# The way to evaluate level of significance for coefficient of eta correlation?

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?

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.