Posts Tagged ‘Common errors in statistics’


1. Why bother?

June 14, 2013

The most annoying health statistics are based on small study groups. 

 Picture 1

eg. 9 out of 10 dentists recommend this toothbrush. Oral B as it turns out.

In maths we call this for obvious reasons a SMALL SAMPLE SIZE.  This may not be a problem when buying a toothbrush, but what if they are trying to sell you – sticking with thedentist theme – a $5,000 procedure that breaks your jaw and resets it to improve your bite?

Where are the numbers? Has there even been any research? Or a large-scale survey about this procedure? Are people happy with this procedure? Did it even work?

You do not want to make a health decision based on a study involving a SMALL SAMPLE. From the above ad, a sample of 1, dentists are a hot date. You may not want to put your faith in this statistic.


4. Stuff Ups 2

June 14, 2013

All medical tests are subject to a % error.



This may not be a problem if you are advised to, say, take more Vitamin D to correct the problem you don’t have. But if you are being advised to undergo major surgery, a second test is advisable.

As statistician Michael Blastland explained in Everyday risks: when statistics can’t predict the future (The Guardian 9 JUN 2013):

False positives are common for the simple reason that if you test a million healthy people, even with a 99% accurate test, you will still have 10,000 wrong results. And that’s not including human error. Hopefully, you will not experience one of these:

x ray


6. Scary Stories, Scary Nos.

June 13, 2013

When it comes to health stats emotions beat facts.

kid walk

Not many children in Australia or the UK walk to school unsupervised or at all. The risks perceived by parents are out of proportion to the real risk. This is more to do with psychology than statistics.


Shocking stories about car accidents and abductions terrify parents. But their fears are not supported by the numbers.  As The Guardian noted, here are the stats for child pedestrian deaths in the UK.

pedestrian sign

In 2008 in England and Wales there were 1,471,100 girls aged between five and nine. The Office for National Statistics says 137 of them died from all causes. One was a pedestrian in a traffic accident. In 2010, there were no pedestrian deaths in this category.

 body count

As for abductions, the big stories capture our attention like the Madeleine McCann case. But as The Telegraph noted, more children in the UK die from window blinds (the chords are a hazard causing 4 deaths per year) than abduction.

We also tend to be more frightened by big numbers than little numbers.

This from the New Scientist.

In one study of this effect, people rated cancer as riskier when told that it “kills 1286 people out of 10,000” than when told it “kills 24.14 people out of 100”


This makes living on the earth very dangerous as, according to the World Health Organization

approximately 156,000 people die a day. And don’t even think to look at your Star Sign. Obviously, 13,000 Geminis die each day and 13,000 Leos. And so on. For those concerned it was not their lucky day.

star signs

Too many death statistics are not good for your health either.


7. Shock! Horror! Newsflash

June 13, 2013

A number of women develop breast cancer who worked in the same office. This happened in ABC offices in Australia in 2006.

A link was assumed but after exhaustive tests no environmental cause was found.

See ABC abandons cancer scare building.


Tragically, independent events can cluster. One episode of Numb3rs explained this possibility very well. If you fire a machine gun at a barn wall and draw a circle around a group of bullet holes later that is a cluster. But don’t try this at home, mathspiggies. 

There is a great explanation of clustering here. Some Aussie road signs show clusters of IDIOTS!




8. You’re All gonna Die 1

June 13, 2013

Red wines good for you. Red wines bad for you. Red wine causes cancer. Ditto coffee etc. What’s going on?

Here is Ben Goldacre in a TED talk called Battling Bad Science.

Everytime a study finds this or that food is good or bad for you they usually make one huge error.


It’s called a BIASED SAMPLE.

Here is an example Real Men Eat Meat and Die

The study showed that “Men whose red meat intake put them in the top 20 per cent consumption band were 22 per cent more likely to die of cancer in the 10 years of the study, compared to men whose intake was in the lowest 20 per cent. For women, there was a 20 per cent increase in risk.”

The problem is big meat eaters tend also to be big drinkers, smokers, obese and the rest. This study has tried to separate out meat eating from other unhealthy lifestyle choices using the Cox Regression. Mathematical wizardry has produced these numbers but they don’t mean much. meat eat 2

If the study used a control group of drinking, smoking, obese vegans then compaing mortality rates over 10 years would be would be interesting. But where do you find half a million of them????????


Meanwhile any survey or study of a self-selecting group (eg. newspaper polls among readers) or a pre-existing group (eg. a church group, college students, yacht club, rock ‘n roll club) produces biased and therefore meaningless results.

eg. 9 out of 10 dentists who are paid to say they recommend Oral B toothbrushes is useless information, a study of paid jerks, really.

Look for a RTC or Randomised Controlled Trial. 

Any study that begins a ‘trial of college students found’ (eg. psychology trials) is a BIASED SAMPLE. Look at the lifestyle of college students. How many people in the general population wear beer hats to parties? If you asked 10 beer hat wearing college students their opinion on Oral B toothbrushes they might not even recall the purpose of a toothbrush!

college beer drink hat

Look for big randomised trials.


9. You’re All gonna Die 2

June 13, 2013

Fat people got no reason

Fat people got no reason

Fat people got no reason

To live

They got big fat hands

Thunder thighs

They plod around

Puffin’ great big sighs

They got littler brains

They got damn iffy backs

They sit on their arses

Asking for heart attacks.

(With apologies to Randy Newman) 

fat people 1

 We are told there is an Obesity Epidemic as if you can catch obesity by standing beside someone packing a bit of cellulite.

If you have to be removed by a crane to get to hospital then you have a health problem. But obesity is presented in the media with such hysteria we could call it a NEGATIVE BIAS. The statistics are rarely questioned. And sometimes, these stats are not so damning.

Take diabetes and obesity statistics. Obesity increases the risk of diabetes.  True.

According to Australian Healthy Weight Week website, an affiliate of the Dieticians Association of Australia, 61% of Australian adults are overweight. Meanwhile, the Australian Institute of Health and Welfare puts the prevalence of diabetes in Aussie adults at 4.4% (all forms). Now wrap your head around this number. Even if all the 4.4% of  Aussies with diabetes  were overweight (they’re not), then 92.8% of fat people in Australia don’t have diabetes. But we still think fat people are evil.

fat people 2

They take up too much space

And breathe too much air

They stuff food in their faces

They don’t even care.


Make them fly freight on planes

They’re such a disgrace

 They should keep indoors

Let thin people run the place.


Fat people got nobody

Fat people got nobody

Fat people got nobody

To love them … (except me, I guess.)