Simple demographics calculation

[DaveC426913]

Hi. I'm reporting some stats on my website, and I want to adjust my stats by the demographics. Been a long time since HS math... and I never studied stats anyway.

The following reads more complicated than it really is.


Of the 4095 users that filled out my questionnaire, 3255(79.5%) are female, 772(19%) are male and 68(1.5%) did not specify.

My users lump themselves into 1 of 14 categories (the categories are unimportant). We need look at only one category for now.

91 users that specified a gender were lumped into category #1. Of those 91 users, 70 were female and 21 were male. or 77% females and 23% males. That's more males than average. And that is the interesting piece of information I want to capture here: that Category 1 is a male-dominated category, despite the sheer number of female users that are in it. (I'll do the same for the other 13 categories.)

What I'm not sure about is how I demonstrate this difference in a graph with numbers. What numbers do I end up with after I've compensated for the gender bias in the above example?

I think I should end up with numbers like this - males: 54%, females:46% or thereabouts. I'm not sure how to get here from there.

 

[DaveC426913]

Wow, not one taker?

 

[DaveC426913]

Let me see if I can simplify.

I have 1000 users: 900 female and 100 male.

Of ten categories, Category 1 has 80 females and 20 males.

If Cat 1 were average, there would be 10 males, but instead there are 20. Clearly, Category 1 is a predominantly male category.

How do I express this numerically? As a percent? A ratio?



Before you answer, can I use the same method of expression if the numbers were more realistic? eg:
Overall: Total: 1023; 833F, 380M
Cat 1: Total: 386; 253F, 143M

 

[Nimz]

One candidate method for how to express the relative gender bias would be to consider the probability a person is in a category given that they are male, and the probability given that they are female. To use the numbers in your op, that would be 21/772 and 70/3255 (2.72% and 2.15%) respectively.

If you want to know what the male and female percentages for that category would be if there were equal numbers of males and females completing the questionnaire, find 100/(2.72+2.15). Then multiply that by 2.72 for males and 2.15 for females.

 

[Paula]

Why don't you just say you have a survey of women? Don't try to be so tricky with the numbers, and tell the truth about what you found.

 

[DaveC426913]

Why don't you just say you have a survey of women? Don't try to be so tricky with the numbers, and tell the truth about what you found.

?? Are you implying something about my motives? [Edit] Oh I see, you didn't bother to read the first post. Holy Jeez, way to go off half-cocked.

1] I don't have a survey of women. I have a survey where 3 women for every 1 man participated. My second post is exaggerating and simplifying the numbers so I can make an algorithm.

2] If category 1 was soccer-watchers, I wish to show that, within my sample, soccer-watchers were predominantly male, whereas category 2 (tennis) was predominantly female.

 

[DaveC426913]

One candidate method for how to express the relative gender bias would be to consider the probability a person is in a category given that they are male, and the probability given that they are female. To use the numbers in your op, that would be 21/772 and 70/3255 (2.72% and 2.15%) respectively.

Ah! So to get numbers that add up to 100...

2.15x2.72=4.87 (total for that category)
100/4.87=20.53
20.53x2.15=44.14
20.53x2.72=55.85

So. For category 1: 56% were male, 44% were female.

Perfect!