Google

The mean squares within groups ($$MS_W$$) is an estimate of population variance based on the differences among the individual scores within each group in an analysis of variance. It is calculated by dividing the sum of squares within groups by the within-groups degrees of freedom, and it serves as the denominator for the $$F$$ statistic.

Mean Squares Within Groups

Stable individual differences refer to the consistent, underlying physiological or psychological traits—such as variations in individuals' nervous systems, muscle reflex speeds, or cognitive abilities—that cause some participants to naturally perform faster or slower than others. In an analysis of variance, these inherent variations contribute to the variability within groups. While they inflate the mean squares within groups ($$MS_W$$) in between-subjects designs, they can be statistically measured and partitioned out of the $$MS_W$$ in within-subjects designs, resulting in a more sensitive statistical test.

Stable Individual Differences

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