Same day, two different polls. Last Tuesday, The Australian looked at the previous weekend's Newspoll and declared: "No budget rebound for Crean." Fairfax waved the ACNielsen survey around and pronounced the opposite: "Poll results put a spring in Crean's step" (The Age), and "Slap for PM's plans gives Crean a lift" (Sydney Morning Herald).

So which was correct?

They differed in three ways. First, in questions asked. ACNielsen found 77 per cent of respondents willing to forgo tax cuts for better services, 38 per cent favouring Simon Crean's health policies over John Howard's (29 per cent liked Howard's more), and 72 per cent opposed to the government's higher-education reforms.

Of Newspoll respondents, 43 per cent judged the budget good for the economy, and 21 per cent did not. Just 27 per cent thought Labor would have delivered a better budget, 51 per cent did not.

So one set flattered the government and the other didn't, but neither contradicted the other.

Second, some almost identical questions returned different results. ACNielsen and Newspoll put Crean's satisfaction ratings at 30 per cent and 24 per cent respectively (both gave Howard 61 per cent) and their preferred PM numbers favoured Howard 61 to 23 and 64 to 17. Most importantly, on voting intentions, ACNielsen found 51 to 49 two-party preferred in the governments favour, a two point shift to Labor, while Newspoll had it stuck on 54 to 46.

There is a small if to this. ACNielsen measures both primary and two-party preferred, while Newspoll gets only primary support and notionally distributes, as the minor party and independent preferences flowed at the last election. But it does so in aggregate, without differentiating between, say, a Green and One Nation vote. This overstates the Coalition's lead, by (and this is complicated by rounding) two points in about every second poll.

Still, even 53 to 47 would be a landslide and 51 to 49 a modest win, so which is correct?

Well, statistically they're both OK. Put simply, surveys of that size have about a 2.5 per cent error margin with a 95 per cent confidence level. That means 19 times out of 20 their result is within 2.5 per cent of the correct figure for the Australian voting population. So when ACNielsen finds 51 per cent Coalition support, it means it is between 48.5 per cent and 53.5 per cent. Probably. There is one chance in twenty that it isn't.

The pollsters know their craft's parameters and were unfussed this week. To them the polls said the same thing. But the papers interpret the figures literally. And news organisations are human concoctions, with cultures and biases. Statistics need colour and minimum equivocation. Writers favour the rhetorical brush. 

We might guess that when the data arrived, journalists went straight for voting intentions, skimmed over the rest and set the story in stone. Everything, including the numbers, then became subservient. Cue the screaming headlines.

They did us a favour on Tuesday, by illustrating the limitations of political opinion polling.

Peter Brent is editor of mumble.com.au, a website that looks at electoral behaviour.