Oz Politics Blog

The sealed section in today’s Crikey included the following analysis:

7.4% of Bennelong voters who supported the PM in 2004 say they intend to back the ALP at the next federal election. If this figure stays the same between now and the poll, these people will deliver around twice the swing needed to lose Bennelong and will put the PM put out to pasture.

The Crikey Morgan Poll taken last week has identified exactly where the sands are shifting. IR is the killer. Out of the shifting 7.4%:

• 59% (all Bennelong electors 38%) think Mr Howard should retire before the next Federal Election compared to 34% (all Bennelong electors 55%) who think he should contest the election.
• 83% (all Bennelong electors 59%) disagree with the Government’s industrial relations reforms compared to 10% who agree (all Bennelong electors 26%).
• 73% (all Bennelong electors 49%) think Kevin Rudd would make a better Prime Minister than John Howard (23% compared to 47% of all Bennelong electors).
• 87% (all Bennelong electors 75%) approve of the way Mr Rudd is handling his job as Opposition Leader compared to 7% (all Bennelong electors 11%) who disapprove.
• 38% (all Bennelong electors 47%) disapprove of the way Mr Howard is handling his job as Prime Minister compared to 45% (all Bennelong electors 44%) who approve.
• 56% (all Bennelong electors 38%) think the ALP will win the next Federal election compared to 40% (all Bennelong electors 46%) who think the Coalition will win.
• 87% (all Bennelong electors 51%) would like the ALP to win the next Federal election compared to 7% (all Bennelong electors 40%) who would like the Coalition to win.
• 67% (all Bennelong electors 62%) think the Government should ask the American Government for David Hicks’ immediate return to Australia compared to 33% (all Bennelong electors 31%) who think Hicks should remain in US custody to face trial.
• 27% (all Bennelong electors 29%) think Australian forces should continue to fight in Iraq compared to 66% (all Bennelong electors 64%) who say Australian troops should be returned home.

Oh dear! Where to begin?

7.4 per cent of 394 people (the total sample), suggests the shifting voter element of these comparisons was based on a sample of 29 people. I am not comfortable with comparative statistics based on such small sample sizes.

Statistical theory depends on the central limit theorem (CLT). With small sample sizes (N less than 30), the central limit theorem cannot be assumed to apply, and reliable population estimates cannot be calculated. Because the CLT may not apply, we cannot assume that sample means would be normally distributed around the population mean, nor can we estimate the standard deviation (σ) of a population from the standard deviation (s) of the sample.

If we assume the sample size was not a problem, the 95% confidence interval (at 50-50 per cent) is around +/- 19 per cent (using the t-statistic). Many of the above differences are not statistically significant.

I found the comparison of shifting voters to all voters problematic, as the sample mean for all voters comprises a number of distinct and different voter groups (e.g. Liberal and Labor voters). The total population means are also affected by the shifting voters with whom we wish to make a comparison. Were the sample size sufficient, I would have been more interested in the individual comparisons of the shifting voter group with both the long term Liberal and Labor voter groups.

Finally, that old maxim applies: correlation is not causation.

Let there be no confusion: I am not arguing against the proposition that IR will be the killer issue in the next election. All I am saying is that these statistics do not provide a sound basis to come to that conclusion. I would classify these statistics as interesting, worthy of further investigation, but not a compelling argument that IR will be the killer issue in the next election. Hopefully a polling organisation will undertake a more robust analysis of this issue in the near future. The Government may well have an insurmountable problem if that more robust analysis confirms these findings.