Incorrect interpretations of statistical results

[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 occurring 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'.

 

[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.

 

[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.

 

[Stephen Tashi]

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.

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.

 

[blue_raver22]

It is important to note that statistical results should always be interpreted carefully and in context. In this case, the initial conclusion that the woman must have killed her babies based on a 1 in a million chance is incorrect. The statistician who later concluded that it is unlikely for her to have killed her babies based on the population size and the chance of death at birth is also not entirely accurate.

There are a few issues with this interpretation of the statistics. First of all, the statistician is assuming that the population size is representative of the population in which the woman's babies died. This may not be the case, as there could be other factors at play such as socioeconomic status or access to healthcare that may affect the likelihood of infant mortality.

Additionally, the statistician is not taking into account other potential explanations for the deaths of the babies. It is important to consider all possible factors and not jump to conclusions based on a single statistic.

Furthermore, the use of Bayes' theorem to calculate the absolute frequency is not appropriate in this situation. Bayes' theorem is used for conditional probabilities and requires prior knowledge of the probability of the event occurring. In this case, there is no prior knowledge and the statistician is only using the population size and the chance of death at birth to make their conclusion.

In conclusion, it is important to interpret statistical results carefully and in context. One should not jump to conclusions based on a single statistic and should consider all possible factors before making any claims. It is also important to use appropriate methods and not make assumptions about the population based on limited information.