Chapter 11 Test

Data for three independent random samples each of size four are analyzed by a one-factor analysis of variance fixed-effects model. If the values of the sample means are all equal, what is the value of MSbetw?

0 (because if the sample means are all equal, per H0: 1 = 2 = 3 = ... = J, then MSbetw will be 0, indicating that there are no or null differences between sample means)

For a one-factor ANOVA comparing three groups with n = 10 in each group, the F ratio would have degrees of freedom equal to a. 2, 27 b. 2, 29 c. 3, 27 d. 3, 29

A) 2, 27 (because the F ratio = or, which means = , such that the between source is 2 and the within source is 27)

For a one-factor analysis of variance fixed-effects model, which of the following is always true? a. df(betw) + df(with) = df(tot) b. SS(betw) + SS(with) = SS(tot) c. MS(betw) + MS(with) = MS(tot) d. all of the above e. both a and b

B) SSbetw + SSwith = SStot (because, per the partitioning of the sum of squares, the term SStotal represents the amount of total variation, which is then partitioned into that variation which exists between the groups, denoted by SSbetw, and that variation variation which exists within the groups, denoted by SSwith, p. 204)

Suppose that n1 = 19, n2 = 21, and n3 = 23. For a one-factor ANOVA, the dfwith would be a. 2 b. 3 c. 60 d. 63

C) 60 (because dfwith = N - J; therefore, [19+21+23] - 3 = 60, such that each group loses 1 df)

If you find an F ratio of 1.0 in a one-factor ANOVA, it means that a. between-group variation exceeds within-group variation b. within-group variation exceeds between-group variation c. between-group variation is equal to within-group variation d. between-group variation exceeds total variation

C) between group variation is equal to within group variation

When analyzing mean differences among more than two samples, doing independent t tests on all possible pairs of means a. decreases the probability of a Type I error b. does not change the probability of a type I error. c. increases the probability of a Type I error. d. Cannot be determined from the information provided

C) increases the probability of a Type I error (because the risk of a Type I error accumulates across multiple tests, despite each individual test being set at a particular level; in other words, the more t tests conducted

Which of the following is not necessary in ANOVA? a. Observations are from random and independent samples. b. The dependent variable is measured on at least the interval scale. c. Populations have equal variances d. Equal sample sizes are necessary.

D) Equal sample sizes are necessary

In a one-factor ANOVA, H0 asserts that a. all of the population means are equal. b. the between-groups variance estimate and the within-groups variance estimate are both estimates of the same population variance. c. the within-groups some of squares is equal to the between-groups sum of squares. d. both a and b

A) all of the population means are equal (because H0: 1 = 2 = 3 = ... = J, p. 202)

Mean square is another name for variance or variance estimate. True or False?

True (because mean square is a variance estimate such that they represent the sum of the squared deviations from a mean divided by their degrees of freedom, like the sample variance s2

A negative F ratio is impossible. True or False?

True (because the F ratio must be greater than or equal to 0 and never holds a negative value)

The homoscedasticity assumption is that the population scores from which each of the samples are drawn are normally distributed. True or False?

False (because the homoscedasticity assumption holds that the variances of each population are equal and it is the normality assumption that holds that each of the populations follows the normal distribution or that the population scores from which each of the samples

In ANOVA each independent variable is known as a level. True or False?

False (because the one-factor ANOVA has only one independent variable or factor with two or more levels and the levels represent the different samples, groups, or treatments whose means are to be compared, p. 199)

For J = 2 and = .05, if the result of the independent t test is significant, then the result of the one-factor fixed-effects ANOVA is uncertain. True or False?

False (because, for the two-group situation, the F and t test statistics follow the rule of F = t2, for a nondirectional alternative hypothesis in the independent t test;

With J = 3 groups, I assert that if you reject H0 in the one-factor ANOVA you will necessarily conclude that all three group means are different. Am I correct?

No (because H1 is purposely written in a general form to cover the multitude of possible mean differences that could arise, which range from only two of the means being different to all of the means being different from one another, and as such

Suppose that for a one-factor ANOVA with J = 4 and n = 10 the four sample means are all equal to 15. I assert that the value of MSwith is necessarily equal to zero. Am I correct?

No (because equality among or between sample means, such that each are equal to 15 among 4 balanced groups with equal n's, does not necessarily indicate that there is zero variance within each of those samples,

A statistician conducted a one-factor fixed-effects ANOVA and found the F ratio to be less than 0. I assert that this means the between-groups variability is less than the within-groups variability. Am I correct?

No (because it is impossible for the F ratio to yield a negative value, as the F ratio must be greater than or equal to 0

The independence assumption in the ANOVA is that the observations in the samples do not depend on one another. True or False?

True (because the independence assumption in the ANOVA, by definition, states that each sample must be an independent random sample from their respective population;

Suppose students in grades 7, 8, 9, 10, 11, and 12 were compared on absenteeism. If ANOVA were used rather than multiple t tests, the probability of a Type I error would be less. True or False?

True (because the overall level for the entire set of multiple t tests, i.e., experiment-wise Type I error rate,

Suppose for a one-factor fixed-effects ANOVA with J = 5 and n = 15, the five sample means are all equal to 50. I assert that the F test statistic cannot be significant. Am I correct?

Yes (because if the sample means are all equal, per H0: 1 = 2 = 3 = ... = J, then MSbetw will be 0, indicating that there are no or null differences between sample means,