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Midterm

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

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Colorado State University

Statistics

STAT 301

Brett Hunter

Fall

Description

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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