# Analysis of proportions over time

My knowledge of statistics is limited and I am looking for resources to read on the matter if possible.

Anyways, I am currently trying to estimate a confidence interval for a proportion over time. The specific example pertains to a trader's Win % as he make more trades. My current idea is to take the first $n$ sample data to calculate a proportion, then see how that changes over the amount of trades. I want to ultimately calculate the variability of the win %. My confidence interval would be calculated as such:

$$p \pm \sqrt[2]{\frac{1}{n} * p(1-p)}$$

I know this is clearly the wrong approach to look into but I would appreciate it if I am pointed to in the right direction.

• I wouldn't be so quick to dismiss this approach as "clearly ... wrong," especially if $np$ and $n(1-p)$ will both be large. It has a theoretical foundation, is easy to compute and interpret, may provide a meaningful envelope around the observed percentage (especially if the square root is multiplied by a suitable constant), and could function well to enhance visual or exploratory examination of the data. One avenue to pursue would be quality-control procedures for count data. – whuber Jun 23 '14 at 20:22
• I will more than likely use a Z-score of 80% confidence. Thanks for the link, I will look into it. – Kevin Pei Jun 23 '14 at 20:34
• An alternative would be to start with logistic regression, and then see if the residuals are correlated in time. – kjetil b halvorsen Jan 27 '17 at 10:35