed test or positive correlation)
7 A. Zhensykbaev Correlation or Ha = {ρ < 0} (lowertailed 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 twotailed 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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This note was uploaded on 02/11/2014 for the course MATH 1390 taught by Professor Christopherstocker during the Spring '13 term at Marquette.
 Spring '13
 ChristopherStocker
 Math, Correlation, Probability

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