Question

Which of the following statements about the one-way ANOVA are correct? (Select all that apply) 

• The larger the variability within groups relative to the variability between groups, the larger the F test statistic tends to be. 

• The results of the ANOVA F test does not tel us which groups are different or how different they are. 

• An F-distribution is symmetrical about 0 and extends indefinitely in both directions 

• In a one-way ANOVA, if the null hypothesis is rejected, we conclude that the population means are all different (i.e. no two of the population means are equal) 

• A random variable with an F-distribution can take non-negative values only? 

• In one-way ANOVA, the mean square for error (MSE) gives a measure of the vanity on within the samples, while the mean square for greps MS gives a measure of variation among the sample means.

Answer 1

The given statement is FALSE. The F-statistic is,

\(F=\frac{M S B}{M S E}\)

So, larger variability within group relative to between groups makes F-statistic smaller.

The given statement is TRUE. The ANOVA \(-F\) test tells us that whether all the groups are from same population or not. They do NOT tell us how different they are.

The given statement is FALSE.

The F-distribution only takes non-negative values.

The given statement is FALSE.

We conclude that all means are not same. We do not conclude anything more than that. we have to do other tests to get any more conclusion

The given statement is TRUE.

As support of \(\mathrm{F}\) distributionis non-negative reals. So, random variable following \(\mathrm{F}\) distr. can only take non negative values.

The given statement is TRUE.

In one-way ANOVA, the mean square for error (MSE) gives a measure of the variation on within the samples, while the mean square for groups MS gives a measure of variation among the sample means.