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In a one-way ANOVA, the shape of the $$F$$ distribution is determined by two distinct degrees of freedom ($$df$$) values. The between-groups degrees of freedom is calculated as the total number of groups minus one ($$df_B = G - 1$$). Simultaneously, the within-groups degrees of freedom is computed as the total sample size minus the number of groups ($$df_W = N - G$$).

Degrees of Freedom (One-Way 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.

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