Statistical Methods – Standard Error and Confidence Intervals

This post covers the 3 applications of standard error required for the MFPH Part A; mean, proportions and differences between proportions (and their corresponding confidence intervals)…

a) What is the etandard error (SE) of a mean?

The SE measures the amount of variability in the sample mean.  It indicated how closely the population mean is likely to be estimated by the sample mean.

(NB: this is different from Standard Deviation (SD) which measures the amount of variability in the population.  SE incorporates SD to assess the difference beetween sample and population measurements due to sampling variation)

  • Calculation of SE for mean = SD / sqrt(n)

…so the sample mean and its SE provide a range of likely values for the true population mean.

How can you calculate the Confidence Interval (CI) for a mean?

Assuming a normal distribution, we can state that 95% of the sample mean would lie within 1.96 SEs above or below the population mean, since 1.96 is the 2-sides 5% point of the standard normal distribution.

  • Calculation of CI for mean = (mean + (1.96 x SE)) to (mean – (1.96 x SE))

 

b) What is the SE and of a proportion?

SE for a proprotion(p) = sqrt [(p (1 – p)) / n]

95% CI = sample value +/- (1.96 x SE)

 

c) What is the SE of a difference in proportions?

SE for two proportions(p) = sqrt [(SE of p1) + (SE of p2)]

95% CI = sample value +/- (1.96 x SE)

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