Question
Download Solution PDFFor the ANOVA table
| Source of variations | Sum of squares | Degrees of freedom |
| Between treatment | 45 | 3 |
| Error | 32 | 16 |
| Total | 99 | 19 |
the F - statistics is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is F-statistics is 7.5.
Key Points
- F-statistics is a ratio of the between-treatment mean square to the error mean square
- It's used in ANOVA to test the null hypothesis of equal population means between different groups or treatments.
- A larger F-statistic indicates larger difference between the groups, and a smaller value indicates more similarity between the groups.
- In ANOVA, the degrees of freedom for the between-treatment mean square is equal to the number of groups minus 1.
- The degrees of freedom for the error mean square is equal to the total number of observations minus the number of groups.
Additional Information
- \(45/3\)The F-statistic is calculated as the ratio of the between-treatment mean square (MSB) to the error mean square (MSE).
- MSB = 45/3 = 15 and MSE = \(32/16\) = 2, therefore F = MSB/MSE = (15/2)=7.5.
- The F-statistic is used in ANOVA to test the null hypothesis that the population means are equal between different groups or treatments.
- A larger F-statistic value indicates a larger difference between the groups, and a smaller value indicates that the groups are more similar.
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