Final answer:
MSwithin in an ANOVA is calculated using the formula MSwithin = SSwithin / dfwithin, where SSwithin is the variation within groups and dfwithin is the degrees of freedom within.
Step-by-step explanation:
The Mean Square Within Groups (MSwithin) is a key component in ANOVA (Analysis of Variance) and is calculated by the formula MSwithin = SSwithin / dfwithin. Here, SSwithin represents the sum of squares within groups, which measures the variation within each sample due to chance. The denominator, dfwithin (degrees of freedom within), is calculated as the total number of observations minus the number of groups (n - k). In the context of an ANOVA table, the Mean Square Within Groups (MSwithin) is used alongside MSbetween (Mean Square Between Groups) to compute the F statistic, which helps to determine if the sample means are from populations with the same mean.