The following table shows the results of an analysis of variance comparing four treatment conditions with a sample of n = 5 participants in each treatment.Note that several values are missing in the table.What is the missing value for the F-ratio?? $$\begin{array} { l c c c c }
\text { Source } & \mathrm { SS } & \mathrm { df } & \mathrm { MS } & \
\hline \text { Between } & 30 & \mathrm { xx } & \mathrm { xx } & \mathrm { F } = \mathrm { xx } \
\text { Within } & \mathrm { xx } & \mathrm { xx } & \mathrm { xx } & \
\text { Total } & 62 & \mathrm { xx } & & \
\hline
\end{array}$$
A)?0.50
B)?3.75
C)?5.00
D)?45.00

Question

The following table shows the results of an analysis of variance comparing four treatment conditions with a sample of n = 5 participants in each treatment.Note that several values are missing in the table.What is the missing value for the F-ratio?? $$\begin{array} { l c c c c } 
\text { Source } & \mathrm { SS } & \mathrm { df } & \mathrm { MS } & \
\hline \text { Between } & 30 & \mathrm { xx } & \mathrm { xx } & \mathrm { F } = \mathrm { xx } \
\text { Within } & \mathrm { xx } & \mathrm { xx } & \mathrm { xx } & \
\text { Total } & 62 & \mathrm { xx } & & \
\hline
\end{array}$$
A)?0.50
B)?3.75
C)?5.00
D)?45.00

Quizplus · Accepted Answer

To calculate the F-ratio, we need to divide the between-groups mean square (MS B) by the within-groups mean square (MS W). We are given MS B = XX, but we need to calculate df B. To do this, we use the formula df B = k - 1, where k is the number of groups. In this case, k = 4, so df B = 3. We can then calculate MS W by subtracting MS B from the total mean square (MS T), which we can calculate by dividing the total sum of squares (SS T) by the total degrees of freedom (df T). We are given SS T = 62 and df T = 16, so MS T = SS T / df T = 62 / 16 = 3.875. Finally, we can calculate MS W = MS T - MS B = 3.875 - XX = YY. We need to choose the value of XX so that when we divide MS B by MS W, we get the correct F-ratio. We are not given the actual value of the F-ratio, but we can deduce its approximate value by looking at the size of the two mean squares. Since MS B is larger than MS W, we know that the F-ratio is greater than 1. Furthermore, since all of the sources of variation are being partitioned into the between-groups and within-groups components, we know that the F-ratio will reflect the extent to which the means of the four groups differ from each other relative to the variability of scores within each group. A high F-ratio would indicate that the group means differ considerably from each other, while a low F-ratio would suggest that the group means are similar. Based on this reasoning, we can eliminate answer choices A (0.50) and D (45.00). The correct answer must be either B (3.75) or C (5.00). Without additional information, it is difficult to say which of these is more likely to be the correct answer. However, based on the fact that the MS B is larger than the MS W, we might guess that the F-ratio is on the higher side, which would point us toward answer choice C (5.00) as the best option.

The Following Table Shows the Results of an Analysis of Variance