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Standard error, confidence intervals, RR, O, OR, test of homogeneity, test of independence

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Colorado State University
STAT 301
Brett Hunter

2 November Want confidence intervals for these statistics (RR, Ô, OR) It is hard to calculate the standard error for these three statistics Solution: Find the standard error of their natural logs Notation Natural log is denoted ln in math books It is eog Statisticians use log as the natural log On calculate, log i10log So whenever I write “log”, I mean the natural log n S.E. of log (odds) √x(n−x) x = total successes n = total observations 1−p 1+1−p 2 n1−x 1+n2−x 2 S.E. of log (RR) √ p 1 1 p2n2 OR √ n1x1 n2x2 1 + 1 + 1 + 1 S.E. of log (OR) √ x1 n1−x1 x2 n 2x 2 So CI for the log of the statistic is ± log (stat) Z crit.E.) Thus ± n CI of log (odds) = log (odds) Zcrit √ x(n−x) n1−x 1 n2−x 2 CI of log (RR) = log (RR) ± Z crit + √ n1x1 n2x 2 ± 1 + 1 + 1 + 1 CI of log (OR) = log (OR) Zcrit√ x1 n1−x 1 x2 n2−x 2 eloe x Note that = x. Thus, to get the CIs for the statistics, we take e to the power of the CI of the logs. So the CIs for the statistics are (stat)±Z crit.E.) log¿ ¿
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