I am conducting statistical tests for my current research project. Within the scope of this research project, I have two samples (divided by country clusters). The samples contain approximately 1500 entries each. The spoken languages differ within the samples but also across the samples.

  • The first sample contains participants' responses and other variables from four countries (e.g. USA, UK) that are similar in their cultural dimensions, while
  • The second sample contains participants' responses and other variables from four different countries (e.g. South Africa, Australia) than in the first sample.

I tried to choose the samples based on the fact that the cultural dimensions of these two samples are as different as possible. By choosing different countries for each sample, I tried to have independent samples. My independent variables are two cultural dimensions, while my dependent variables are:

  • 2 categorical variables (excluded from the ANOVA because of the measurement scale requirement)
  • 4 interval variables

My supervisor wants me to conduct tests on independence to be sure that the samples are independent of each other so that I can use an ANOVA (or another non-parametric equivalent) in the next step.

For the interval variables, I have already conducted Shapiro Wilks Tests as well as created histograms and GGQ plots. These showed a non-normal distribution. I also applied the Levene Tests that showed homogeneity for two out of the four interval variables.

However, to start with my actual analysis, I still need to find a way how to check the independence across samples. Thus, my question is:

Is it possible to conduct a Chi-Square Test for Independence on these two samples to find out whether they are independent or paired? I would run a Chi-Square Test for each dependent variable separately. Or is there another statistical test to determine whether my samples are statistically independent or paired?

  • $\begingroup$ Somehow I don't think your question tells enough of the story for us to give good advice: What data does your adviser propose you use to check for independence? If you're ultimately testing whether the two samples differ as to responses, how would ANOVA be used instead of a two-sample test? Are responses normally distributed--or even continuous numerical variables? // ZA = South Africa? AU = African Union? $\endgroup$ – BruceET Jul 1 '20 at 20:30
  • $\begingroup$ @BruceET Thank you for the information, I added the missing information to my original question. I hope the question is clearer now. Thank you for your help! $\endgroup$ – Annanas Jul 2 '20 at 8:07
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    $\begingroup$ It is hard to answer this because normally the question of whether two samples are independent or paired is one of the study design so one would not need a test to establish it. As it stands I would assume a response from someone in the US was independent of a response from someone in any other country but that is so obvious that I feel I do not understand your question. $\endgroup$ – mdewey Jul 2 '20 at 12:12
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    $\begingroup$ I agree with @mdewey except that I think the misunderstanding may lay elsewhere - that either your professor is confused or that what he said isn't what you thought he said. Having dealt with many grad students in various fields over the years, I think both of those are quite possible, but that the possibility that the professor is confused is underestimated. $\endgroup$ – Peter Flom Jul 2 '20 at 13:27

Expanding on what @mdewey said in a comment: The question of whether two samples are independent is part of study design and is established by logic and knowledge of the field and the particular study. This can get confusing because we also use "dependent" and "independent" in other ways; in particular, we say that one variable depends on another.

Samples are dependent when something about the observations in one sample tells you something about the observations in the other sample.

Suppose we wish to test whether married men have different IQ from married women. One way to test this would be to get a random sample of married men and a random sample of married women, give them all IQ tests and then analyze (perhaps with a t-test or maybe a regression, with covariates). Here the samples are independent and an independent sample t-test or (the usual) regression would be appropriate.

Another design would be to get a random sample of couples and give them all IQ tests. Here, the samples are dependent -- people don't choose spouses at random and, while people don't (usually!) choose spouses based on IQ, they do choose from among people they know and this introduces dependence -- if you meet people at school or work they are likely to have similar IQs. Here, the dependence would have to be accounted for (e.g. by paired t-tests, a multilevel model, or some other method).

Unless I have missed something or there is something that you left out about the design, your samples are independent.

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    $\begingroup$ Thank you, @Peter Flom! I really appreciate your answer! $\endgroup$ – Annanas Jul 2 '20 at 19:59

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