Sir, – Your report on the opinion poll evidence regarding the Fine Gael leadership race (March 4th) states that “the results give Mr Coveney a small lead over his presumed rival”. Your editorial on the same day put it more strongly: “Probably the most significant finding of all is that Mr Coveney is five points ahead among Fine Gael supporters”. In fact, no such finding can be justified based on your poll data.
It is true that the difference of 5 per cent between the sample percentages of Fine Gael voters of 49 per cent for Mr Coveney and 44 per cent for Mr Varadkar would be regarded as statistically significant if they were based on the full sample of 1,200, where a “margin of error” of plus or minus 3 per cent for individual percentages is typically assumed.
In fact, the margin of error for a difference between two percentages based on a sample of 1,200 is bigger than that, around plus or minus 5.5 per cent. This would mean that the observed difference of 5 per cent is just on the border of statistical significance according to the usual convention.
However, a critical point in this case is that the two percentages quoted are based on a much smaller sample, that of the Fine Gael voters, amounting to 28 per cent of 1,200, or 336. Based on this much smaller sample size, the margin of error works out at around plus or minus 10.5 per cent so it is impossible to say that the observed difference is anything other than sampling error.
This argument applies equally well to the detailed breakdowns shown under the heading “Simon v Leo head-to-head breakdown”, making this table less than meaningful as well as undermining your further editorial commentary based on these breakdowns. – Yours, etc,
Dr MICHAEL STUART,
Department of Statistics ,
Trinity College Dublin,
Dublin 2.