OR Odds Ratio: Survival of Women vs. Men

Suppose we know the probabilities of survival for women and for men. What are their relative odds of survival? [color=#bb3344]Click and drag the slider [math]p_w[/math] to fix the probability of survival for women.[/color] [color=#666600]Click and drag the big brown plus sign on the x-axis to vary [math]p_m[/math] the probability of survival for men.[/color] Watch the odds change and then check out the odds ratio OR and look at how we write the result in "people language".

It is important to notice that we are calculating [math]OR_wm=/frac{O_w}{O_m})[/math], that is, the odds ratio of [b]women to men[/b]. Typically books write OR and you must check the order of the ratio. Also, we are relating 3 things, namely the probability of survival of women [math]p_w[/math], the probability of survival of men [math]p_m[/math] and their relative odds OR of survival. It is impossible to draw a 2D graph of this! So the function we graph here [list] [*] fixes [math]p_w[/math] - watch the function change as you move the slider for [math]p_w[/math] and [*] uses [math]p_m[/math] as the x-variable and the odds ratio OR as the y-variable - notice OR is always directly above big brown plus sign [math]p_m[/math]. [/list] [b]Questions:[/b] When does OR=1? What happens if [math]p_w \lt p_m[/math]? Who is more likely to survive? What is the opposite situation? Fix p_w= and then find p_m such that OR=2, i.e. such that women are twice as likely to survive as men.