For 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:

Question

Question

This question was previously asked in

SSC CGL Tier-II ( JSO ) 2021 Official Paper ( Held On: 10 August 2022 )

Answer 1

The 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.