1.
Statistics
for Journalists
Adrian MacLeod
adrian@writethinking.co.uk
2.
Percentage starting points
Wheat in millions of tonnes
Produce Consume
China 99.7 115.4
EU 104.4 91.2
Change
%= x 100
Starting value
3.
Percentage starting points
Wheat in millions of tonnes
Produce Consume
China 99.7 115.4
EU 104.4 91.2
EU produces 4.7% more wheat than China
China produces 4.5% less wheat than the EU
China consumes 26.5% more than the EU
The EU consumes 21% less than China
The EU produces 14.5% more than it consumes
The EU consumes 12.6% less than it produces
4.
Rates and decimals
In scientific notation:
10n means 1 followed by n 0s
2.1 e 10n means 2.1 followed by n 0s
2.1 e 10-n means 2.1 with the point moved
n places to the right
2.1 e 102 = 210
2.1 e 10-2 = 0.021
2.1 e 10-5 = 0.000021 or 2.1 out of 105
(105 = 100,000)
5.
Rounding
Too much detail confuses so rounding help
the reader understand.
3,123,918 is better written as 3.1m
If the part you are throwing away begins
with 4 or less, just through it away. If it
begins with a 5 or more, increase the final
digit of your rounded number by one.
3,138,487 is 3.1m
3,176,918 is 3.2m
Beware rounding errors (percentages may
add up to 99% or 101%)
6.
Probability
If 2 out of 10 cars has a defect, the probability
that any given car has a defect is
2/10
or 0.2
or 20%
Don’t confuse probability with quantity
More does not necessarily mean more likely
7.
http://www.guardian.co.uk/society/2003/mar/27/medicineandhealth.lifeandhealth
Skin cancer kills thousands of Britons
Guardian Thursday 27 March 2003
Thousands more Britons than Australians die from skin cancer even though more cases of the
disease are diagnosed in Australia, new figures showed today.
Cancer Research UK, Britain's biggest charity, and the government today launched a
nationwide campaign to encourage more Britons to protect themselves and their children
from the sun's harmful rays.
Figures released as part of the Sun Smart campaign show that in the last five years there
have been 8,100 British deaths from malignant melanoma compared to 4,900 in Australia.
The figures showed that nearly 8,000 cases of malignant melanomas are diagnosed in
Australia each year, and nearly 6,000 in the UK. Yet 600 more people die from the disease
each year in Britain than in Australia.
Dermatologists, from CRUK said that a lack of public awareness about skin cancer is leading
to needless deaths.
Many patients failed to use proper protection in the sun and others did not spot early
symptoms of malignant melanomas, they added.
People should seek medical advice if they notice that a mole changes shape, gets bigger,
alters in colour (particularly getting darker or multi-shaded) bleeds or becomes itchy or
painful.
The campaign stresses that pre-cancerous moles are easy to treat and are usually removed
under local anaesthetic. An early melanoma can be cured in this way, but if left, the disease
can spread.
The main risk factor for malignant melanoma is ultraviolet light from the sun or sun beds.
People are considered more at risk if they have lots of moles, are fair skinned with blue eyes,
tend to sunburn easily or have freckles.
Dr Charlotte Proby, consultant dermatologist for CRUK said: "Malignant melanoma
is a preventable cancer. We need the public to be aware of what they can do to
help prevent the disease."
She added: "The success of sun awareness campaigns in Australia is self evident."
8.
Are you more likely to die in the UK?
Population Number of Chance of
deaths* dying
UK 63 million 8,100 1: 7,700
Australia 20 million 4,900 1: 4000
* Deaths over five years due to malignant melanoma. Source: Cancer Research UK.
Impression given: twice as likely to die
from skin cancer in the UK.
Truth: half as likely to die from skin cancer
in the UK.
9.
Averages
Mean or average = sum of values/number of values
Median = Rank values and find middle
Mode = Value that occurs most frequently
Mean useful for comparing groups of figures which
have a normal distribution
Median useful for comparing groups of figures which
do not have a normal distribution
Warnings:
Do NOT average averages
Average does not necessarily mean typical
10.
Normal distribution
Mathematical
curve
Real bell-shaped result
11.
Standard deviation
Measures the spread of data.
s, sn, sn-1, sn and sn-1 are all different ways of
calculating the spread but give more or less the same
answer provided the number of values in the data
sample is more than 20
Large SD
Small SD
12.
Standard deviation
For a normal distribution:
1s 67% of the data is within one standard deviation of the mean
2s 95% is within two standard deviations of the mean
3s 99% is within three standard deviations of the mean
1 SD 1 SD
2 SDs 2 SDs
3 SDs 3 SDs
Mean
13.
