Final answer:
When dealing with missing data in an analysis, the sum of squares for error (SS within) must be used to account for unexplained variation within each group. SS within is derived from subtracting SS between from SS total and is essential for calculating MS within and testing statistical significance.
Step-by-step explanation:
When data is missing from the analysis, especially in the context of an ANOVA (Analysis of Variance), the sum of squares for error (SS within) must be used. This sum of squares accounts for the unexplained variation within each group or sample, which includes random chance or individual differences not due to the experimental treatment. The error sum of squares is calculated by subtracting the between-group sum of squares (SS between) from the total sum of squares (SS total). The formula can be expressed as: SS within = SS total - SS between. This measure is critical for testing hypotheses about whether the differences observed in sample means are significant or can be attributed to chance.
To clarify the concepts using an example, if SS within is 374.5 and SStotal is 621.4, the SS between would be SS between = SStotal - SS within, which represents the variation due to the factor being tested. Knowing SS within is also essential for calculating mean squares within groups (MSwithin), which is an estimate of the population variance, by dividing SS within by its respective degrees of freedom.