World of Happiness-Lecture Slides (Statistical Shenanigans)-Literature, Slides for Psychology of Happiness. The University of Sheffield
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World of Happiness-Lecture Slides (Statistical Shenanigans)-Literature, Slides for Psychology of Happiness. The University of Sheffield

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These are the lecture slides by Dr. Danny Dorling who is a well known lecturer in the field of Happiness Studies. These Slides are from his lectures delivered in 2010. The following are the main points; Statistical Shena...
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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 much

that we take for granted

ain't necessarily so

Danny Dorling Royal Statistical Society

Annual Conference, Brighton 17th

September 2010 12:15pm - 1:35pm

Plenary 6 - Significance

Auditorium 2 - Hewison Hall

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)”

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).

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?”

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?

Think about education stats

Note: in the figure that follows I have chosen

The 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).

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?

Figure 2: Distribution of children by

proficiency in science, according to the

OECD, 2006 (%) Children

….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?

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 we

Been getting

Cleverer?

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 what

we still do now appear

so often to replicate mistakes

that we made in the past?

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)

-20

0

20

40

60

80

100

120 -2

0 0

-1 0

0 0

1 0

0

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0

3 0

0

4 0

0

5 0

0

6 0

0

7 0

0

8 0

0

9 0

0

1 0

0 0

normal(N)

binomial(B)

data(D)

Too good to be true?

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?

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)

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‟.

Here‟s one I made up earlier

Some 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.

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………….....)

0

250

500

750

1000

1250

1500 4

0 c a

d a

y

7 0

c a

d a

y

1 .4

$ a

d a

y

3 $

a d

a y

6 $

a d

a y

4 0

0 0

8 0

0 0

1 6

0 0

0

3 3

0 0

0

6 6

0 0

0

1 3

1 0

0 0

2 5

0 0

0 0

5 0

0 0

0 0

Europe

Americas

Asia

Africa

How we got today‟s inequalities

1977

1973

1968

1969

-20%

-10%

0%

10%

20%

30%

40%

50%

60% 1

9 5

5

1 9

6 0

1 9

6 5

1 9

7 0

1 9

7 5

1 9

8 0

1 9

8 5

1 9

9 0

1 9

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2 0

0 0

Africa

Asia

Americas

Europe

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

But how well off are the rich?

Ability to get by

Very Difficult

6% Difficult to

Manage

15%

Coping

48%

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.

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.

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.

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.

Peace Prizes – and a final puzzle

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

5%

3% 4%

5%

8%

4% 4% 4%

7%

9%

0%

0%

2%

4%

6%

8%

10% 1 9 0 0 s

1 9 1 0 s

1 9 2 0 s

1 9 3 0 s

1 9 4 0 s

1 9 5 0 s

1 9 6 0 s

1 9 7 0 s

1 9 8 0 s

1 9 9 0 s

2 0 0 0 s

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

Conclusion

So 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 

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