statistical shenanigans: from sweet peas to nobel prizes, how much that we take for granted...

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Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so Danny Dorling Royal Statistical Society Annual Conference, Brighton 17 th September 2010 12:15pm - 1:35pm Plenary 6 - Significance Auditorium 2 - Hewison Hall Watch multimedia versions of the Sasi slideshows at http://sasi.group.shef.ac.uk/presentations/

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Plenary Talk by Danny Dorling held at the Royal Statistical Society Annual Conference, Brighton 17th September 2010

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Page 1: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Statistical Shenanigans:From Sweet Peas to Nobel Prizes,

how muchthat we take for granted

ain't necessarily so

Danny DorlingRoyal Statistical Society

Annual Conference, Brighton 17th September 2010

12:15pm - 1:35pmPlenary 6 - Significance

Auditorium 2 - Hewison Hall

Watch multimedia versions of the Sasi slideshows at http://sasi.group.shef.ac.uk/presentations/

Page 2: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Objectives

“This talk presents a short and somewhat irreverent tour through social statistics, asking how unbiased our great statisticians really are, examining the 19th century pioneers of social statistics and giving a few examples from their work (including on sweat peas and paupers)”

Page 3: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Method/Models

Looks for statistical clues in the distributions of Nobel Peace prizes as to how greatness in science is assessed, but starting with the modern day presentation of international statistics in education as an example of how great traditions of partiality might be being continued. Most of the examples shown are taken from the recent book: “Injustice - why social inequality persists.” (Bristol: Policy Press).

Page 4: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Results and Conclusions

“Underlying all these stories is the question of how best we can "collect, arrange, digest and publish facts, illustrating the condition and prospect of society in its material, social, and moral relations." - as read the original aims of the Royal Statistical Society. How impartial are the

statistics of each age?”

Page 5: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Politically innumerate?

• There is no such thing as a neutral social statistic

• But don’t be afraid of social statistics

• Consider two numbers:– £70,000,000,000 – structural

deficit 2010– £77,000,000,000 – rise in

wealth of the richest 1000 people in the UK 2009-2010.

(Sources – both the Sunday Times Newspaper)

Are they comparable?

Page 6: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Think about education statsNote: in the figure that follows I have chosenThe following short labels for OECD’s data: • ‘None’ implies possessing no knowledge

(as far as can be measured). • ‘Limited’ implies possessing very limited knowledge. • ‘Barely’ stands for barely possessing adequate

knowledge in the minds of the assessors. • ‘Simple’ means understanding only simple concepts. • ‘Effective’ is a little less damning. • ‘Developed’ is better again;

Source: OECD (2007) The Programme for International Student Assessment (PISA), OECD’s latest PISA study of learning skills among 15-year-olds, Paris: OECD, derived from figures in table 1, p 20.

That Source gives the PISA study report's own descriptions of these categories I have given my own interpretations above. You should judge whether these are justifiable – see the journal Radical Statistics issue 102 (forthcoming).

Page 7: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Figure 1: Children by student proficiency in science in the Netherlands, according

to the OECD, 2006 (%)

2%advanced

11% developed

26% effective27%

simple

21% barely 11% limited

2% none

Is this how children in the Netherlands really are?

Page 8: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Figure 2: Distribution of children by proficiency in science, according to the

OECD, 2006 (%) Children

0

5

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World Nether-lands

UK USA

none

limited

barely

simple

effective

developed

advanced

….maybe this is all b- b- b- baloney (mustn’t use a rude word now, not if we are well-educated). Look at the shape of those curves ……. They are all very similar aren’t they?

Page 9: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Figure 3: School-leaving age (years) and

university entry (%), Britain, 1876-2013

Note - school leaving age in years, left hand axis and line marked by X's; university entry % by age 30, right hand axis and line marked by filled black circles – for sources see “Statistical clues to social injustice” Radical Statistics Journal, v102.

Haven’t weBeen gettingCleverer?

Page 10: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

What could be different?

• If there was not such a need to get the qualifications quickly to get above others in the labour market students could begin to learn and think rather than increasingly cram and drink.

And how does whatwe still do now appearso often to replicate mistakesthat we made in the past?

Page 11: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Figure 4: Geographical distribution of paupers, England and Wales, 1891

Source: Figure redrawn from the original. Pearson, K (1895) ‘Contributions to the mathematical theory of evolution – II. Skew variation in homogeneous material’, Philosophical transactions of the Royal Society of London, Series A, Mathematical, vol 186, pp 343-414, Figure 17, plate 13)

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normal(N)

binomial(B)

data(D)

Too good to be true?

Page 12: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

A couple of hypothesis

• Statisticians have been implicated in holding back progress in education since the beginnings of their subject; most of the discipline’s founding fathers (they were almost all men) were complicit.

• Karl Pearson’s teacher, Francis Galton, drew a graph concerning sweet peas and their hereditary properties where one of the very limited number of sample points hits the mean of both distributions exactly spot on – fixed?

Page 13: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Don’t the little dots form a pleasing pattern? - maybe a

little too pleasing. I just point this out to suggest

someone checks.

