Thursday, February 21, 2013

How stats work.

As a minor point in a recent blog post Ben Radford included this remark.

"Except that I didn't; Myers misread it. I actually didn't write the "one billion" figure that Myers misquotes me as saying; that was Ensler's number. What I actually wrote (check it yourself) was that "one-third of women [have been victims of] homicide, intimate partner abuse, psychological abuse, dating violence, same-sex violence, elder abuse, sexual assault, date rape, acquaintance rape, marital rape, stranger rape and economic abuse." (One in three women is not the same as one billion if you do the math, though perhaps that's just my hyperskepticism.)"

Seeing as it was an easy calculation I followed this up in the comments section with a quick back of the envelope calculation.

7billion people on earth x 1/2 women X 1/3 facing these abuses = 1.16 billion women

The math was simple 7/6 or 3.5/3 or about 1. So I'm really not sure where Ben got the idea that 1/3 wasn't 1 billion. So I left in the comments got no reply no correction was made and the comments ( including some by Radford) ignored it. OK fine it was there for anyone to see. I wake up this morning and Michael Kingsford Gray has  responded to my calculation.

"#13 Michaeld:
~ 1/2 are women.
Not true at all, unless your definition of “women” strangely includes female infants.
2/10. Must try harder at arithmetic."
This wouldn't be a problem with my math this would be a problem with what statistics or base assumptions  I used. The math works given the assumptions. Then further down

"#49 Amphigorey
You realize that infants get abused, too?
Yes, rather oddly, I do!
But utterly irrelevant to the blanket categorisation of infants as “women”. An error that you have just amplified.
For reasons that observers can only guess at.
The poster made an error.
They included “infants” in the category of “women”.
Is it not that hard to admit that?"

Is it not that hard to admit that? Well yeah. I'm not going to use your 2/10 or factored 1/5 statistic and here's why, it's apples and oranges. I don't know why I'm always stuck being the one to look things up but here's what you have to do.

If you want to criticize my ratio for women the first step is to find the source of the 1/3 stat and then see how they defined women. If you don't use the same definition then you might as well throw that stat out. There is nothing to say that there is a proportionality to that 1/3 stat (ie girls under 14 might account for 3/4 or 1/10 of that stat) so you can't modify it after the fact you have to go find the new statistic for your new definition of women. OK so where did that the 1/3 statistic come from. To google. This unifem fact sheet sites a report to the UN entitled In-depth study on all forms of violence against women Report of the Secretary-General 2006. Another quick google and we have that report. Now in order to make sure the same definition of women is used in the 1/3 and 1/2 stats we have to check the methodology section.

If my assumption of the definition of women was wrong MKG may well have had a point. Unfortunately page 12 paragraph 20 includes this comment "The term “women” is used to cover females of all ages, including girls under the age of 18." Then just for added measure you can look up the global gender ratio and its estimated at about females to males 984:1000 or 984/(984+1000)= 0.495 rounded 1/2. Thus it makes no sense to use a different stat for women then the original paper does. It would be like doing half your calculation in imperial units and half in SI units you get an answer but it doesn't necessarily mean anything useful cause you didn't keep your variables straight. In fact its even worse because at least those normal units have simple conversions these statistics do not.

So please don't tell me I can't do math when I bit of research shows you don't understand how to use statistics.

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