#### Margin of error

The Margin of Error (MOE) shows the largest possible distance (due to sampling error) that could exist between the estimate and what would have been produced had all people been included in the survey, at a given level of confidence. It is useful for understanding and comparing the accuracy of proportion estimates. Confidence levels can vary (e.g. typically 90%, 95% or 99%), but in this publication, all MOEs are provided for estimates at the 95% confidence level. At this level, there are 19 chances in 20 that the estimate will differ from the population value by less than the provided MOE.

The 95% confidence level MOE is obtained by multiplying the standard error by 1.96.

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

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

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

These can 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.