Standard deviation example
If a survey shows that average height of athletes on a
team is 175cm with a standard deviation of 10cm
then it is reasonable to estimate that:
67% of athletes are between 165 and 185cm
95% of athletes are between 155 and 195cm
14.
Graphing
Pie charts good for showing how a whole
is made up of parts. NB Groups should be
distinct and separate.
Bar charts for comparing. NB the impact
of bar charts can be distorted if the origin
is not zero or if 3-D columns are used.
Line graphs are good as showing how
things change over time. Y origin should
be 0. Dates should be evenly spaced
15.
Estimating from a sample
Using a sample of a population to predict something
about the whole population
Estimates can never be 100% accurate so they should
come with a margin of error
Margin of error at 90% confidence is 0.82/ n
Margin of error at 95% confidence is 0.98/ n
Margin of error at 99% confidence is 1.29/ n
** Provided the whole population is a large number,
the margin of error is NOT dependent on population
size **
16.
Estimating from a sample
Sample Margin of error
size (95% confidence)
50 ±13.9%*
100 ±9.8%*
200 ±6.9%*
300 ±5.7%*
400 ±4.9%*
500 ±4.4%*
750 ±3.6%*
1000 ±3.1%*
2000 ±2.2%*
* % is actually percentage points
17.
Estimating a mean
The margin of error of the mean can be calculated
thus:
Margin of error at 2(sample’s standard deviation)
=
95% confidence
number in sample
Margin of error at 1.7(sample’s standard deviation)
=
90% confidence
number in sample
Use this formula only for sample sizes greater than 30
18.
How scientists work
Observational (epidemiological)
research
Experimental studies
Peer review
Systematic review (meta analysis)
Risk factor based on converging
data
50:1
19.
Inference
To draw conclusions from data, you need to have
confidence in that data.
The statistical measure of confidence is p. The smaller
the number the better.
p is a probability between 0 and 1
In social science the p value should be at most 0.05
In medicine the p value should be at most 0.005
Often, all you have to do is check that the p-value is
appropriately small.
20.
Correlation r
The correlation of two factors is calculated with the
correlation coefficient (r) ranging from 0 to 1. Near 0
means little correlation. Near 1 means closely correlated.
r=-1.0 means an inverse correlation.
EG: The weight of people in a sample is likely to be
correlated with height (tall people are heavier) and
inversely correlated with life expectancy (heavier people
die younger)
21.
Correlation based on a sample
Correlation based on a sample with p= 0.05
For a sample of 10 if r is greater than 0.63 then there
is a (non-trivial) correlation
For a sample of 30 if r is greater than 0.36 then there
is a (non-trivial) correlation
For a sample of 100 if r is greater than 0.2 then there
is a (non-trivial) correlation
22.
Coefficient of determination
The value of r2 for two characteristics gives the %
variation in one quantity that is explained by another
EG:
If the correlation coefficient between weight and
2
height is r = 0.07 then r = 0.49 which means that
about 49% of the variation in weight is explained by
height. 51% will be explained by other factors
NB: Correlation does NOT imply causation
If correlation between X and Y is high then we can
say X is a good predictor of Y
If r is v small and confidence is high (p is also small)
then may be statistically significant but not significant
isn the real world
23.
Correlation does NOT imply causation
Facebook fuelling divorce, research claims
n
io
Telegraph 21 December 2009
at
The social networking site, which connects old friends and allows users to make
us
new ones online, is being blamed for an increasing number of marital
breakdowns.
ca
Divorce lawyers claim the explosion in the popularity of websites such as
Facebook and Bebo is tempting to people to cheat on their partners.
http://www.telegraph.co.uk/technology/facebook/6857918/
y
pl
Suspicious spouses have also used the websites to find evidence of flirting and
even affairs which have led to divorce.
im
One law firm, which specialises in divorce, claimed almost one in five petitions
they processed cited Facebook.
Facebook-fuelling-divorce-research-claims.html
T
Mark Keenan, Managing Director of Divorce-Online said: "I had heard from my
NO
staff that there were a lot of people saying they had found out things about
their partners on Facebook and I decided to see how prevalent it was I was
really surprised to see 20 per cent of all the petitions containing references to
Facebook. es
do
"The most common reason seemed to be people having inappropriate sexual
chats with people they were not supposed to."
n
Flirty emails and messages found on Facebook pages are increasingly being
io
cited as evidence of unreasonable behaviour.
at
...
