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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