Calculating the percentage change of 2 values If I have two different percentages and I wanted to know the change, I would simply use the percentage change formula...but what if I want to compare two percentages that have different amounts: 
Ex: August - there was 539 right answers out of 743 = 72.5 %
September - there was 498 answers out of 820 = 60.7%
How can I do a monthly comparison of change between those 2 percentages?
It was suggested to me that I use LCD, but those numbers could be massive if I have a larger set of numbers like in the thousands.
So, should I analyze the months separately or what should I do?
**I want to do a comparative analysis on the students who took the exam in august vs the students in september. LCD = lowest common denominator.  Can this be done?
 A: The percentages have different levels of accuracy determined by the respective sample sizes. If you assume the number of correct answers is binomial in each month with unknown parameter p$_1$ (unknown) and n$_1$=743 in August and p$_2$ (unknown and possibly different from p$_1$) and n$_2$=820. Then assume the August and September samples are independent. Consider the difference of the sample estimates.  The variance for that difference is p$_1$(1-p$_1$)/743 + p$_2$(1-p$_2$)/820.  The standard deviation is the square root of that variance.  The sample estimates of p$_1$ and p$_2$ can be plugged in to get an estimate of that standard deviation.  You can divide by it and use the normal approximation to get approximate confidence intervals or a pooled estimate of the standard deviation for hypothesis testing.
A: I think you're looking for a complicated solution to a relatively simple problem. Unless I'm misunderstanding, you want to compare August's 539 / 743 = 72.5% to September's 498 / 820 = 60.7%. The difference, in percentage points, is a fine comparison: The accuracy dropped by  11.8 percentage points (11.8 = 72.5 - 60.7). You could also calculate the percentage difference in the percents using the "percentage change formula" 11.8 / 72.5 * 100 = a drop of 16.3% in the percent accuracy, but part of the advantage of converting to percents in the first place is that you don't have to do anything more to give the numbers scale.
Related XKCD
