Incorrect interpretations of statistical results

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. Base rate fallacy - Wikipedia, the free encyclopedia). 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'.

Re: Incorrect interpretations of statistical results

Considering the advanced tech in britain, 10 deaths per 10 000 000 is quite alot and 10 lives should be thought to be a large number as it is precious lives they are talking about.

Re: Incorrect interpretations of statistical results

as you said without something to compare it to the phrase "very frequent" is meaningless. Compared to the number of people that spontaneously change gender 10 out of 10 million is quite frequent. Compared with the number of people that take sugar in their coffee it's not very frequent at all.

Re: Incorrect interpretations of statistical results

What if we compare the two subsequent deaths of the babies of specific case of this mother to the amount of subsequent deaths of babies that happen in a population of 10 million people?

Re: Incorrect interpretations of statistical results

Quote:

Originally Posted by

**s7475** What if we compare the two subsequent deaths of the babies of specific case of this mother to the amount of subsequent deaths of babies that happen in a population of 10 million people?

10 deaths in 10 million is 1 in a million so the two are equivalent. If the number of infant deaths is 10 in 10 million, Then the chances of a single mother's two infants both dying is given by

Pr[2 out of 2 infants dying] = $\left(\dfrac 1 {1000000}\right)^2 = 10^{-12}$

So the initial assertion of how likely a single mother losing both infants was off by a factor of a million.

It does seem unlikely that a single mother losing 2 infants is due to chance alone. But that is hardly justification for homicide charges without further evidence of foul play.