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It is possible to compare a variable, for example age, between an entire group of patients and a subgroup of patients (a part of the entire group)?

Dimitrie
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    You have to be more precise because it is not clear what you are asking. Compare what to what? Could you give an example? – Tim Jan 23 '15 at 09:47
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    You mean like asking the question "is the mean age of patients suffering from Alzheimer's significantly different from the mean age of all patients in the hospital?"... sounds like a reasonable thing to compare to me – Dan Jan 23 '15 at 09:47
  • I have 221 patients that were evaluated in a study. From the entire population, 167 patients were also evaluated by echocardiography. I was wondering if the mean age (among other variables) was similar between the entire population and those who had also the ecocardiography. – Dimitrie Jan 24 '15 at 22:10

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Yes you can.

However, I would think its only appropriate if you remove your subgroup from the "entire group" data such that they are independent measures.

Next I would also worry about the interpretation of the result. Is this leftover "entire group" really representative of something now that you've remove some subgroup of interest?

But to repeat, just in terms of "can you compare to groups' ages to one another"... Yes of course.

Under parametric assumptions a t-test will do just fine.

Mensen
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  • One could leave the subgroup in but take account of the dependence ... but the result would be the same as the (simpler) choice of removing the subgroup and comparing without having to deal with that source of dependence. – Glen_b Jan 23 '15 at 16:44
  • Thank you for all the answers. I thought that this was the answer, but my problem was that, in my opinion, they were dependent. – Dimitrie Jan 24 '15 at 22:08
  • @Glen_b How can I consider the dependence of the group and subgroup in a, for example, a t-test? – giordano Aug 24 '15 at 12:49
  • @giordano As I explain above, the result is the same as just doing an ordinary t-test applied to the whole-without-the-subgroup vs the subgroup. – Glen_b Aug 24 '15 at 15:07
  • @Glen_b That's clear. But I was not interested in the result but in how to cope with dependence, how to take account the dependence. – giordano Aug 25 '15 at 20:12
  • In the t-statistic, you need to calculate the variance of the numerator correctly (i.e. $\text{var}(\bar{y}-\bar{x})$, to use in the calculation of the denominator), and show that the numerator and denominator are still independent. Then the statistic will have a t-distribution (though you also need to take care when finding the degrees of freedom). The variance of $\bar{y}-\bar{x}$ can be found from basic properties of variance; it's $\text{var}(\bar{y}) + \text{var}(\bar{x}) - 2 \text{cov}(\bar{y},\bar{x})$ – Glen_b Aug 25 '15 at 23:02