Distribution of the F Ratio

What is the correct mathematical formula for computing the F statistic in an analysis of variance (ANOVA)?

Based on the mathematical structure of the F-statistic formula ($F = \frac{MS_B}{MS_W}$), rank the following research scenarios from the one that produces the largest F-value to the one that produces the smallest F-value.

A researcher concludes that because the variability within their groups ($MS_W$) is larger than the variability between their group means ($MS_B$), the resulting $F$ statistic ($F = \frac{MS_B}{MS_W}$) provides sufficient evidence to support their claim that the experimental treatment was effective.

In an analysis of variance (ANOVA), the $F$ statistic is calculated by dividing the mean squares within groups ($MS_W$) by the mean squares between groups ($MS_B$).

A researcher conducts a psychological experiment and analyzes the data using an analysis of variance (ANOVA). Conceptually, what does it mean if the computed $F$ statistic ($F = \frac{MS_B}{MS_W}$) is substantially greater than $1.00$?

A clinical psychologist studying the effect of different therapy types on anxiety scores finds that the mean squares between groups ($MS_B$) is 18.0 and the mean squares within groups ($MS_W$) is 6.0. Using the formula $F = \frac{MS_B}{MS_W}$, the calculated F value for this study is _____.

In a one-way ANOVA, the F statistic is calculated as $F = \frac{MS_B}{MS_W}$. Match each component or concept to the role it plays in this formula.

A cognitive psychologist tests memory recall under three room temperature conditions (cold, comfortable, hot) and conducts a one-way ANOVA. Match each component of the $F$ statistic formula ($F = \frac{MS_B}{MS_W}$) to its correct application in this experiment.

A researcher conducting an ANOVA finds that the mean squares between groups ($MS_B$) and the mean squares within groups ($MS_W$) are identical. Based on the formula $F = \frac{MS_B}{MS_W}$, the calculated $F$ statistic will be _____.

Rank the following ANOVA research outcomes from the one most indicative of real group differences (highest computed $F$ value) to the one least indicative of real group differences (lowest computed $F$ value).