The size of a self-selecting sample is often unimportant.

Richard Tice, the Reform party leader, asserted on Twitter:

FASCINATING: huge poll, totally at odds with YouGov ( Govt propaganda arm) that says 71% favour them. Is YouGov so discredited it’s better to believe the opposite of many of their polls?

Twit me baby one more time.

The cited YouGov survey had a different subject (nightclubs) and wording:

Would you support or oppose people being required to show they have received both doses of the Covid-19 vaccine as a condition of entry into nightclubs?

To reiterate: self-selecting surveys are not reliable ways to measure public opinion.

A self-selecting survey means…


Exploring a paradox of high vaccine coverage.

In the Washington Post, columnist Kate Cohen argues for two regular statistics:

I propose a running tally in bold type: covid deaths among unvaccinated vs vaccinated citizens. Two numbers, side by side.

This proposal may sound simple. Many public health analyses demonstrate effectiveness of approved Covid-19 vaccines against infection and hospitalisation. In a population without high coverage, most deaths from a disease will be among those not vaccinated.

Survival analysis suggests high effectiveness against hospital admission. (Image: Public Health England)

When coverage widens, immunisation failures can outnumber unvaccinated outcomes. There are numerous explanations of this phenomenon, including in my co-written column in The Observer.

Going forwards in the calculation

One way is to take the reader through…


I reflect on my third year as an RSS Statistical Ambassador.

Back in June 2018, the Royal Statistical Society chose me as one of their Statistical Ambassadors. The purpose is to help journalists, policy-makers, researchers, and the public understand statistics.

Third Year

This article looks at my third year as a Statistical Ambassador.

Statistics of the Year, with quality information

I helped with the RSS 2020 Statistics of the Year. I checked the submitted figures. As part of that work, I wrote quality and methodology information for each main entry.

Helping journalists during the pandemic

The Covid-19 pandemic persists. After the third national lockdown in England, the Huffington Post had a quote from me about case numbers.

I also helped the Press Association check statistics…


What do ‘numbers dying between exact ages’ mean in life tables?

Life tables are an important demographic tool. These tables help actuaries and others analyse death rates and life expectancy.

How do analysts calculate national life tables?

Step 1: The analyst starts with 100,000 simultaneous births in one country, and of one sex. (This is often denoted l₀.)

Step 2: They multiply that population of 100,000 by the mortality rate between age 0 and 1 (denoted q₀). That gives the number of deaths at age 0 (d₀).

Step 3: They then subtract that number of deaths (d₀) from the living population (l₀). That gives the number surviving to age 1 (l₁).

Step 4: Analysts then apply this iterative…


A survey on Twitter cannot mask actual social research.

The broadcaster GB News claims:

Covid: GB News poll suggests most will not wear masks after Freedom Day

The article uses the result of a Twitter survey ran on the GB News account:

The result of the GB News poll shows that 72% of people would not wear a face mask if it was no longer a legal requirement.

No inferences from self-selecting surveys

A self-selecting survey allows respondents to put themselves in the sample. Another name for this kind of survey is an open access survey. …


Public Health England statistics do not show vaccinations increasing risks of Covid death.

A conspiracy site asserted on Twitter:

Public Health England data shows that the fully vaccinated have a 885% higher chance of dying due to C0V1-D than the unvaccinated…

The Public Health England report does not show this.

The Daily Expose article confuses the case fatality rate among Delta (B.1.617.2) cases for the “chance of dying due to” Covid-19.

The case fatality rate is the number of surveillance deaths divided by the number of cases. In England, a confirmed death means a person died within 28 days of a positive test. Other countries may also count suspected cases and deaths, without…


R is for reproducible workflows.

Colin Angus, a policy modeller, wrote on Twitter:

A few years ago, my workflow tended to be to find interesting data, usually in an Excel file, then tidy it up *in Excel* and export a clean csv to then import into R for plotting…

That sounds familiar.

I recognised this pattern of working, as I do it too.

(Image: GIFer)

The NHS England weekly vaccination reports contain much information. Those statistics are not held in clean formats. We want to see a table, by age groups, of vaccination doses and population estimates. …


Despite high coverage, an effective vaccine can still have breakthrough cases.

On 13th June, a MailOnline headline states:

Study shows 29% of the 42 people who have died after catching the new strain had BOTH vaccinations as cases soar another 40%

In Public Health England’s briefing on 25th June, 50 out of 117 Delta-related (B.1.117.2) deaths had two vaccine doses.

As vaccine coverage rises, the share of Covid-19 deaths with prior vaccinations grows. If everyone had two doses, all people dying (from any cause) would have been fully vaccinated.

Suppose there were 100 people who would die after infection without a vaccine. …


Some polling companies weigh by educational attainment.

A former adviser to the UK government wrote on social media:

There’s literally *a BIG alignment* in UK/US over years which is why e.g pollsters now must do as Vote Leave did in 2016 & *weight by education*

What does “weight by education” mean?

In survey research, weights correct for some imbalances between samples and the population.

The typical goal of surveys is to be a representative slice of the population. Researchers adjust responses so the sample looks more like that targeted population. For example, suppose we know there are — in proportion — more women in the population than in our sample. They ‘weight’ the…


Factors affect both vaccination status and Covid-19 death rates.

One major question during the pandemic is: how effective are vaccines? Observational studies look at people without vaccines, comparing outcomes to vaccinated people.

Two possible study designs are:

  • Prospective cohort: the study follows groups of individuals over time. The study then examines how vaccination affect outcomes (such as Covid-19 deaths).
  • Matched control: the study matches vaccinated people to similar people without vaccination.

Systematic errors may remain in these observational analyses. Such studies use statistical analysis to adjust for confounding factors. Confounding variables affect both exposures and outcomes of interest. …

Anthony B. Masters

This blog looks at the use of statistics in Britain and beyond. It is written by RSS Statistical Ambassador and Chartered Statistician @anthonybmasters.

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