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Simple demographics calculation

  1. May 1, 2006 #1

    DaveC426913

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    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.
     
    Last edited: May 1, 2006
  2. jcsd
  3. May 10, 2006 #2

    DaveC426913

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    Wow, not one taker?
     
  4. May 10, 2006 #3

    DaveC426913

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    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
     
  5. May 11, 2006 #4
    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.
     
  6. May 11, 2006 #5
    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.
     
  7. May 12, 2006 #6

    DaveC426913

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    ?? Are you implying something about my motives? :mad: [Edit] Oh I see, you didn't bother to read the first post. :uhh: :uhh: 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.
     
    Last edited: May 12, 2006
  8. May 12, 2006 #7

    DaveC426913

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    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!
     
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