The Economist (2022-02-26) Riva

TheEconomistFebruary26th 2022

GraphicdetailFishycovid-19data

85

More equal than

others

S

ometimesthenumbersaresimplytoo

tidy to be believed. Irregular statistical

variation has proven a powerful forensic

tool for detecting possible fraud in aca-

demic research, accounting statements

and election tallies. Now similar tech-

niques are helping to find a new subgenre

of faked numbers: covid-19 death tolls.

That is the conclusion of a new study to

be published in Significance, a statistics

magazine, by the researcher Dmitry Kobak.

Mr Kobak has a penchant for such stud-

ies—he previously demonstrated fraud in

Russian elections based on anomalous tal-

lies from polling stations. His latest study

examines how reported death tolls vary

overtime. He finds that this variance is

suspiciously low in a clutch of countries—

almost exclusively those without a func-

tioning democracy or a free press.

Mr Kobak uses atestbasedonthe“Pois-

son distribution”. This is named after a

French statistician who first noticed that

when modelling certain kinds of counts,

such as the number of people who enter a

railway station in an hour, the distribution

takes on a specific shape with one mathe-

matically pleasing property: the mean of

the distribution is equal to its variance.

This idea can be useful in modelling the

number of covid deaths, but requires one

extension. Unlike a typical Poisson pro-

cess, the number of people who die of

covidcan be correlated from one day to the

next—superspreader events, for example,

lead to spikes in deaths. As a result, the dis-

tribution of deaths should be what statisti-

cians call “overdispersed”—the variance

should be greater than the mean. Jonas

Schöley, a demographer not involved with

Mr Kobak’s research, says he has never in

his career encountered death tallies that

would fail this test.

That should make it easy to pass. And

the vast majority of countries reporting

datato the World Health Organisation do.

This does not mean that their death tallies

were necessarily accurate—undercount-

ing still plagues many countries with in-

sufficienttesting(whichiswhyTheEcono-

mistestimates the pandemic’s death toll

using excess deaths). But it does suggest

that the numbers reported are not being

deliberately tampered with.

Yet data from 17 countries had the oppo-

site pattern. In many weeks, the variance

of each distribution was less than the

mean. This is a statistical smoking gun. “It

seems reasonable to conclude that there’s

no way these are independent observa-

tions,” says David Steinsaltz, a professor of

statistics at the University of Oxford.

Imputing motives is harder. A benign

explanation would be bureaucratic bottle-

necks in processing death certificates. Yet

there are other irregularities: the usual

drop-off in weekend reporting is often ab-

sent. According to Mr Kobak, the likelier

explanation is cackhanded tampering.

The Russian numbers offer an example

of abnormal neatness. In August 2021

dailydeath tallies went no lower than 746

and no higher than 799. Russia’s invariant

numbers continued into the first week of

September, ranging from 792 to 799. A

back-of-the-envelope calculation shows

that such a low-variation week would

occurby chance once every 2,747 years.

Abnormal tallies suggest some

countries reported false covid-19 data

→ Reported covid-19 death tallies have an expected amount of variance. But in some countries, variance is abnormally low

New confirmed covid- deaths per million people

*Lessthan%ofexpectedvariationSources:“Underdispersioninthereportedcovid-9caseand death

numbersmaysuggestdatamanipulations”,byD.Kobak,workingpaper,;OurWorldinData;JHU CSSE

Mar

Apr May Jun Jul Aug Sep Oct Nov Dec Jan

Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan

0

5

10

15

20

Brazil

United

States

Russia

Turkey

Genuine death counts vary

from day to day, as people

do not fall ill uniformly

Recent data from Russia are

also suspiciously smooth

Turkish data during the first

year of the pandemic have a

dubious lack of variation

60

65

86

86

29

79

81

67

54

26

28

92

90

69

58

62

80

% abnormal

↓

Mongolia

Cambodia

Russia

Lebanon

Turkey

Albania

Uzbekistan

Algeria

Kyrgyzstan

Syria

Egypt

Venezuela

ElSalvador

Azerbaijan

Belarus

Serbia

Saudi Arabia

Very low*

Weeks with normal variation

Weeks with abnormally low variation