#### Margin of error

Another measure of sampling error is the Margin of Error (MOE). This describes the distance from the population value that the sample estimate is likely to be within and is particularly useful to understand the accuracy of proportion estimates.

The MOE is specified at a given level of confidence. Confidence levels typically used are 90%, 95% and 99%. For example, at the 95% confidence level, the MOE indicates that there are about 19 chances in 20 that the estimate will differ by less than the specified MOE from the population value (the figure obtained if the whole population had been enumerated). The 95% MOE is calculated as 1.96 multiplied by the SE:

\(M O E=S E \times 1.96\)

The RSE can also be used to directly calculate a 95% MOE by:

\(M O E=\Large\frac{R S E \% \times e s t i m a t e \times 1.96}{100}\)

The MOEs in this release are calculated at the 95% confidence level. This can easily be converted to a 90% confidence level by multiplying the MOE by:

\(\Large\frac{1.615}{1.96}\)

or to a 99% confidence level by multiplying the MOE by:

\(\Large\frac{2.576}{1.96}\)

Depending on how the estimate is to be used, a MOE of greater than 10% may be considered too large to inform decisions. For example, a proportion of 15% with a MOE of plus or minus 11% would mean the estimate could be anything from 4% to 26%. It is important to consider this range when using the estimates to make assertions about the population.

Estimates of proportions with an MOE more than 10% are annotated to indicate they are subject to high sample variability and particular consideration should be given to the MOE when using these estimates. Depending on how the estimate is to be used, an MOE greater than 10% may be considered too large to inform decisions. In addition, estimates with a corresponding standard 95% confidence interval that includes 0% or 100% are annotated to indicate they are usually considered unreliable for most purposes.