The UK’s divorce rate has fallen in recent years, but two in five marriages are
el
still failing according the latest statistics.
rr
Mr Keenan believes that the general divorce rate will rocket in 2010 with the
Co
recession taking the blame.
24.
Surveys
Sample should be random
High response rate
Don’t depend on volunteered responses
Careful in constructing questions: not good if you are
interpreting the answers; if the answers are
ambiguous; if the phrasing of questions pushes
people towards a particular answer
Always state who conducted survey and give margin
of error
25.
Experiment
Treatment = the thing you are testing
Control group = group not treated for comparison
Random assignment = people are assigned to control
group or treatment group randomly
Placebo = fake treatment given to control group so
they do not realise they are the control group
Double blind = neither those being experimented
upon nor those giving the treatment know who is
getting the the treatment and who the placebo.
26.
'Seafarers' disease' scurvy on rise among
children due to lack of vitamin C in diet
Daily Mail 7 November 2009
Scurvy is making a comeback among England's children.
Caused by a lack of vitamin C, the potentially fatal disease was a scourge of
Seafarers-disease-Scurvy-rise-children-lack-vitamin-C-diet.html
pirates and sailors in the heyday of the British Empire, but was thought to be
largely a thing of the past.
However, newly released statistics show that the number of children admitted
http://www.dailymail.co.uk/health/article-1225905/
to hospital with scurvy soared by over 50 per cent in the past three years.
Released following a parliamentary question, the figures show that in 2004/05
there were 61 children admitted with scurvy in England.
But by 2007/08, the latest year for which figures are available, there were no
fewer than 94 cases: up 54 per cent in three years.
Because the figures cover only those admitted to hospital with scurvy as a
primary or secondary diagnosis, the actual numbers with the disease will be far
higher as many will not get further than their GP.
Others may be listed under the wider term of 'malnutrition'.
Scurvy occurs if people do not eat enough foods containing vitamin C such as
fruits, tomatoes, potatoes, liver and oysters.
Scurvy leads to spots on the skin, particularly the legs, as capillaries break
down. There is cracking and bleeding of the lips, nostrils and ears. Gums go
spongy and teeth fall out.
... continues
27.
'Seafarers' disease' scurvy on rise among
children due to lack of vitamin C in diet
. . . continued
Wounds cannot heal properly, and old scars reappear. There is internal
haemorrhaging and left untreated, victims will die.
Seafarers-disease-Scurvy-rise-children-lack-vitamin-C-diet.html
Conservative health spokesman Stephen O'Brien, who uncovered the figures,
said: 'It is shocking that this disease of 17th-century pirates is on the rise again
in 21st-century England.'
http://www.dailymail.co.uk/health/article-1225905/
Ursula Arens, of the British Dietetic Association, said it was not possible to say
how the children were getting scurvy: whether it was from a poor diet, or as a
by-product of other diseases such as cancer.
'There may be examples of children just living on bread and jam and nothing
else because of poverty,' she said.
'It is such an unusual thing now that perhaps it is something that many GPs
would not be able to diagnose.'
A spokesman for the Department of Health said: 'Families in lower income
groups tend to consume less vitamin C in their diet.
'The Department of Health promotes consumption through its "five a day"
campaign and Healthy Start, which provides free vitamin supplements for
beneficiaries.'
28.
'Seafarers' disease' scurvy on rise among
children due to lack of vitamin C in diet
Scurvy cases
Data on which Mail story was based 2007-08 94
showed primary and secondary 2006-07 101
hospital diagnosis of absorbic acid 2005-06 68
deficiency (scurvy). 2004-05 61
2003-04 72
Problems:
1) Showed all patients not just children
2) Based on small numbers with large
year-year variations (noise)
3) Picked two years with biggest
difference (longer time period and
window average would have been
more convincing)
4) Data contains no info about CAUSES
of scurvy. Actually more likely to be
caused by increased cancer survival.
29.
Media studies graduates
The Press Gazette reports that Media Studies graduates
are among the most successful at finding jobs.
It is true that 73.6% are in employment compared with
66.9% figure for all graduates.
The implication is that you are less likely to be
unemployed. But PG has excluded the figures for people
who stay in education.
Actually the figure for those who are unemployed is
more revealling: 10.1% for media studies compared
with 6.9% for all subjects.
Perhaps a more significant story is that only
11.5% found jobs in the media. Those ending up
as secretaries, shop assistants and bar staff
adds up to a far higher figure.
30.
