An economist wants to determine whether average price/earnings (P/E) ratios differ for firms in three industries. Independent samples of five firms in each industry produced the following results after conducting a one-way ANOVA. SSB (sum of squares between groups) = 258.82 and SST (sum of squares total) = 424.04. Based on this information, what would be the exact value of MSB (mean square between)?
Question
An economist wants to determine whether average price/earnings (P/E) ratios differ for firms in three industries. Independent samples of five firms in each industry produced the following results after conducting a one-way ANOVA. SSB (sum of squares between groups) = 258.82 and SST (sum of squares total) = 424.04. Based on this information, what would be the exact value of MSB (mean square between)?
Solution
The Mean Square Between (MSB) is calculated by dividing the Sum of Squares Between (SSB) by the degrees of freedom between the groups.
The degrees of freedom between the groups is calculated as k - 1, where k is the number of groups. In this case, there are three industries, so k = 3.
So, the degrees of freedom between the groups is 3 - 1 = 2.
Therefore, the MSB is calculated as follows:
MSB = SSB / (k - 1) = 258.82 / 2 = 129.41.
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