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22 August 2020

Innumeracy

Tag(s): Foreign Affairs, Politics & Economics, Pedantry
One constant in all the many crises that seem to be happening at the same time is that the politicians, civil servants, and the media seem incapable of understanding the numbers that lie behind them. In the catastrophe of the A-level grading it has emerged that the Royal Statistical Society (RSS) offered Ofqual, the exam regulator,   help with developing the methodology of estimating the grades. Ofqual was willing to offer two places in its project team only on condition that RSS signed a non-disclosure agreement not to publicly discuss the matter for many years. RSS was willing to avoid giving a running commentary on the matter but for reasons of integrity would not bind their hands for such a long time. The beleaguered Secretary of State for Education Gavin Williamson, at least at the time of writing, has conspicuously declined to take responsibility for the shambles and in the process has severely damaged the reputation not only of himself but of his party and government. Once it was decided that the exams could not take place, a fateful and probably unnecessary decision, Williamson set Ofqual the reasonable objective that he did not want to see grade inflation. As a result of the shambles grade inflation has been the largest on record with over one third of students now receiving an A* or an A Grade. For many years there was significant grade inflation. Not so long ago only 10% of students got an A* or an A grade. That proportion has climbed steadily over the years to over a quarter. When Michael Gove was Secretary of State he set out a strategy to hold this back which has been largely successful. Not now.

Now that the teachers’ predictions have been taken as the basis for grades the grade inflation is enormous. While teachers no doubt have many skills their ability to predict the future is no greater than that of any of us. There are so many other factors that influence the result of an examination at the individual level, not just the work that the teachers themselves see but also all sorts of other issues in the lives, the behaviour and the minds of the students. This is not just about an inability to predict the future with great accuracy but the fact that on average teachers  by a significant margin predict a better grade than is actually achieved. Now that that is the result following a whole series of U-turns and it would seem arguments between the Secretary of State and Ofqual to whom it reports, it means that the grades of this year’s A-level student students will always be held in doubt. This has been a very unfortunate process but the universities are now taking more students who apparently have met their offers than they would normally expect. There are various caps on some disciplines and some students are being offered places in next year’s intake. But that will not be fair on the class of 2021. So not only is this terrible affair scarring this year’s crop of graduates but also next year’s.

Of course, this awful experience has arisen as a result of the pandemic. In order to manage the health crisis there needs to be a good understanding of the statistical basis for decisions. In the UK this has simply not been the case. In the last few weeks the government has adopted a policy of distinguishing different countries depending on the number of cases that they are encountering per 100,000 over a 14 day period and the arbitrary figure of 20 has been chosen as the cut off.  Above this figure a country leaves the green zone and people arriving from those countries must self-quarantine for 14 days. There is no particular scientific evidence as to why 20 is a particularly high or particularly low number but the consequence of these decisions is a hammer blow to the travel industry in general and indeed even to the economies of neighbouring nations that we traditionally at least have regarded as friendly.
But not only is this a completely inappropriate methodology, it is also measuring the wrong thing. While we are still a long way from fully understanding this coronavirus what we do know is that it is only likely to be fatal to the elderly and to those who have a number of pre-existing health conditions such as obesity, diabetes and high cholesterol. A more salient measure of what is happening in a region or country is not the number of new cases but the number of new hospitalisations and then the number of those who die. In Leicester the number of new cases did rise as a direct result of an increase in the number of tests carried out because of greater testing capacity and particularly among the young. But the number of hospitalisations actually declined as did the number of deaths. And yet the national authorities reacted with their usual hysterical mode of operation and ordered the local authorities in Leicester to conduct a new form of lockdown.

Over the past few months the number of deaths from influenza and pneumonia in the UK has exceeded the number of deaths from Covid-19 by a factor of six. I repeat, six times as many people in the UK have died over the last few months from the normal influenza and pneumonia that exist in this country than have died from the new Covid-19. But actually even that is not an accurate record of what is the statistical significance of this difference. A great many people in the UK are inoculated against influenza as indeed am I, and therefore the significance of the number of deaths from influenza and pneumonia during this period is greater than a factor of six because many fewer people are at risk. Between 70% and 75% of people over 65 take the vaccine each year, one of the highest rates of immunisation in the world.

