# Incorrect interpretations of statistical results

1. Apr 10, 2014

### 15123

There had been a case in the UK where a woman's two babies died one after the other. Then some apparent statistician concluded 'If the chance of that occuring is 1 in a million, then she must have killed her babies'. Later, a very long court of law had been doing research on it and she appeared to be innocent because some clever statistician then concluded: "1 in a million in a population of 10 million means she likely did not kill her babies because the chance is great they die at birth, in her population".

My professor stated:
"If there is a 1/1000.000 chance of a baby dying at birth, then if the population is 10.000.000 people, such deaths occur very frequently because it happens 10 times in 10.000.000."

I don't understand this reasoning at all. How is 10 times in 10.000.000 considered as 'very frequent'? Completely illogical to me.
When I asked someone else, they said that you cannot state it is very frequent by that number alone and that you need a 'base amount' (cf. http://en.wikipedia.org/wiki/Base_rate_fallacy). Frequency should be relative to the base amount.
The relative frequency in this case is 10/10.000.000. The absolute frequency could perhaps be obtained by using Bayes' theorem?

I still don't understand the logic behind the claim that 10/10.000.000 is 'very frequent'.

2. Apr 10, 2014

### Stephen Tashi

As far as I know, the terms "frequent" and "very frequent" have no standard definitions in mathematical statistics. The opinions you are quoting are subjective. Perhaps you can rephrase the question so it has some objective interpretation.

3. Apr 10, 2014

### daveyrocket

Perhaps what he means is that it's frequent enough that when a single such instance is examined, you can't conclude that she murdered her babies based on the statistical improbability of it happening. The first claim was that if it happens at all, it's got to be murder because it's too improbable of it happening by chance.

4. Apr 10, 2014

### Stephen Tashi

Those are subjective possibilities also. I think the question of what constitutes evidence to various people is best discussed in the "General Discussions" sections or wherever forensic science questions belong. Or perhaps, someone can formulate a specific mathematical question that is relevant.