Today saw the release of what, at first glance, seem promising improvements in employment in Australia.

The headlines are saying that unemployment has dropped from 6.2% to 5.9%. Supposedly 58,600 jobs were created in October, 40,000 of them full time, with monthly hours worked increasing by 19.1 million hours.

Those are, of course, the seasonally adjusted estimates, which are subject to a great deal of volatility. Trend estimates are considered the best indicators of the underlying behaviour in the labour market.

If we refer to the trend estimates we get a slightly different story which shows the unemployment rate remaining steady at 6.1% with 18,800 jobs created and monthly hours worked increasing by 5.7 million hours.

Since October 2014, trend employment has increased by 260,500 persons, while the civilian population aged 15 years and over grew by 288,200 persons over the same period, so job growth has fallen short of population growth by some 27,700.

The Labour Force Survey is based on a sample of about 26,000 dwellings and covers approximately 0.32% of the civilian population of Australia aged 15 years and over. Extrapolating from these figures is therefore subject to sampling variability.

The ABS acknowledges this and publishes, under the heading sampling error, a 95% confidence interval ie there is a 95% chance that the true value of the estimate lies within that interval. These figures highlight just how wrong the headline figures could be.

We can be 95% sure that employment went up by somewhere between 400 and 116,800 in October. That’s a hell of a range, 58,600 +/- 58,200, and there’s a 5% chance that the real figure lies outside even that very large spread.

Likewise for the number of unemployed people. We can be 95% sure that it ranged anywhere from decreasing by 71,600 during that month to increasing by 4,800: 33,400 +/- 38,200. The unemployment rate could be anywhere between 5.5% and 6.3%.

So when you see Scott Morrison and Michaelia Cash preening at the various press conferences today, keep in mind that these figures are likely statistical noise with trend figures presenting a different picture. I hope the trend will eventually bear out these improvements but I certainly wouldn’t put money on it.