Final answer:
MSwithin group is based on the deviations between individual scores and their respective group mean. It estimates within-group population variance and is part of the ANOVA test calculations. It is calculated by dividing the sum of squares within by its degrees of freedom.
Step-by-step explanation:
The MSwithin group, which stands for Mean Square Within groups, is calculated based on deviations between individual scores and their respective group mean. It measures how much the data within each group vary around their own group mean, not the mean of other groups or the grand mean.
In the one-way ANOVA test, MSwithin provides an estimate of the population variance within groups. It involves computing the average of the squared deviations of each observation from its group mean. This is different from MSbetween, which deals with the variation between group means and the grand mean.
To calculate MSwithin, you first find the sum of squares within (SSwithin) by adding up all the squared deviations of individual data points from their respective group mean. You then divide SSwithin by its respective degrees of freedom (df), which is typically the total number of observations minus the number of groups.