Where graduates are after six months
All subjects
Employed (73.6%)
Study (9.1%)
Employed (66.9%)
Study (18.7%)
Unemployed
(10.1%)
Unemployed
Media studies (6.9%)
31.
4%
8%
12%
16%
Marketing, sales, PR advertising
Commercial, public sector managers
Scientific research, analysis
Engineering
Health
Teaching
All subjects
Business & Finance
Media studies
Information technology
Nursing & health associate
Business & finance associate
Media, literary, design, sport
Other porfessional & technical
Types of work
Numerical clerks & cashiers
Other clerical & secretarial
Retail assts, waiting & bar staff
Health & childcare
Armed forces & public protection
Other
Unknown
32.
Apples & oranges
August 2000 US Justice Policy Institute’s claimed that
“more African American men are incarcerated than
enrolled in college.”
You can go to prison at any age, for any length of time,
but most people go to college for only a few years during
their late teens and twenties.
33.
The new phenomena phenomenon
Actual figures
Perception
Cases of AIDS
55 60 65 70 75 80 85 90 95 00 05 10 15
Year
34.
Care with comparisons
A new study claims that Autism has risen ten-fold in
the US in the past decade.
Most media sources reported this as proof that a
worrying increase in the condition has gone unnoticed,
while others raised the possibility of a link to the
substance thimerosal, an ingredient in childhood
vaccinations.
In fact, the increase was probably due to a massive
increase in the definition of autistic disorders over the
past 10 years.
35.
Dangerous conclusions
Burglary
Robbery
International Crime
Assault
Victimisation Survey
2000
UK 6.0% 1.2% 2.8%
South Africa 5.8% 4.6% 6.3%
Conclusion: UK nearly as dangerous as South Africa?
Murder rate (1997 figures):
UK 1.4 per 100,000
SA 58.4 per 100,000
36.
Sampling
26 February 2002 former US Secretary of Health,
Education and Welfare Joseph Califano’s claimed that
under-age drinkers consume a quarter of all alcohol
drunk in the United States.
The survey over-sampled teenagers. As The New York
Times conceded in a subsequent correction, the actual
figure is only 11%.
37.
Time periods
11 June 2002 The New York Times claimed the
average temperature in Alaska “has risen about seven
degrees over the last 30 years.”
This surprised experts at the Alaska Climate Research
Center, whose figures show an increase of only 2.5
degrees in the same period.
The Times corrected its mistake on 11 July, but still
claimed an increase of 5.4 degrees, which it justified
by using the period from 1966 to 1995, rather than the
“last 30 years” from 1973 to 2002.
39.
Massaged figures
A US government task force on college drinking
claimed that 1,400 students are killed and 600,000
are assaulted each year because of alcohol.
That figure would represent two thirds of all the
assaults in the US, according to the FBI.
But the “assaults” included everyone who said they
were “pushed or hit” by anyone as a result of someone
drinking. And the deaths included fatal auto and other
accidents in which anyone (not only drivers) tested
positive for any amount of alcohol.
40.
Fear from simplifying
Lancet: "fear of breast cancer is so pervasive among US
women that it is causing them to ignore far more serious
health threats."
The commonly reported figure that 1 in 8 figure women
will develop breast cancer only applies to those already
in their 80s
Office of National Statistics shows that the risk for
women under age 35 is 1:625, rising to 1:56 by age 50.
Before the age of 50 only one woman out of 136 dies of
breast cancer. By the age of 60 this is one out of 65.
And by the age of 80 only one woman in 26 dies of
breast cancer, which represents the lifetime risk for
most women - that means the other 25 will die of
something else.
41.
Breast cancer figures
80+ 1:8
80 1:26
60 1:56
50 1:136
35 1:625
42.
Questions
WHO? Reputable statistician or hopeful charity?
Political spin doctor or civil service department.
Ask yourself how reliable you think the
organisation compiling the statistics is and rate
the results accordingly.
WHY? Do they have a vested interest in producing a
particular result? If so is the way they compiled
the data reasonable? Did they ask the right
questions? Have they focused on the most
helpful result to them and distorted the truth in
the process?
HOW? Was the sample representative? Was it big
enough? Was there bias built into the way they
conducted the survey?
43.
Checklist
Where possible, go back to original numbers and check
assumptions and spin
Ask yourself whether the numbers you are reporting tell
the whole story
Like any other aspect of journalism, check sources
Watch time periods
Take care with percentages and other rates
With surveys, find out what questions were asked
Question the conclusions that you and others derive from
figures
Watch out for spin - figures selected or presented for one
party’s advantage
Check that comparisons are valid
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