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Let's say I have two experiments of the same type, where I measure something x times in one location and y times in another location, is there any point in looking for a dependency in values between these two experiments? In case it matters, there's a difference in sample size and both samples have a near normal distribution.

For example, if I would want to measure the length of people in Asia and the length of people in Europe, I could investigate a null hypothesis test H0 'The average length of Asians is smaller than the average length of Europeans.'. This is a valid study.

However, it seems awkward to wonder if the length of Europeans could be influenced by the length of Asians. After all, the length can be influenced by other potential factors, like food, weather, genes, ... If the world population were suddenly to take in growth hormones, then the average length of both Asians and Europeans are likely to increase. It seems silly to assume Europeans increased in length because Asians did. Europeans did increase in size along with Asians, but not because of a direct result.

Is it only worth considering whether two variables have any sort of dependency if they have paired values (like age and weight)? If not, what would be the logical next step to take in order to test for dependency?

I've also noticed that I cannot perform any kind of correlation test since I do not have any paired values. Can I assume as an immediate result that my two variables have no linear dependency?

I tried to find the answer myself, but there are quite a lot of tests and things to be aware of; it gets a little overwhelming for a novice.

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You can certainly do a t-test between the heights of Europeans and Asians. The two sample t-test requires independent data; you seem, somehow, that it requires dependent data.

You may be confusing dependent/independent data with dependent/independent variables. See this blog post of mine

Independent samples t-tests compare the means of the same variable in two different, independent samples (e.g. height in Europeans vs. Asians). Correlation examines the linear relationship between two different variables in the same sample (e.g. height and weight of Asians).

Neither correlation nor a t-test gets at causation.

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  • $\begingroup$ Right. I realize the difference, but I may have been uncareful in my phrases. If I follow the example in your blog with the kids in the same class being considered dependent data, I guess you could say the same for the Asians and Europeans. So I have dependent data, but independent variables, correct? That means I cannot perform the two sample t-test. If I could use it though, how would it work? On wikipedia it says it tests whether the mean of both variables are the same. How should I interpret the result if the hypothesis is likely to be false (in terms of dependency)? $\endgroup$ – Babyburger Dec 1 '13 at 1:53
  • $\begingroup$ No, you don't have dependent data. Where is the dependency ? The t-test does not tell you whether data are dependent or not, it tells you if the means are equal. $\endgroup$ – Peter Flom - Reinstate Monica Dec 1 '13 at 12:55
  • $\begingroup$ @Babyburger It seems that you are keen to seek a test that works in the presence of a number of other (external) factors. In the available literature, we have statistical tests that presume fixed effects. $\endgroup$ – Subhash C. Davar Dec 1 '13 at 13:36
  • $\begingroup$ @Peter In one of the examples in your blog, you say you have dependent data because you chose a particular set of kids in the same class to take a sample of. I figured this applies as well in my example as I select the population from Asia and not from Africa. Local food and climate could have an impact on the length. $\endgroup$ – Babyburger Dec 1 '13 at 19:17
  • $\begingroup$ @davar: I actually don't have any information about any external factors. I used it wrongly in my example as I thought dependency/correlation between two variables necessarily means one variable describes the other variable. Seeing how a dependency between two variables doesn't mean there's a causation, this now confuses me more as I'm not sure what information a dependency between two variables tells me now. $\endgroup$ – Babyburger Dec 1 '13 at 19:25

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