# How to graphically compare distributions of a variable for two groups with different sample sizes?

I'm not familiar with statistics terminology, so I can't google it unless I know what it's called.

My problem is this: I have a "test" (for lack of a better term) where I ask people to choose an answer. At the end of the test I'm asking if the person is a programmer or a designer, I assign a score from zero to ten and then I want to graph the results from both populations.

Problem is, right now I have more answers from developers (about 2 to 1). What is the fairest way of normalizing this data? The results are looking a lot like bell curves, should I just scale the graphs so that they match?

You can see the test here: http://method.ac/test

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## 2 Answers

### Some graphing options

• I agree with @John's suggestion of converting the scores into within-group proportions. If the score only has 11 scale points (0 to 10), you may want to align histogram bins with each of these 11 values.
• You could generate density plots for the two groups. Quick-r has an example using the sm.density.compare function in the sm package.

### Some broader options

• However, taking a step back, you may wish to also report some numeric descriptive statistics for the two groups. For example, you could compare the mean, median, skewness, standard deviation, and various quantiles for the two groups. Having unequal group sizes is not a problem when comparing these descriptive statistics (other than the fact that your estimates of the smaller group will be less precise than that for the larger group).
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It sounds like you're graphing a histogram. Convert the y-axis from counts to proportion of the total. Make sure that the range on the two graphs is the same after this conversion.

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Ah thanks, I wasn't sure if graphing it proportionally would be statistically valid. Thanks! –  Duopixel Aug 1 '11 at 23:58
(then accept the answer fo future generations) –  John Aug 2 '11 at 7:35
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