Graeme Archer is a statistician and a former winner of the Orwell Prize for Political Blogging.

I must know the weight of the potato. I promised the editor 800 words on what the potato’s weight means. There are 86 days of copy about the weight of potatoes to fill.

So I go to the kitchen, stick my hand under the sink, find the bag where the tubers sleep, and pull a potato out, at random. (I know better than to select it according to my own prejudice!)

The scales are two drawers down from the cutlery. Press the on-button: these e-scales are our pride and joy – £55 quid they cost, Scales-R-us. Place the potato on the tray, and carefully don’t ask it any leading questions.

There was a time when no-one really cared how much potatoes weighed … so I’m told, anyway. Back then, apparently, people cared about the taste of the whole meal. “Taste”: too close to the taboo concept of “judgement.” The scales are beeping.

290 grams.

To the laptop; start tapping.

– – – – – – – – – –

Barnet was alight today at news that the potato now weighs 290 grams. This is an overnight decrease of 5g, with calorific implication [add something later]. Asked to comment on the figures…

Who should I ask? My friend Sandy is a potato-nerd; they made a film about him. He’s online. I ping him.

“Hi Sandy.”

Hi Graeme. What are you doing?”

“Writing about potatoes. Today the potato weighed 290g.”

“5g change from yesterday? Amazing!”

“I know! I just wondered how it made you feel…? Sandy?”

“It’s just I’m wondering if you’d thought about measurement error? You know the scales aren’t 100 per cent accurate? So maybe you should weigh the potato 10 times, and take the average? To reduce the error.”

“That’s a great idea, mate!”

“And I’ve just realised, now that scales are so cheap, I could get my own set, and make my own measurement.”

“Sounds good. Better get on. This copy doesn’t write itself.”

Barnet was alight today at the latest potato news. Commentator Sandy Jenkins said “This changes everything; all Barnet will be holding its breath until tomorrow’s measurements arrive, to see if this is a one-off, or a long-term (two-day) trend.”

Tomorrow is another day…

– – – – – – – – – –

291g. And that’s –

” – An average of 10 measurements. I weighed the potato ten times, and took the average, so I’m even more certain now that the potato weighs less than 295g, Sandy.”

“Well done mate. I did the same with my new scales. I got 293g. Actually, I pulled out ten separate potatoes…”

“Did you replace them between each weighing?”

“Uh, no!”

“Well, what we should do… no-one’s thought of this before… we should take the average of our two values, since if each estimate is a lower-error average, then the average of the two — that’s got to be the best estimate of the weight of the potato that’s ever been seen?”

“292g! Get writing!”

“What scales did you go for, by the way?”

“The Weightotron. It weighs rice, too. Dunno though. It’s a whole other kettle of fish, that rice.”

– – – – – – – – – –

Stop press.

The man in charge of ordering veg was increasingly isolated last night, as his claims of economic competence were called into question by a significant drop in potato size, re-opening back-bench divisions over his approach to potato markets. “Foreign seeds have done this,” shrieked Hilary Froth, the (male) member for England South.

The figures provided  much-needed breathing space for Opposition leader Dave Rubberband, whose comments on predatory potatoes had led to calls for his head only yesterday, when everyone thought potatoes were getting heavier. “Now we know they are getting smaller, this is the sea-change that British politics has been crying out for,” shouted Diane Shout, MP for England North, in Greek.

Kiosk H et al. Measurement Error in Household Scales (2015) Annals of Measuring Things, Vol 4, No.2, 1021-1025.

While our tests showed that, as expected, no household scales were free of bias, we did find a wide range of variation in that bias. At the top of the range, Scales-R-us were found to under-estimate the weight of potatoes by an average of 3g, while at the other end, the Weightotron showed a negative bias of 4g.

– – – – – – – – – –

We recognise that abstruse academic deliberations about the difference between random variation and non-random (no machine for measurement is perfect) bias are unlikely to set the popular press alight. But the increasingly common approach of that press, to publish the average weight of potatoes measured across a range of different kitchen implements, seems to rely on an unconscious application to the law of large numbers; an unspoken assumption that by taking the average of different systems, only an increase in the precision by which the potato’s weight is estimated will be achieved.

But the averaging of two estimates, each of which has a different systematic bias, cannot produce an estimate of the truth which is free from that bias – except in the unlikely case that the biases are of equal magnitude but opposite direction, or if they randomly fluctuate around zero (in which case they are, by definition, not bias.) No statistical law of average will reduce that bias to zero “in the limit.”

In the rest of our article, we illustrate our important points by using a “toy” example. Since the weight of the potato is so contentious, we thought to increase the clarity of our exposition by shifting the reader’s attention to something of vanishing importance…

– – – – – – – – – –

Thus we will consider the case of opinion polls of voting intention, about which hardly anyone is interested.

Suppose one pollster produces an estimate of Conservative support of 35 per cent, while another records a figure of 31 per cent…” [Ct, p.94]