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To find the difference in ages of patient under 2 different groups (drug 1 and drug 2).

age_drug1
[1] 34 34 34 37 40 43 46 47 51 60 62 25 28 30 34 36 38 50 50 50 53 56 60 63

age_drug2
[1] 28 30 34 34 36 39 39 41 43 47 58 68 22 24 36 40 45 55 61

I have tried the Pearson correlation, since the distribution of the age in both groups were normal under Shapiro's test. However, when i try to do the correlation using Pearson's method, corr.test(), it shows error

Error in cor.test.default(age_drug1, age_drug2, method = "pearson") : 
'x' and 'y' must have the same length

Is there another way to check the association? I did try Student's t test unpaired, but I am not sure if that is the right option.

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    $\begingroup$ Correlation does not make much sense here since we don't have paired observations. The samples each seem bimodal and you might want to investigate that. In R, plot(density(age_drug2)); lines(density(age_drug1), col = "blue") $\endgroup$
    – G. Grothendieck
    Feb 28, 2020 at 16:29
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    $\begingroup$ Since it is impossible to apply the usual concept of "correlation" to this situation, please explain to us what you mean by "correlation," "association," or "difference in ages." $\endgroup$
    – whuber ♦
    Feb 28, 2020 at 16:54

2 Answers 2

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It doesn't seem like you are looking for a correlation. First of all, your samples are not paired. Second of all, a correlation won't tell you anything about the absolute difference in ages. For example 1,2,3,5,7 and 98,99,100,102,104 have a perfect correlation of 1 - because they increase in the same increments, but are very far apart.

A two sample Student t-test, like you mentioned, is actually a good way to compare the means of two groups. You can also have a look at the Wilcoxon test.

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A $t$ test will show that the difference in means is not convincing. It's as or more important for most purposes to look at all the data.

enter image description here

This display shows

  • the ages in order (quantile plots; the modality mentioned in a comment does not seem notable to me, but some repeated ages do show up as steps)

  • box plots with percentile whiskers out to 5% and 95% (for the smaller group, these are reported as the extremes)

  • horizontal reference lines showing the means.

The slightly higher mean and median ages for drug 1 are combined with a bigger range for drug 2, but these are small samples, and such features should not be over-interpreted, and much hinges on how they were produced.

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