Final answer:
The F-ratio evaluates mean differences between treatments, calculated from the MSbetween and MSwithin in ANOVA. A higher F-ratio suggests significant differences between treatment means and may lead to the rejection of the null hypothesis.
Step-by-step explanation:
The statistical measure that evaluates mean differences between treatments is the F-ratio. The F-ratio is calculated by dividing the mean square between groups (MSbetween) by the mean square within groups (MSwithin). MSbetween represents the variation among the different samples (also known as the variance due to treatment or explained variation), and MSwithin represents the variation within samples that is due to chance (an estimate of the population variance).
To calculate the F-ratio, it's essential to know SSbetween (sum of squares between), which is calculated as SStotal minus SSwithin, and the degrees of freedom associated with each. Then, MSbetween is found by dividing SSbetween by its respective degrees of freedom (df for the numerator), and MSwithin is calculated by dividing SSwithin by its degrees of freedom (df for the denominator).
The F-ratio is used in the analysis of variance (ANOVA). If the null hypothesis is false and there is a true difference in group means, the F-ratio tends to be larger than 1 because MSbetween will generally be larger than MSwithin. This leads to a higher F statistic, which might cause us to reject the null hypothesis, suggesting significant differences between treatment means.