Many who argue against the routine use of vaccinations pray in aid statistical arguments to the effect that vaccines do not work.

You may have seen the argument, which usually goes something like this:

In March 1997, in Marstlepit High School, there was an outbreak of trembles. 100 children caught the disease and 70 of those children had previously received trembles vaccinations. A massive 70% of children catching the disease were vaccinated, clearly showing the total inefficacy of the trembles vaccine.

(NB – Both Marstlepit High School and the trembles disease are completely fictional. They must be, I just made them up. Also fictional is the nasty side effect of marbling, which I will come onto later.)

Hold on. Does that really work? Don’t we need to know how many children there were in Marstlepit High School, and how many were vaccinated?

Take these three illustrations, each assuming that we are dealing with a population of 1000 children at Marstlepit High School:

(A) 970 children had been vaccinated against trembles, 30 hadn’t. All 30 unvaccinated children caught the disease, while only 70 out of the 970 vaccinated children (i.e. only 7.2%) caught the disease. The vaccination reduced the risk of catching trembles in the event of an outbreak from 100% in unvaccinated children to 7.2% in vaccinated children, so the vaccinated children had a much reduced risk of catching the disease than the unvaccinated ones.

(B) 700 children were vaccinated, 300 were not. Of the 100 children that caught trembles, 70 were vaccinated and 30 were not. The proportions were exactly the same and vaccination made no apparent difference to a child’s chances of catching trembles in the outbreak.

(C) 100 children were vaccinated, 900 were not. In the outbreak, 70 vaccinated children (i.e. 70%) catch trembles and only 30 unvaccinated children (i.e. 3.3%) catch the disease. Here, children who have been vaccinated are at a massively increased risk of catching the disease in an outbreak.

See what I mean?

Before the figures can mean anything, you need to compare the proportion of vaccinated children who caught the disease with the proportion in the relevant population.

Is a vaccine fairly described as “ineffective” if any vaccinated child catches the disease? I would say not. I would say that a vaccine significantly reducing the numbers of children catching the disease is an effective vaccine. That it may fail in some individual cases is not enough to call the whole vaccination effort a failure.


On the other side of the fence, those arguing for vaccines can be equally guilty of using statistics which are incomplete and thereby creating a misleading picture of vaccine safety.

Again, you’ve probably seen the argument used. It goes something like this:

With the vaccine against trembles, there is a 0.1% chance (one in a thousand) that the patient will experience the dangerous side effect of marbling. However, if the patient were to catch trembles naturally, there is a much greater chance of marbling, at around 1%. Therefore, it does not make sense to worry about marbling as a side effect of the vaccine.”

This argument usually ignores, or conceals, a number of important points.

Firstly, we need to know what proportion of unvaccinated people catch trembles:

(A) Suppose that 5% of unvaccinated people catch trembles. In that case, if you left your child unvaccinated, she would have only a 5% chance of catching trembles and then a 1% chance of marbling if she did catch trembles. In all, the chance of marbling is 1% of 5% i.e. 0.05%. This is, we can see, a much lower risk of marbling than occurs if you vaccinate.

(B) Suppose that 10% of unvaccinated people catch trembles. Doing the same calculation, the chance of marbling is 1% of 10% i.e. 0.1%. The same as the vaccination risk.

(C) Finally, suppose that 50% of unvaccinated people catch trembles. The same calculation gives a marbling risk of 1% of 50% i.e. 0.5%. This is significantly higher than the vaccination risk (but still only half what is suggested by the claim under discussion, which altogether misses out the point that the chance of catching trembles is a relevant factor).

Secondly, we need to know what level of protection the vaccination provides. We need to understand both whether the immunity is permanent and also whether 100% of vaccinated children become immune. If the vaccination does not provide 100% permanent protection then the child could be at risk of marbling twice: once when the vaccination occurs and then again if the child later catches trembles despite having been vaccinated.

Thirdly, we need to know how many shots of trembles vaccine are needed to create immunity, and how the risks change with each successive shot. Is the child at the same risk of marbling both after the first shot, and the second, and the third… If so, then with three shots the risk of marbling is potentially 0.3% – much higher than advertised!

Finally, I would like to examine that risk of marbling after catching trembles in more detail. It is put at 1%, but let us suppose that a recent study showed that the risk of trembles complications such as marbling is strongly associated with Vitamin Q deficiency.

While the overall figure for trembles-related marbling may be 1% of trembles cases, when you break the figures down into groups (e.g. Vitamin Q deficient or not) a very interesting picture emerges. Children who are deficient have a 10% chance of suffering marbling as a complication of trembles. Children who are not deficient have only a 0.1% chance of suffering that complication. This is the same as their chance of suffering marbling as a side-effect of the vaccination!

And – here’s the clincher – they still only have a 10% chance of catching trembles at all, so the real risk of marbling in an unvaccinated child can be reduced to a mere 0.01% simply by ensuring that they get enough Vitamin Q. A child is therefore much better off, from a marbling perspective, being given vitamin drops than the trembles vaccine.

Of course, for “Vitamin Q deficiency” you can substitute any other factor that is associated with an increased risk of marbling as a complication of trembles. For example, a failure to treat trembles quickly enough, or unsanitory living conditions might increase the risk of marbling – yet these kinds of factors are entirely ignored by the “pure” statistical arguments.


Those presenting the case either for or against vaccinations need to present their figures fairly if they are to do the public anything but a disservice.

All the relevant factors need to be brought into consideration to help parents understand the true risks they are taking when deciding whether or not to vaccinate their children. Otherwise we may as well pretend that we are in a debating society where it does not matter who is right, and all that matters is who scores enough points to win the debate.

Moreover, it is difficult to take an argument seriously when it does not deal with the issues honestly or fairly, but seeks to misrepresent the true picture by misleading use of obviously incomplete statistical evidence. If the vaccines are at least to some extent effective, those presenting the case against vaccines would do well to acknowledge this honestly in their arguments. To the extent that the vaccines do have side effects, then comparisons with the consequences of catching the disease must be made honestly and fairly.

No matter how right your conclusion may be, if I can see that your argument to that conclusion is dishonest then I cannot take you seriously and will not listen.