paraphrase: The critical value threshold in hypothesis testing determines whether the observed data are sufficiently extreme to reject the null hypothesis in favor of the alternative hypothesis. This critical value depends on the type of test, the significance level, and the degrees of freedom (Woo, 2019). In ANOVA, which tests for differences in any direction without specifying whether one group's mean is greater or less than the others, a two-tailed test is appropriate (Salkind & Frey, 2022). When manually determining the critical value (F crit) from Table B.3 for t-values needed to reject the null hypothesis (Salkind & Frey, 2022, p. 386), for a two-tailed test, the numerator is the degrees of freedom between groups (df between) = 2, the denominator is the degrees of freedom within groups (df within) = 46, and = 0.05. To avoid inflating Type I Error (false positives), the denominator will be rounded down to the next closest value, df within = 45