# Difference in means vs difference in proportions

Can i use difference in proportion test to compare two ratios i.e the average height of two groups a and b are 1.4m and 1.6 respectively. Assuming i have the sample sizes of these groups, can i use difference in proportions calculator (test) to evaluate whether there is a significant difference between the heights of the two groups instead of difference in means hypothesis test?

What happens if the heights are 0.7m and 0.6m respectively?

Is using difference in proportions calculator to identify whether there is a significant difference between the two groups highlighted above a right approach. If not, how does this flawed interpretation change w.r.t to the values being compared?

• Could you explain how you would convert a length like 1.4 meters into a proportion? What proportion would that be?? – whuber Sep 26 '17 at 20:25

## 2 Answers

The simple answer here is "No". A slightly longer answer is "No, and why would you want to do that?"

The problem of testing the difference in means (or other measures of location) of two groups is very well studied and has lots of solutions depending on the exact circumstances, but the most basic is a simple t-test.

At the start of your question you mention ratios. I'm not sure why you do that, but ratios are also not proportions. If you want to test the difference in two ratios, that would be a different question, but here you seem to have just one ratio.

• The actual test here is as below. – Hari Oct 1 '17 at 6:47
• The actual test here is as below The death rate below 30 years of two groups A and B is .46 and .59. The sizes of A and B are 1786 and 1325 respectively. What hyp test should I be using for this one and why not the other two among Diff in means, Diff in props and Diff in ratios. I know the statistic calculation for the three, although not the ratios test, but I will figure it out. Is it the assumptions of distribution or the statistics alone that have a say in this problem. I am reading hp test regarding all the three and the answer to this questions sets in place a lot of my understanding – Hari Oct 1 '17 at 6:58
• You can teset difference in proportions. – Peter Flom Oct 1 '17 at 12:28

If I understand you correctly you are talking about comparing a measured value with a test normally used for rates. There is a distinction in the underlying distribution. One would expect the measured value to be distributed somewhat normally and the rate to be distributed binomially. To compare in each of these scenarios there is no canonical test. A typical one for Gaussian case is the Students t-test. For the Binomical case the Fisher exact test is pretty common.