significant change in binomial data?

I want to determine how much of a change in pass rates do I need to observe for it to be statistically significant. For example: pretend there are 2,000 people who took English101 in the last 4 years, and 1500 of them passed the class. 1500/2000 = 0.75 pass rate. I want to set a goal of improving pass rates by X amount in the next 1 year, 2 year, 3 year (etc). How to I determine a statistically significant change? What should my X be? I can estimate the number of future data points. That doesn't change much. Pretend it continues at 500 students per year.

I don't want anything overly complicated. Obviously the data can be grouped by year or as one set. It seems like I should be able to view this data as one set, but I'm not sure if I am oversimplifying it.


TS Contributor
first you need to define a difference in percentage passed that is practically significant for you, i.e. do you even bother if the improvement is 1% ? 5%? The point is you need to define this first, then the sample size.

If you have the practical significance defined, you can simply use any power and sample size calculator from the net to get the necessary sample size.

If you have a pre-determined sample size you can use the power calculator to find the smallest difference that you can detect with a given probability (the power). Then again you need to decide whether that difference is of any practical interest.

I hope this helps