Galtons’ 1877 graph: Source: Magnello, E. and B. V. Loon (2009). Introducing Statistics. London, Icon Books. (Page 123)

Page 14: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Floating a boat

If someone finds that Galton’s famous sweet pea graph was a little too good to be true this does not mean that sweet peas did not behave in this way. It is just an example of what was then normal and what, in a slightly tempered form, is still normal amongst many statisticians: to get a little carried away with underlying theories that everything is normally distributed and, if that is not found to be the case then fit the data to such a curve to make it ‘normal’.

Page 15: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Here’s one I made up earlierSome distributions are normal, but it is not normal that they should be so: take the world distribution of income drawn using a log scale (next figure).

It partly appears normal because I drew it by adding up log normal curves. I knew the mean and medians of incomes in almost every country in the world and also information on the range and hence standard deviation.

In a few countries inequalities are so great that the actual distribution is bimodal, in other countries income distributions are less skewed.

When summed, these errors tend to cancel each other out (with, including the sum of errors, a little ‘natural normal’ variation maybe for once). What Figure 6, the figure which is shown next, does not tell you, however, is that we have not always lived like this.

In the very recent past incomes tended to be much more equitable for most people in most places in the world.

Page 16: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Figure 6: Distribution of income showing inequality (US$), worldwide, 2000

Source: Figures (in purchase power parity, US$) derived from estimates by Angus Maddison, from a version produced in spreadsheets given in ww.worldmapper.org, based in turn on UNDP income inequality estimates for each country. See Dorling, D., 2010, Injustice:

(..$$$$.....annually………….....)

0250500750

100012501500

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c a

da

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Page 17: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

How we got today’s inequalities

1977

1973

1968

1969

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95

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Figure 7: Real growth per decade in GDP (%), per person, by continent, 1955–2001 . The log normal distribution we see today was due to 1980s divergence

Source: as Figure 6

Page 18: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

But how well off are the rich?Ability to get by

Very Difficult6%

Difficult to Manage

15%

Coping48%

Living Comfortably

31%

Figure 8: Households’ ability to get by on their income in Britain, 1984–2004

Source: Derived from ONS (2006) Social Trends (No 36), London: Palgrave Macmillan, table 5.15, p 78, mean of 1984, 1994 and 2004 surveys.

Page 19: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

And how unusual are our times?

0%2%

4%6%8%

10%12%14%16%

18%20%

1920 1930 1940 1950 1960 1970 1980 1990 2000

Figure 9: Share of all income received by the richest 1% in Britain, 1918–2005 Note: Lower line is post-tax share.

Source: Atkinson, A.B. (2003) ‘Top incomes in the United Kingdom over the twentieth century’, Nuffield College Working Papers, Oxford (http://ideas.repec.org/p/nuf/esohwp/_043.html), figures 2 and 3; from 1922 to 1935 the 0.1% rate was used to estimate the 1% when the 1% rate was missing, and for 2005 the data source was Brewer, M., Sibieta, L. and Wren-Lewis, L. (2008) Racing away? Income inequality and the evolution of high incomes, London: Institute for Fiscal Studies, p 11; the final post-tax rate of 12.9% is derived from 8.6%+4.3%, the pre-tax rate scaled from 2001.

Page 20: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

And is recession really over?

Figure 10: The crash: US mortgage debt, 1977–2009 (% change and US$ billion)Source: US Federal Reserve: Debt growth, borrowing and debt outstanding tables (www.federalreserve.gov/releases/Z1/Current/) Right-hand axis, net US$ billion additional borrowed - Left-hand axis: percentage change in that amount.

Page 21: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

So what happens next?

What will happen? Nobody knows. But you can update the graph every quarter using the link to the Federal Reserve given as the source. You can get access almost as quickly as any finance minister. This may not be the televising of a revolution but it is the making public of a change in times. I think that the numbers are made public because the people releasing them do not imagine that there is anyone out there who is numerate and with a different view of the world. “How could there be?”, they’ll think. “People exist along a normal curve of ability”, they believe. At the top are us economic-statisticians who know that there is no alternative.

Page 22: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

Peace Prizes – and a final puzzle

So are times changing? For source data: See: http://www.sasi.group.shef.ac.uk/injustice/

5%

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Figure 11: Female Nobel laureates (%), by decade, worldwide, 1901–2009

Why in one decade was not a single women awarded a prize?

Claim it was very unlikely to have happened by chance, just as the 2009 prize distribution was extremely unlikely

Page 23: Statistical Shenanigans: From Sweet Peas to Nobel Prizes, how much that we take for granted ain't necessarily so

ConclusionSo how best we can "collect, arrange, digest and

publish facts, illustrating the condition and prospect of society in its material, social, and moral relations."

These were the original aims of the Royal Statistical Society and where the aims when I joined. We need to keep asking how impartial are the statistics of each age?

There is no such thing as a neutral

statistic, but some statistics may be

more neutral than others

Watch multimedia versions of the Sasi slideshows at http://sasi.group.shef.ac.uk/presentations/