# Converting binary data to percentage

I've done an experiment where I recorded a positive or negative result from a cell. My data is set in tables of counts of events and trials, but I don't know how to do statistical analysis on binary data, I need to test the significance between the groups I tested. Can I convert to percentage and do a stats test on that, converting it to continuous data?

• I gather your response is binary (positive vs. negative). What is the status of your explanatory variables? Do you have any (eg, experimental condition vs. control condition)? Are there more than 2 groups tested? Do you want to control for, or assess the influence of, any other variables (eg, number of mitochondria in each cell)? The appropriate analysis will depend on these features. – gung May 4 '13 at 21:12
• I tested two doses of a drug, and recorded the number that stained positive for what I was testing, and recorded the total number of cells I counted. I also included a control of no drug, and a control, which included a substance that was found in the drug solution I was using. For each variable, I had three samples. I carried out this test on two separate cell cultures. – user25250 May 5 '13 at 10:38

You could do, providing the denominator of each proportion is about the same (or you'd be treating $\frac{1}{2}$ as equivalent to $\frac{500}{1000}$). And it would probably be a good idea to use a variance-stabilizing transformation: for proportion $p$ the angular transformation gives a response $y=\arcsin\sqrt{p}$.

But all that's a bodge & not much less effort than doing it properly with a generalized linear model: look up log-linear models for contingency tables or logistic regression.