Labour is definately obsessed with death and killing.

Just to bore you to death Graeme, one mile is 1760 yards, 5280 feet or 1610 metres. A pound is 16 ounces, and there are 14 pounds in 1 stone. A stone is 6.35kg and kilogram is 2.2lbs roughly. To convert Fahrenheit into Celsius, subract 32 from the degrees Fahrenheit and then multiply by 0.56 OR to convert Celsius to Fahrenheit multiply the Celsius by 1.8 then add 32. I learnt it in maths at a grammar school :-)

Have fun on the rest of your trip.

This, dear readers, is the very same Graeme Archer who recently took me to the London Fields Lido one late summer afternoon, where he encouraged me to join him in his usual ONE MILE swim. We then joined friends to drinks CUPS of coffee and BOTTLES of red wine. He knows!

Whilst you are in Blackpool I do hope you will take a stroll down the Golden 1.6 kilometres.

Highly entertaining as ever....

Graeme, I seem to recall reading an analysis you did of polling methodology some time back. The general approach was (I think but cannot be sure) to set out why different pollsters could not be compared and why, from a stats perspective, taking averages was meaningless. Do you have that posting somewhere to hand by any chance? If so, I'd be very interested to see it again.

(PS Sorry to ask such a dull question - your writing does inspire more interesting ones do not fear. It's just that I've been meaning to ask you for a copy of that posting for ages, that was all.)

Hello "support the strivers". I don't know where that post went, but I'll try and resummarise. It's a bit stats-y. For simplicity, consider the objective of using a poll to estimate the true support for the Conservatives.

Call the true level of support T.

Now, if any opinion pollster sampled completely at random - say they selected 1000 voters completely at random from the entire electorate - they would get an estimate - call it t - of T. t would not be equal to T, because it would be based on a sample and not the entire population.

Statistiicans write: t = T + e, where e is a random variable with zero mean and a variance - a standard deviation - which is a function of the size of the sample.

If the total number of electors is N and the random sample is based on n, then with probability 1 t -> T as n -> N.

If two pollsters produced estimates of Tory support in this way, giving unbiased estimates of tory support t1 and t2, say, then it would be completely admissable to construct a BETTER estimator of Tory support by averaging t1 and t2. Call this t3. Since t1 and t2 are unbiased, then so is t3, and it also has smaller variance. Thus it is a better estimator of T than either t1 or t2.

HOWEVER.

No opinion pollster produces an unbiased estimator of T, because none of them sample completely at random. This is a good thing, because to sample at random and get reasonable standard errors would require much larger polls than are carried out (the tradeoff between bias and variability is one of the fundamental mathematical theorems in classical statistical estimation theory).

So they deliberate introduce some bias into their sample. So a statistician might write the estimate t* from the biased poll as

t* = t + b + e

t and e are the same as above, but b is a systematic bias (I'm simplifying - any other statisticians reading - I would write b as the sum of a fixed and random effect term, with its own variance - but for simplicity am shoving that into e).

What this means is that as n -> N, we no longer have that t* -> T. Instead t* -> T + b. So no matter how many averages you take of this pollster's poll, you will not remove the systematic bias built into its construction.

The situation is, of course, worse if one does the following - as ConHome does, every bloody week - add together the estimates from different pollsters, all of whom use different methodologies and who therefore have different systematic bias terms in their estimates. Consider two pollsters giving t1* and t2* estimates of tory support. Using the same model as above, if you average t1* and t2* you get T + .5*(b1 + b2) as the expectation - i.e. a biased estimate, the bias of which we have no way of understanding.

So the manner by which ConHome constructs its poll of polls is flawed, misleading, biased and statistically degenerate. If an undergraduate statistician suggested it to his/her tutor, they would be marked down.

BUT. If we have two consecutive polls from the first pollster: t*1 and t*2 - and we assume - as I think is sensible - that the systematic bias in the same pollster's monthly polls does not change - then if we construct the DIFFERENCE between the two months we get:

t*1 - t*2 = T1 + b - T2 -b +e - e = T1- T2

In other words, the difference between consecutive polls from the same pollster is an UNBIASED (statistically sensible) estimate of the change in Tory support from month 1 to month 2.

If you did this for TWO pollsters you would have TWO unbiased estimates - and if you averaged these you would get, as we saw right back at the start, an ever better estimator (still unbiased but higher precision) than any individual one.

So the Conservative Home recipe should be as follows:

For each pollster, calculate the within-poll differnece in Tory support NOW and (say) 1 month ago.

Take the average between-poll of these differences.

This average would be an unbiased and highly precise estimate of the true CHANGE in Tory support over the last month.

cheers and cheers to Simon who is also a magnificent swimmer :-0)

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