h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: How To Understand Statistics - A1054117
Author: Atlantic_Cable - U196159

I thought this was a worthy subject for an entry.

Any thoughts or suggestions?

good work.

an interesting fact, some of the more complicated automatic tools won't let you generate a mathematically invalid set of statistics. they do tricks like checking that if a method only works on data with a normal distribution, then the data has a normal distribution.

on often missed problem when working with statistics is the sample size and margin of error. you can often find that with small samples, a change in 1 sample can completely change the results.

Hi

This is a really good entry, and is definatly something people should know more about. After I did this in GCSE statistics I often found myself screaming at the TV 'your graphs have no scale, you are meaningless' quite often disturbing a family member

The only thing that lost me a bit was the mean and average part, may just be me being stupid but i found it hard to understand what you were saying.

Besides that was great

michelle

average is a fairly fuzzy term refering to central tendency.

unfortunately, it is used to refer to all thre of median, mean and mode. as these all have different but related meanings, it is often a cause of confusion, especially with statistics.

Thanks for the feedback. I have made a few corections, mostly about average.

I'll add some example numbers later.

I've now updated the entry with some statistics about the recent cot death cases raising problems with stats in court.

ouch, a really nasty error in there about cot deaths.

you say "Cot deaths statistics should be treated the same way as multiple die roll probabilities", but this is exactly wrong, and what caused her to be locked up in the first place.

it assumes that like dice roles or coin tosses, each case have the same independant probability. in the case of cot death, if I remember the numbers acurately, the odds were 1 in 8000 of a cot death.

however once you have a cot death, the odds go to about 1 in 100 for a second one, and something even more likely that you will go on to have a third.

as you can imagine, this makes quite a difference to the statistic quoted in court. under your independence assumption (which was what the supposed expert used), you get 1 in 64,000,000 for the second case, and 1 in 1024,000,000,000 for the third.

in actual fact they are not independant, and you get much lower numbers, to such an extent that when you reach the third child dying from cot death, cot death is the most likely cause even before you have done a post mortem.

and that is before you add in other evidence like infectionsbing detected. calling mothers of multiple cot deaths serial infantasists is analagous to assuming all air crashes are pilot error, eventually you have to change the assumptions sothat you stop getting miscarriages of justice.

popsting that made me think, and realise that another common error was not getting a mention at all.

fundamental to the mathematics of probability is the requirement for conitional probabilities to be independent of each other, else the maths stops working, and your answers stop making sense.

however a lot of statistics are worked out at a distance from the core events you are working with, so working out if the results are valid can be next to impossible.

oops, that should be conditional propabilities.

Ouch, what a mistake to make. And in this entry of all others! Ouch!

Thanks for pointing out the error, that could have been embarrasing.

I've changed it a little and added some of your comments. What do you think? I hope I haven't made another mistake.

seems fine to me.

in fact, I would sugest that it is now not only ready for peer review, but should fly through it and get selected quickly.

well done.

Thanks, I've moved it.

Is there some easier way to move it other than finding it in writing workshop, remove it and then re-submit it for peer review.

Thanks for your help with it.