Statistical Significance

When an estimate achieves statistical significance, the thing estimated is likely to be not zero, and so becomes especially worthy of further attention. Significance tests are applied to univariate statistics, such as the mean; to bivariate statistics, such as Pearson's correlation coefficient; and to multivariate statistics, such as the slope coefficient in a multiple regression equation. For example, if a Pearson's correlation coefficient between variable X and variable Y attains statistical significance at .05, the level most commonly used, then we can reject the [Page 1081]null hypothesis that X and Y are not related in the population under study. If, however, the correlation is not found significant at .05, we tend to think, at least initially, that the link between X and Y does not merit further study. Thus, statistical significance serves as a gatekeeper, encouraging further consideration of coefficients that “pass through the gate” and discouraging further consideration of coefficients that fail to “pass through the gate.”