In conducting one-way Analysis of Variance, which of the following test…
2023
In conducting one-way Analysis of Variance, which of the following test statistics would be used?
Answer: D. F — CONCEPTOne-way analysis of variance tests whether several population means are equal by partitioning total variability into variability between groups and…
- A.
Z
- B.
t
- C.
χ2 (chi-square)
- D.
F
Show answer & explanation
Correct answer: D
CONCEPT
One-way analysis of variance tests whether several population means are equal by partitioning total variability into variability between groups and variability within groups. The relevant test statistic must compare these two independent estimates of variance.
APPLICATION
Compute the between-group mean square: MS_between = SS_between / (k − 1), where k is the number of groups.
Compute the within-group mean square: MS_within = SS_within / (N − k), where N is the total number of observations.
Form the ratio F = MS_between / MS_within. Under the null hypothesis of equal group means, this ratio follows an F distribution with (k − 1, N − k) degrees of freedom.
CROSS-CHECK / CONTRAST
Z standardizes an estimate using a normal-theory standard error.
t standardizes one estimate or a two-mean difference using an estimated standard error.
χ² aggregates squared standardized discrepancies and is used for categorical counts or variance inference.
F compares two variance estimates, exactly matching the ANOVA construction.
Therefore, the test statistic used for one-way ANOVA is F.