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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 determining the statistical significance of a manually calculated Pearson's $$r$$, what condition must be met when comparing the sample value to a reference table?

In manual statistical testing, a Pearson's $$r$$ value is considered statistically significant if the calculated sample correlation is closer to zero than the critical value found in a reference table.

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