Question

In: Statistics and Probability

1. Data for three independent random samples, each of size 4, are analyzed by a one-way...

1. Data for three independent random samples, each of size 4, are analyzed by a one-way ANOVA fixed-effects model. If the values of the sample means are all equal, what is the value of MSbetween? ______________.

2. In a one factor-ANOVA , Ho asserts that  

a. All the population means are equal

b. The between groups variance estimate and the within-groups variance estimate are both estimates of the same population residual variance

c. The within-groups sum of squares is equal to the between-groups sum of squares.

d. Both a and b

Solutions

Expert Solution

1. , for "k" number of groups, where is the sample mean of "i"th random sample and is the overall mean.
If the sample means are all equal, then they are consequently equal to the overall mean. Hence, MSbetween will become zero.

2. H0 asserts that all the population means are equal in a one factor ANOVA and also asserts that the between groups variance estimate and the within-groups variance estimate are both estimates of the same population residual variance.
Hence, Option D is correct.


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