The ABS, however, has been commissioned to obtain “statistical information” about the opinion of the Australian adult public on the matter of same-sex marriage. It has not been commissioned to conduct a vote.

So it will not treat this like an election where you add up the votes and declare a winner. In effect, the ABS will be treating the “votes” or, more correctly, “survey answers”, as a great big sample of the whole population which must be corrected for sampling error, as all good statisticians do.

Usually, samples are quite a small. So for unemployment figures or household spending the ABS asks a few thousand and deduces the total picture from the sample. The ABS, like all pollsters, asks demographic questions – like age, gender and address. And if the sample does not match the general population (say the sample is 80 per cent male and 20 per cent female when in the whole population it is 50-50) it makes adjustments.

You might ask: “Should children get pocket money?” and get an overall result of 55 per cent No and 45 per cent Yes. However, if all of the 20 per cent female response was Yes and 55 percentage points of the 80 per cent male response was No (68 per cent of males answering No), the No victory is clearly suspect.

The statistical adjustment is to say that the 20 per cent female vote should account for 50 per cent of the total actual opinion and the 80 per cent male vote account for the other 50 per cent of total actual opinion. This would mean an accurate expression of the population’s opinion approving pocket money would be all 50 per cent of female opinion plus 32 per cent of the 50 per cent male opinion, or 16 percentage points, totally 66 per cent Yes. That equals a decisive 66-34 per cent Yes to pocket money even though the raw figures suggest a 55-45 victory to the No vote.

When the ABS collects age data from the marriage plebiscite it is likely that the youth vote will record a low turnout because the postal process is alien to them, and the older vote will be higher because they are familiar with it.

So the ABS will make a correction along the lines of our male-female example. The crunch is that the correction is likely to be much more pronounced than perhaps the statistician and commentators hitherto have imagined. This is because of the following effect.

It is very likely that the sort of young person who votes is very determined to express a Yes and the young people who do not vote are either indifferent or more tending to No. On the other hand, the sort of older people who vote are more likely to be determined No voters.

When the correction is done the assumption will be that those who did not vote in a particular age group have, overall, the same percentage of people who think Yes or No as those who did vote in that age group.

That assumption may be fine for things like household spending and unemployment but it is extremely suspect in gathering hotly contested moral opinions. It is much more likely that those who vote will have strongly held opinions and be different from the non-voters in their respective age groups. The young people who bother to vote will be more in favour of Yes than young people who do not vote. Conversely, older people who vote will be more likely to favour No than older people who do not vote.

The upshot is likely to be that when the votes cast (which the ABS views as a sample of the whole population) are adjusted for age, the adjustment will favour the Yes vote by too much.

It means that the possibility of a majority No in votes cast but a Yes result in the adjusted result is higher than you might think.

It would be a terrible result for Prime Minister Malcolm Turnbull. He would have blown $120 million to get this issue off the table only to have an inconclusive No actual vote and a Yes adjusted vote – a problem that would not arise with an electoral commission vote because there would be no gathering of demographic data and adjustment for it.

It will be hugely embarrassing because the Government concocted this “gathering statistical information” exercise to avoid the constitutional and legal challenges of an unlegislated full-scale compulsory vote conducted by the Australian Electoral Commission. It saw an existing legislative base in a ministerial directive to the ABS.

But the ABS must provide “statistical information”. So it must adjust the sample for the whole. Otherwise it is not “statistical information” under the Act. And maybe that is why the statistician (an independent statutory officer) has decided to collect the age, gender and geographic information and make the adjustment.

Incidentally, the adjustment process is quite mathematically precise. You look at the age break-up of voters. You compare it with the age break-up of the population as a whole. And adjust accordingly. If 18 to 25 year-olds are 10 per cent of the adult population and only 5 per cent of them vote, the adjustment is to double the weight of their votes.

It may well be that the gathering of information about moral opinion is not statistical information anyway, and that could be the subject of a legal challenge arguing that the Treasurer’s directive was beyond statutory power.

www.crispinhull.com.au

Thoughts? Let them know in the comments below.

* Readers are encouraged to use their full details below to ensure comment legitimacy. Comments are the opinions of readers and do not represent the views of Newsport or its staff. Comments containing unlawful, obscene, defamatory or abusive material will not be published.