The doc recommends an MRI scan. A problem is identified and an operation, perhaps, recommended. But here is the problem. The back problem identified in the scan may not be the cause of the pain.
In maths this is called FALSE ATTRIBUTION.
You get all the pain – financial and physical – but no gain.
Dentists suffer a higher incidence of lower back pain … Maybe from prancing around in towels in front of mirrors. Wait. That was only a small sample of 10 paid dentists.
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.
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:
The asked 8800 people about their health, lifestyle and television watching behaviour, and then followed them over the next six years, during which time 284 of them died. Among people who spent more than 4 hours a day in front of the TV, it found, the risk of their dying within the period of the study was 46 per cent higher than among those who watched less than 2 hours a day.
The error is confusing CORRELATION with CAUSATION. The risk might involve the sitting rather than TV. Or it could be that those who sit in front of TV longer are not well.
THIS IS A COMMON AND DANGEROUS ERROR INVOLVING HEALTH STATISTICS
Now that we have more screening tools we must be more cautious.
Angelia Jolie had her breasts removed because of testing positive forthe BRCA 1 and BRCA 2 genes, which are linked to an increased risk of Breast Cancer.
This is her decision. Anyone facing breast cancer would seriously consider this option.
BUT, be wary if you face this decision.
Think of Asthma. If we started our research into asthma looking for asthma genes we would have found them.
Genes create a pre-disposition for Asthma (hence the correlation) but they do not cause asthma. The dust mite, pollen, cat, dairy and other allergies cause asthma. If researchers had concentrated on genes alone our knowledge of asthma would be limited.
Another study showed that 80% of prisoners in Australia smoke. Isn’t it obvious? Smoking causes criminal behaviour!!!!!
When it comes to health stats emotions beat facts.
Not many children in Australia 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.
It is a FAMILIARITY BIAS.
Parents are constantly shocked by images of car accidents on the news (and kidnapped children. That’s another story.)
Likewise, parents in the UK worry about their children walking to school. But, as The Guardian noted, here are the stats for child pedestrian deaths in the UK.
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.
We also tend to be more frightened by big numbers than little numbers.
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″
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.
Too many death statistics are not good for your health either.
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!
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.
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!
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.
Angelina Jolie has had both breasts removed because of the risk of developing breast cancer.
But did she understand the Maths?
She may be right. This could be the best way for her to avoid breast cancer. And it IS her decision.
But maths isn’t that clear cut. Referenced information about BRCA1 and BRCA2: Cancer Risk and Genetic Testing can be found at The National Cancer Institute here.
in the general population will develop breast cancer sometime during their lives compared with about
60 percent of women (600 out of 1,000)
with gene mutation in BRCA1 or BRCA2. This is FIVE TIMES the risk over a lifetime.
BUT and this is a big but …..
It is important to note, however, according to The National Cancer Institute (USA), most
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research related to BRCA1 and BRCA2 has been done on large families with many individuals affected by cancer and the cancer risk associated with BRCA1 and BRCA2 mutations have been calculated from studies of these families. Because family members
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share a proportion of their genes and, often, their environment, it is possible that the large number of cancer cases seen in these families may be due in part to other genetic or environmental factors.
Factors that could affect these risk factors include food, lifestyle, location, inherited temperament and even the air they breathe.
Statistics are a useful tool. But statistics are based on random selection. This is IMPORTANT. Once you bias the data, your results are corrupted.
Removing cancerous breast tissue makes sense. Removing perfectly healthy breast tissue based on the maths … well … you’d want to think about it.
To put this another way the BRCA genes may be correlated with breast cancer, but this event is not independent of all other events in one family. There may be many, yet to be discovered, links . This is a common error in statistics made not only by journalists, but by experts too. (See below)
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Conviction by Maths Error
On 9 November 1998 at Chester Crown Court Sally Clark, a Cheshire solicitor, was convicted, by 10-2 majority, of smothering her two baby boys.
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Clark’s first son died suddenly within a few weeks of his birth in 1996. In 1998, when her second son died in similar circumstances she was arrested and tried for the murder of both sons.
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The prosecution used paedeatrician Prof Roy Meadows as a expert witness. He had discovered Munchausen Syndrome by Proxy (MSbP). Sally Clark was found guilty and spent 3 years in jail.
Prof Roy Meadows testified that the chance of two children from an affluent family suffering sudden infant death syndrome was 1 in 73 million. He arrived at this number by squaring 1 in 8500 for likelihood of a cot death in similar circumstances.
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He was wrong and was later struck off the medical registrar. He assumed that these were independent events. They were not. Maybe the heater was at fault. Or the cot. Or the house paint. Or, as suggested in The Observer article, faulty genes in the family.
Sally Clark died several years later of alcoholic poisoning. More information.
Here are two brilliant ways of using maths to create something awesome. Firstly, using fantubes, you can build a chair.
You would have to work out how many fantubes you need. Measure up a standard armchair and then divide the width and depth by the diameter of the fantube.
Or you could just count the number of fantubes in this picture. More info here. Then – this is the PR bit – invite the School Principal into Maths Class to sit on the chair. Will your principal have faith? Or chicken out?
Secondly you could make this folding cardboard chair.
