H, I have a question where I am not sure if what I calculated is correct.

So there are two therapies, A and B with 48/60 and 25/40 being healed respectively. I shall calculate the 95% CI

I now should calculate the confidence Intervalle for the difference of „proportions“ ( not sure what the English term is, i tried to look it up, but cant find anything useful) I am using the formula

$$(p_1-p_2 )+-Q_(1-\alpha/2)(N(0,1))* \sqrt{p_1(1-p_1)/n_1 + p_2(1-p_2)/n_2}$$

I am still getting used to math Jax....

So that would give me (-1/200, 71/200) And that negative sign just makes no sense imho. How can a proportion be negative.... but i cant find where i made the mistake....

I would be so grateful for your help :)

  • $\begingroup$ The confidence interval depends on the distribution of probabilities. By considering a normal variable for something that is supposed to be limited to (0, 1), then you get errors because the Gaussian law can take any value, not just in (0, 1). $\endgroup$ – Matthieu Brucher Dec 21 '18 at 11:53
  • $\begingroup$ Hmm, ok, to be honest our professor just gave us this formula and we are supposed to use it. How would i do it differently? I don’t have very much knowledge to start with. It’s an intro course and all we got in the handout and in the lecture is this formula and 3 more for other CI. I am somewhat lost... $\endgroup$ – Lillys Dec 21 '18 at 12:18

This is a common cause for surprise. You are calculating the confidence interval of the difference in proportions, not the proportions themselves. So it is perfectly possible for the difference to be negative. The difference has to lie between -1 and 1.

Just for completeness in his paper entitled "Interval estimation for the difference between independent proportions: comparison of eleven methods" available here Robert Newcombe gives some better methods which ensure the difference remains legal.


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