Google

To determine if there are significant differences among group means in an ANOVA, researchers evaluate the computed $$F$$ statistic by finding its corresponding $$p$$-value or comparing it against a predetermined critical value from an $$F$$ table. If the computed $$F$$ ratio is greater than the critical value, the associated $$p$$-value is less than the alpha level (typically $$.05$$). In this outcome, the researcher rejects the null hypothesis and concludes that the population means differ. Conversely, if the $$F$$ ratio is less than the critical value, resulting in a $$p$$-value greater than $$.05$$, the researcher retains the null hypothesis, concluding there is insufficient statistical evidence to claim any differences exist.

Evaluating Statistical Significance in ANOVA

To illustrate a one-way ANOVA, consider a health psychologist comparing the calorie estimates of three distinct groups: psychology majors, nutrition majors, and dieticians. The sample means are $$187.50$$, $$195.00$$, and $$238.13$$, respectively. Using statistical software or an ANOVA table, the researcher finds the between-groups mean square ($$MS_B$$) is $$5,971.88$$, the within-groups mean square ($$MS_W$$) is $$602.23$$, and the resulting $$F$$ ratio is $$9.92$$. With $$2$$ and $$21$$ degrees of freedom, the computed $$F$$ score ($$9.92$$) exceeds the critical value of $$3.467$$. Correspondingly, the $$p$$-value is $$.0009$$. Because this $$p$$-value is less than the standard $$.05$$ alpha level, the researcher rejects the null hypothesis and concludes that the population mean calorie estimates for the three groups are significantly different.

Learn Before

Related