Hugh Osmond is an entrepreneur.

It is an indictment of the state of statistical rigour and numeracy in politics that a recent article by Ryan Bourne on this site about the wisdom of the Eat Out to Help Out scheme is gaining traction in some circles, without critical examination.

The thesis of the article is largely based upon one single chart produced in a recent Public Health England surveillance report, reproduced below, which shows events and activities reported by people testing positive, in the 2-7 days prior to symptom onset.

As we can see, a lot of people report that they had eaten out in the previous two to seven days, from which Bourne concludes that restaurants are a likely source of infection.

While a superficially attractive explanation, my O-level maths teacher would certainly have ejected me from the class for making this deduction without supporting evidence. So, before jumping to conclusions, here are a few important questions:

1. Given we know that approximately 50p out of every £1 spent on food in the UK is now spent eating out, is it surprising that 12,734 people out of 45,087 remembered going to a restaurant in the previous two to seven days? Does this fact therefore convey any information at all about where infection occurred?

2. Would this chart look any different for all the people who didn’t test positive that week? Or indeed from a cross section of the population of similar age and social profile to those who were tested?

3. Does this chart just represent a list of what you would expect a group of 45,000 people to remember doing in a week?

Without troubling the statisticians, I think we can answer a likely no to both parts of (1) and (2) and a very likely yes to (3). Which it makes it pretty much game over without further analysis.

But the article then goes on to make an even more egregious assertion. Faced with a chart showing that very few named contacts occurred in restaurants, it asserts: “But this is misleading. People don’t know strangers in restaurants to give them as named contacts.”

I confess I read this twice wondering if it was a joke. After all, we all know that restaurants are entirely full of people sitting on their own or randomly at tables with people they don’t know the names of. No, we don’t – I have been in the restaurant industry for more than 35 years, and can safely say I am confident that most people who visit restaurants sit at tables with people whose names they know – certainly by the end of the meal if not at the start. In fact, I would hazard that it is no more likely that you sit in a restaurant with people whose names you don’t know than you live in a house with unknown guests.

I am prepared to accept that, in a busy nightclub or stand up drinking pub, people get very close to strangers in poorly ventilated settings. But, in a sit-down restaurant with well-spaced tables and Covid-secure measures in place, I find the idea of mass infection by strangers from the table next door, facing the opposite direction, pretty hard to swallow.

The article gets worse as it next turns to the chart below:

Allegedly, this shows that incidents in restaurants grew significantly as a result of Eat Out to Help Out in weeks 32-35. (restaurants are the tiny purple bar). But if restaurants are a big source of infections, surely the big event would have been when they all reopened on July 4th? Or was the virus waiting to take advantage of Sunak’s special offer? After all EOHO added only maybe 10-20 per cent to sales, so one would expect to see the big surge after the grand industry reopening of pubs and restaurants on July 4th, followed by a small further blip up from week 32.

So, if restaurants are the problem, why can we barely even see the purple bar on the chart in the weeks following the grand reopening on 4th July?

No, all this actually shows is that, until restaurants reopened on July 4th, there were unsurprisingly no incidents in restaurants at all, and that, since reopening, a tiny percentage (three per cent – one in 30 – in the week shown) of incidents have been reported there.

“Significance” is entirely absent, as can be seen by comparing fluctuations in restaurant incidents with fluctuations in “other”. And why the fall in incidents in week 34, bang in the middle of EOHO, when you would expect to see the biggest effect? And why would these rise the week after EOHO ended and fall back in the following two weeks? In other words, total nonsense.

By contrast, as expected, what the chart actually shows (and all it shows in terms of significance) is that infections increased massively in care homes, educational settings and the workplace. Reprinted from the same report below of Acute Respiratory Incidents:

  • 772 new ARI incidents have been reported in week 38 (Figure 19).
  • 195 incidents were from care homes where 134 had at least one linked case that tested positive for SARS-CoV-2
  • 36 incidents were from hospitals where 31 had at least one linked case that tested posi- tive for SARS-CoV-2 and 1 tested positive for rhinovirus
  • 341 incidents were from educational settings where 222 had at least one linked case that tested positive for SARS-CoV-2
  • Six incidents were from prisons where 4 had at least one linked case that tested positive for SARS-CoV-2.
  • 124 incidents were from workplace settings where 102 had at least one linked case that tested positive for SARS-CoV-2.
  • 22 incidents were from food outlet/restaurant settings where 17 had at least one linked case that tested positive for SARS-CoV-2.
  • 48 incidents were from the other settings category where 22 had at least one linked case that tested positive for SARS-CoV-2.

Hmmm. 22 reported incidents in all food outlets and restaurants across the entire UK, out of 772 incidents in total; compared to 195 in care homes, 341 in schools and 124 in the work place. I mean, it’s obvious restaurants are a major source of infections according to the Government’s own report isn’t it? No. Actually, it shows that yet again, the major source of infections, and where they are by far the most dangerous, is in care homes.

In mathematical terms I could tell you that the statistical support for Bourne’s article’s hypothesis is zero. But that would be wrong: in fact, the statistical evidence points very strongly in entirely different directions.

Surprisingly to all of us in hospitality, there was absolutely no sign whatsoever of a rise in community infections following the reopening of pubs and restaurants on July the 4th; in fact, community infection rates continued to fall. I cannot explain this, but that’s what the data suggests. By contrast, the sudden jump in Week 37 is worst in care homes, then in educational settings and at work. Evidentially, this points the finger away from restaurants and instead at these other locations.

In other words, the data included with the article prove almost precisely the opposite to what was being suggested.

Finally (and it is not really necessary) I would mention actual transmission studies (as compared to theoretical contact tracing), most of which were conducted outside the UK, and which I don’t pretend are completely authoritative.

These indicate that secondary attack rates sitting a metre apart in a restaurant are around two to three per cent, compared to seven to 15 per cent (still low) in a household and potentially 60 per cent plus in a care home, hospital, ship or prison.

Although I do not have hard evidence for my next statement, I would suggest that, with social distancing and other Covid measures in place, this 1/50 chance of passing an infection on in a restaurant is now very much lower, further supporting all the other data suggesting that restaurants are not a common setting for infections.

In summary, the evidence and data all point the other way.