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 value of MSW (mean square within)? Round your final answer to two decimal places.
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 value of MSW (mean square within)? Round your final answer to two decimal places.
Solution
To calculate the Mean Square Within (MSW), we need the Sum of Squares Within (SSW) and the degrees of freedom within.
The SSW can be calculated as follows:
SSW = SST - SSB = 424.04 - 258.82 = 165.22.
The degrees of freedom within is calculated as N - k, where N is the total number of observations and k is the number of groups. In this case, there are 5 firms in each of the 3 industries, so N = 5*3 = 15 and k = 3.
So, the degrees of freedom within is 15 - 3 = 12.
Now we can calculate MSW:
MSW = SSW / (N - k) = 165.22 / 12 = 13.77.
So, the Mean Square Within (MSW) is 13.77.
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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, the degrees of freedom associated with the SSW (sum of squares within groups) is equal to
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