# Can you calculate descriptive statistics (SD, SE particularly) from percentages and ratios?

I'm a cell biologist and a lot of my data is expressed as a fraction (percentage) of the total number of cells in a single experiment in a number of separate categories (generally 5 or so). The number of cells in any given experiment is usually in the hundreds, but the number of individual experiments (replicates) is usually three.

Currently what I'm doing is pooling all the data from the three independent experiments and expressing each category as a percentage e.g. Cat1 70%, Cat2 15%, Cat 3 10%, Cat 4 3%, Cat 5 2%. In the figure legend I state supply the total number of cells and the number of independent experiments they derive from.

However, it would be nice to have some sense of how much those category values vary across the three experiments. A colleague recommended that instead of pooling all the data, I calculate the percentages from each experiment, and then calculate mean/SD/SE from the three percentages in each category (one from each independent experiment).

Is this valid? I seem to remember from school that descriptive statistics are based on the assumption that the data are continuous, and that expressing them as a percentage (or fraction) has already converted them to a discontinuous variable. If it's not valid, is there a better way of doing it? It would be desirable to be able to continue to express the results as a fraction/percentage of the total, as the number of cells per experiment will never be exactly the same.

• If you consider 1 experiment as one observation, then it makes sense to treat a percentage as a continuous variable. But technically, I think an observational unit in your case is a single cell, not an experiment, so your outcome is categorical. Is there a reason why you do 3 experiments instead of doing all cells at once? Do you keep count of how many cells you had? Also, keep in mind that you can calculate sd/se for categorical variables very easily too. – Hotaka May 21 '15 at 16:29
• Three experiments are done to control for human error. A single large experiment may contain any number of unintended human errors (hopefully none! but you can never be sure). If the same/similar results are obtained in multiple independent experiments then one can be reasonably sure of the conclusions. I do keep count of how many cells I have but the total number will vary from one experiment to the next (not by a huge amount, but still). – bcm_22 May 22 '15 at 15:35
• I see. Then it might be good if you reported the reliabilities/consistency between the 3 experiments, then report the pooled results of the 3 experiments. – Hotaka May 22 '15 at 16:05
• OK, great. What is the best way of reporting the reliabilities/consistency between the experiments? Or can you recommend somewhere I can learn how to do this? Huge thanks in advance. – bcm_22 May 24 '15 at 14:49