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I have a group of 10 users. Each user receives a daily notification for one week. Ideally, each user will click on all notifications received. At the end of the week I collect the number of clicks per user.

I would like to measure confidence level interval. I made a histogram of all users' click through rate and found it to be highly skewed. I understand from the literature that I should treat the distribution as binomial and then approximate it to a normal distribution based on few conditions.

I need the click probability $p$ and sample size $n$. How can I obtain the probability value? Shall I (1) calculate $\bar{x}$ and $sd$ for all six clicks or trials for each user, or instead (2) look at the total 60 trials?

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  • $\begingroup$ It depends on whether it is a user or group level analysis. The way you start discussing it, "I have a group of 10 users", suggests that it is a group analysis, so you would use 60 trials, but it is likely that p is not constant for all users, which is a violation of the assumptions of a binomial distribution. It is not a bad place to start, though. $\endgroup$ – mandata Jul 15 '15 at 4:38
  • $\begingroup$ It is a group analysis. So far I have calculated p from the total clicks I have in the group divided by the total nunber of notification. So the normal approx np is the number of clicks and if im not mistaken the binomail distribution will get more and more normal and concentrated around this mean. Is this the right way to go? $\endgroup$ – Yuval Shachaf Jul 15 '15 at 8:48
  • $\begingroup$ It is correct if you work within the limits and the assumptions of the model. If your data reflects the characteristics of the binomial model, then you have a good fit and probably would not need to go further, but if the data does not fit the model, you will need a new one. $\endgroup$ – mandata Jul 15 '15 at 13:47

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