# Spearman’s Critical Correlation Calculator

Instructions: Use this Spearman's Critical Correlation Calculator to find the critical values for Spearman's correlation $$r_s$$, by specifying the significance level $$\alpha$$ and the number of pairs $$n$$ in the form below:

Significance level $$\alpha$$ (0.10, 0.05 or 0.01) =
Number of pairs $$n$$ (Integer) =
Type of Tail:

Critical Values are used to be compared with a test statistic to assess whether or not the null hypothesis is rejected. In this case, Spearman's sample correlation $$\rho$$ will be compared with the critical correlation values $$\rho_c$$ found by this calculator.

For a two-tailed case, the null hypothesis is rejected if $$|\rho| > \rho_c$$. For a right-tailed case, the null hypothesis is rejected if $$\rho > \rho_c$$ and for a left-tailed case, the null hypothesis is rejected if $$\rho < \rho_c$$. In each case, the critical Spearman's correlation is computed accordingly depending on the type of tail, significance level and sample size.

## Spearman's Rank Critical Values Table

Observe that typically the critical correlation values, both Pearson's and Spearman's correlation critical values are given in tables. Sometimes, those tables are hard to read and it may take long to read the actual value you are looking for.

One advantage of this calculator is that it will give you quickly the exact number you are looking for.

## What does Spearman's correlation show?

Spearman's correlation assesses the degree of linear association between two variables measured at the ordinal level. More specifically, it is assess the linear association of the ranks for a paired sample $$(X_n, Y_n)$$.

## When should Spearman correlation be used?

Using Spearmans correlation is appropriate when the data we are working with is measured at the ordinal level. That is typically is case with data that is related to rankings, etc.

For interval or ratio levels, you should use instead this Pearson's critical correlation calculator, to take advantage of a more statistically powerful test.

In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us.

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