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When calculating a correlation coefficient manually without software, statistical significance is determined by comparing the sample $$r$$ value against critical values listed in a reference table for the corresponding sample size and alpha level. If the sample correlation is more extreme than the established critical value, the result is considered statistically significant.

Critical Values of Pearson's $$r$$

When evaluating a manually calculated Pearson's $$r$$, what condition indicates that the result is statistically significant?

When a researcher manually calculates a Pearson's $$r$$, the correlation is deemed statistically significant if the calculated sample value is less extreme than the critical value found in a reference table.

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