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Lies, dammed lies and statistics.
This famous saying is true even if its attribution is in doubt. When dealing with the effectiveness of a treatment, there is seldom a clear cut answer to the question, "does it work?". The best that can be said is that it "worked" for X% of people in the same group as you.

There at least two problems with this statistic. The first is obvious, what do you mean by "worked", did it "cure" the complaint or at least, did it reduce the symptoms. The second is less obvious and is widely missed or misunderstood. If it worked for X% of people, many will take that to mean there is an X% chance it will work for them. That is simply not true. The proportion of the group for which the treatment worked in no way predicts the chance that it will work for you. A simple example will make this clear. About 50% of the population is female, does that mean there is a 50% chance that you are female? Clearly not! The statistics of the population at large have no direct bearing on the statistics of the individual. There is an approximately 50% chance that a person chosen at random from the population is a female but your gender is already determined.

Statistics of the population are used to determine if a useful number of people may receive a benefit from a treatment. If the study reported that the proportion of people helped was high it shows there are a lot of people that "could" be helped, not that you may be one of them. If many could be helped, clearly it is a good idea to continue with the study in order to find out who they are.

There are other misleading statistics. A favourite of those seeking to promote a particular course of action is to show their chosen belief is the "fastest growing" in order to imply the quality of their idea. There are at least two ways that the statistics to support this statement are "true" but still give the wrong idea. The first way is to use percentages. If idea X occurs in say 2% of cases, then if it changes to 4% in a week, the proportion is "doubled". The reason this can be misleading is best shown by an example. Suppose 100,000 people use treatment A and 100 people use treatment B. Suppose also that after a week, the number of those using treatment A has gone up to 101,000 and that 104 people are now using B. By quoting only the percentages, treatment B looks a real winner! In this case it is not the maths that is wrong, it is the language used. Something may be increasing the fastest, but it may be heading for a complete collapse if it is realised it does not work.

The second way to show something is growing very fast is to restrict the report to a limited time period. Suppose treatment C is used by 50,000 people and that every week, it is used by 1000 more people, After just 10 weeks it will be used by 60,000 people. Suppose treatment D is used by 2000 people and that over most weeks, 200 more people start to use it but over an exceptional week, 2500 more use it. By reporting this week only, proponents are not telling "lies" exactly, they are just being selective with their information. Listen carefully and you will hear this form of distortion in many party political broadcasts. Not wrong but misleading.

Some times you will see figures that look sensible but are mathematically wrong. Looking at the table of fictitious results below, there are 4 values for the number of people using treatment F. Each one has a percentage rise shown in the second column. If the average percentage rise is required, this must be calculated from the values, it cannot be found by averaging the individual percentage values. If the percentage rise column is averaged, it gives the incorrect result of 5.625%, the correct result of 9.07%. 5.625% of 4350 is 244.688 not 394.75 as it should be. Percentages cannot be averaged but this mistake is widespread. If only the percentage changes are given in a study, it is not possible to recover the average percentage change.

Averages themselves are frequently misused or misunderstood. Most people in the population have more than the average number of legs! If 2 people out of 100 only have 1 leg each and the other 98 have 2 legs each, the average number of legs in the group is 198/100=1.98 legs each! This means that most have an above average leg count. The problem is the type of average used. Students of mathematics are taught there are 3 kinds of average. The first is the "normal" one more accurately called the mean where the column of figures to be averaged is added then divided by the number of entries. The second kind counts the most frequently occurring value. In the case of the leg count, this would be given as 2 as most folk have 2 legs and is known as the mode. The third kind is of no use in the leg count, it is the middle value and is known as the median value.

Sadly many think maths is a best forgotten part of their schooling but to understand some of the claims and counter claims of drug companies, governments or advisors, a little understanding helps. So does a little scepticism!

Happy surfing

Howard

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