In comparing the number of cases between countries the majority of commentators, newsreaders and indeed politicians when it suits them, fail to adjust their comparisons for the number of population. Admittedly in the rules over quarantine the UK government does adjust by population but when countries are described it is usually the gross number that is used and so there are repeated stories in all the media that the United States is the worst affected country in the world for the number of cases. What they mean is that the United States to date has reported a higher number of cases than any other country but the United States has one of the highest populations in the world. So you would expect it to have one of the highest numbers of cases of a pandemic that is clearly global in reach. if the number of cases is correctly reported for each country, which of course is not the case, even on those public statistics then the country with the highest number of deaths per million is Belgium with a significantly higher rate than the United States . So the correct headline would be that Belgium is the worst affected country in the world for the number of cases.

President Trump knows this but in his defence of the United States he makes such ridiculous assertions that no independent person would give him any credibility. Rather than simply pointing out that the United States does not have the highest rate of infection reported in the world but it does have one of the highest you would be much more credible. New Zealand has had one of the very best records in the world owing to an earlier and more disciplined lockdown than the majority of countries. There has recently been an increase in the number of cases for the first time after several months of reporting no new cases. President Trump reported this as a “major surge in cases in New Zealand”. The actual number of new cases that have been reported is 48. The US daily average is around 40,000.

These false comparisons also occur in the reporting of economics. Even well-qualified journalists often seem to get this one wrong. I read an excellent weekly publication called Money Week which gives a fairly steady view of what is happening in finances, both public and private, around the world. I like most of its journalism and most of its style. I wish they wouldn’t keep pushing gold as an investment. Obviously at the present time the price of gold has gone up enormously and may go up further but the problem with gold is it has no productive benefit either to the individual in the form of income or to the economy in the form of production. Thus an investment in gold is actually a disinvestment in the economy.

Recently Money Week reported on a subject close to my heart, that is the dominance of the technology giants and whether they should be broken up. There are arguments for and against but here is my complaint.  I quote “Jeff Bezos of Amazon, Tim Cook of Apple, Sundar Pichai of Google and Mark Zuckerberg of Facebook, whose four companies have a combined market capitalisation of around $5 trillion-roughly equivalent to the GDP of Japan.” This is an ignorant comparison. To compare the market capitalisation of a company to the GDP of a country is comparing not just apples and pears but apples and potatoes. The market valuation of the company tells us at any one time what investors believe is the worth of that company in terms of its ability to produce future revenues, income and dividends. It is also a function of a market in which there are buyers and sellers so at any one time it is simply not telling us a snapshot of what the company is actually worth because the share price may not genuinely reflect the true value of the company. The GDP of a country is a quite different animal, vegetable or mineral. It tells us in a very imperfect way the value of what that country has produced in one year. If we were to attempt to measure what the country of Japan might be worth in market value, which would be the sum of its geographical property, it’s physical infrastructure, its intangible assets and its people’s ability to generate income and wealth then the total would be many hundreds, even thousands of trillions of dollars.

But as I have observed on these pages before GDP is a very imperfect measure of a nation’s income. In the second quarter of this year the GDP of the UK economy fell by over 20%, the largest such fall in recorded history. We are told that this took the economy back to its level in 2003. That is simply looking at the total and it is not adjusting for population, back to the problem at the beginning of this blog. Back in 2003 the population of the UK was 59.5 million. In 2020 it is estimated to be 67.9 million, a growth of 14%. So we would have to go much further back than2003 to find an equivalent GDP per capita.

Further this means that technically the UK is now in recession, as the recession is defined as two consecutive quarters of negative growth. There is a problem with this. The impact of the pandemic has been so dramatic that the economy is likely to be deeply scarred for some considerable time. However, continuing to measure it by quarter it is probable that there will be some slight growth on a comparative basis in the coming quarters which means that technically we will emerge from recession quite soon but the economy will still be very considerably smaller than it was before. The politicians and civil servants and journalists will struggle to explain all this until they can get their heads round the statistics that underpin all this activity. Maybe a crash course in statistics is needed. But then they’ve given us a crash course in crashes.



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