Comparing estimates

When comparing estimates between different groups, it is important to recognise that the differences are also subject to sampling error. As a rule of thumb, a conservative estimate of the standard error of the difference can be constructed by adding the squares of the estimated standard errors of the component estimates and then taking the square root of the result.

For example, suppose the estimates of total cash receipts were $100 000 in the beef industry and $125 000 in the sheep industry – a difference of $25 000 – and the relative standard error is given as 6 per cent for each estimate, then standard error of the difference can be estimated as:

√ [(0.06 x $100 000) + (0.06 x $125 000)]
= $9605
so the relative standard error of the difference is:
($9605 /$25 000) x 100 = 38%.

It should be noted that there are changes in populations from one year to the next. If these population changes are substantial, differences in estimates might be caused by more the changes in population than changes in the variables themselves. There may also be differences in data quality between the two estimates being compared: final estimates are more reliable than preliminary estimates.