I have a small sample size of 6 (they're conservation projects). They have been scored for 5 project design parameters (5 independent variables). And they have been scored for 2 desired project outcomes (2 [possibly] dependent variables).

What I want to know is do either of these two dependent variables correlate with any of the 5 independent variables - are they dependent? If so how strong are the correlations and can we compare?

With such a small sample size (6 projects) I really don't know what statistical analysis I'm supposed to run. I also don't know what statistical figures I should be paying attention to and comparing.


I would

  1. give up on hopes of finding strong evidence of anything.
  2. avoid a null hypothesis statistical testing framework (i.e. don't trust any p-values).
  3. do an exploratory analysis consisting of looking at lots of plots (to start with, every independent variable against each of the dependent variables) and simply calculating correlation coefficients (while ignoring the p-values).
  4. if you want to be ambitious, you can write a Bayesian regression model and define priors for all the relationships, but it's probably not going to get you much more than an exploratory analysis in this case.
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    $\begingroup$ Abandon all hope, ye who seeks statistical significance with N=6. At traditional type I/II error rates, the correlation coefficient would have to exceed 0.97 before it becomes significantly different from 0. $\endgroup$ – Nuclear Wang Sep 6 '19 at 13:21
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    $\begingroup$ @NuclearWang And even worse, if you find significant results, they are surprisingly likely to be in the wrong direction. Andrew Gelman calls this a 'Type S' (for 'sign') error, as opposed to a 'Type M' (magnitude) error. $\endgroup$ – mkt - Reinstate Monica Sep 6 '19 at 13:27

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