Final answer:
In one-way ANOVA, MS(Error) is used within the F-ratio to measure the individual variance within each group, which is compared to the variance between group means to determine if significant differences exist.
Step-by-step explanation:
In one-way ANOVA, MS(Error) or Mean Squares Within is used within the F-ratio as a measurement of the variance of individual observations. Specifically, this component of the F-ratio represents the average of the squared differences between the observations in each group and the respective group mean, which is an estimate of the variance within groups. The one-way ANOVA F-ratio is the ratio of the variance between the group means (Mean Squares Between or MS(Between)) to the variance within the groups (MS(Error)).
To calculate the F ratio, two estimates of the variance are compared: the variance between samples, which reflects the variation in the sample means (sometimes referred to as the treatment effect), and the variance within samples, which reflects the variation due to individual differences within each group.
The goal of a one-way ANOVA test is to determine if there is a statistically significant difference among the group means. This is done by analyzing and comparing the variances within and between groups to decide whether the observed differences in sample means are likely due to random chance or whether they reflect a real effect.