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There is a strong possibility of a major debacle over the result of the marriage-equality plebiscite in November. My colleague Peter Martin explained this week that the Australian Statistician has injected some statistical rigour into the process. The Statistician, David Kalisch, argues that the ABS is within the normal process of gathering "statistical information", in the words of the Census and Statistics Act, to inform public policy. The ABS is going to engage in a unique process. Never before has information on the age, gender and geographical location of voters been gathered and counted so it can be compared with that of the general population (as known through the census) and hence that of people who did not vote. In the counting process, the actual Yes or No vote will be stripped away and anonymously counted with all the other votes in that electorate, but the envelope containing the ballot with a bar code that contains information about age, gender and electorate will be kept and collated. This process is different from that of the Australian Electoral Commission. The electoral commission process is solely to determine who is elected – who got a majority of votes cast after distribution of preferences. The electoral commission does not consider whether a whole lot of people spoilt their ballot papers or did not turn up to vote and try to estimate that opinion to give a more accurate overall picture. 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. Alas, the ABS will not be correcting the "Yes" and "No", as all good statisticians do, because the ministerial direction telling the ABS to do the survey does not allow for that. But that does not mean that others cannot attempt a correction using opinion polling data that break up age and gender with "Yes" and "No" vote. 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. It is a pity that the ABS is not doing this when it 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. But others will no doubt do the adjustment, especially is the exercise results in more No surveys than Yes surveys. Even so, the largely statistically illiterate masses will still call it a No win. For that reason it is imperative that whatever one thinks of the "plebiscite" exercise, it is important for those in favour of Yes to make the effort and engage in the survey. The possibility of a majority No in votes cast but a Yes result when properly adjusted result is real. It will legitimately give rise to calls of "we was robbed" and give every reason for a future government to ignore the result. 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 vote. 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 used that directive in a political way to prevent a rigorous gathering of statistical information. crispinhull.com.au Correction: An earlier version of this article said the ABS would be adjusting the figures it gathered on the marriage survey to correct for sampling bias. This is not correct and the article has been updated.

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