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How I can check the significance level of eta correlation? To assay to see the significance of Pearson correlation, we compare the coefficient with r table, but for eta correlation what can I do?

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The easiest is to use a computer package such as SPSS or STATA to evaluate the significance, I don't think you can easily use tables for this.

If you are a programmer you can use the permutation test (which I think is implemented in some computer packages). With observations $(x_1,y_1),\ldots(x_n,y_n)$, randomly generate $m$ permutations $(y_{(1)},\ldots,y_{(n)}$) and compute eta for $(x_1,y_{(1)}),\ldots(x_n,y_{(n)})$. So you get $m$ permutation values of eta, and the proportion of these that are bigger than the observed eta value is the $p$-value.

Note this is called an exact conditional $p$-value, where the conditioning is done on the observed marginal distributions. You can also do this for the Pearson correlation, and for small samples that may give more accurate p-values than significance tables.

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  • $\begingroup$ Dear WicherThanks for the reply. Your mean is to compare the computed Eta coefficient with the statistical table of the Pearson correlation coefficient. $\endgroup$ – mohammad Jan 12 at 18:42
  • $\begingroup$ You can't use the same tables, in fact I don't think you can use tables for the eta coefficient because it depends on several quantities of the data, so you'll need a statistical computer package such as SPSS or STATA. $\endgroup$ – Wicher Jan 12 at 18:58

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