Deck 18: Testing for Differences Among Three or More Groups: One-Way Analysis of Variance and Some Alternatives

Question 1

A particular personality inventory has 22 different scales for measuring 22 different traits. Each scale is standardized to have a mean of 50 for a national norm group. Dr. Snorf administers the entire inventory to a sample of college students and, for each scale, tests

against

( $\alpha$ = .05). Significant results are found only for the Responsibility Scale. On the basis of these results, Dr. Snorf reports that his college students are more responsible than the national group. Any comment?

Answer 1

For
we would expect 5%, or approximately 1 of Dr. Snorf's 22 tests to be significant even if were true in every case; his single significant result out of 22 tests may well be a Type I error.

Question 2

Six chronically depressed patients are randomly assigned to three therapy programs. At the end of 3 months, each is rated on his or her behavior in a standardized interview situation. The results are shown below. (a) Express and . (b) Calculate the F ratio.

Answer 2

(c) retain at both levels; sample differences not sufficient to conclude real differences among therapy programs.

Question 3

The theoretical orientation scores for four samples of psychology graduate students are given below.
(a)Express and
(b) Calculate the F ratio.

Answer 3

(b) reject at .05 level and conclude real differences among the four graduate concentrations; retain at .01 level.

Question 4

Dr. Smith wishes to compare three widely used sleeping preparations with regard to possible "hangover" effects. Twelve volunteers are given a problem-solving test at 9:00 a.m. after having been administered the standard recommended dose of one of the preparations (according to random assignment) the night before. The results are given below.
(a) Give $H_0 and H_A$ . 
(b) Is there a significant treatment effect $(use \alpha = .05)$ ?
(c) If significant results are obtained in (b) use Tukey's HSD test (α = .05) to make all possible pairwise comparisons among the groups. Draw final conclusions.

Question 5

One-way analysis of variance can be considered an extension of

A) t test of
B) test for homogeneity of variance
C) simple randomized design
D) simple ANOVA

Question 6

One-way analysis of variance is applicable when there are

A) at least two groups
B) at least three groups
C) at least five groups
D) no more than five groups

Question 7

In one-way analysis of variance involving three groups, the alternative hypothesis would be considered correct if, in the population,

A) all means were equal
B) two means are equal but the third is different
C) all three means have different values
D) either (b) or (c) above is true

Question 8

Individuals treated the same way still differ in performance. This is referred to in the text as

A) between groups variation
B) inherent variation
C) differential treatment effects
D) individual performance variation

Question 9

When
is true for a one-way ANOVA, variation of the group means is a reflection of

A) inherent variation
B) differential treatment effects
C) non-differential treatment effects
D) a combination of (a) and (b) above

Question 10

Variability of scores about their group means affords an indication of

A) inherent variation
B) variation attributable to treatment effect, when present
C) a combination of (a) and (b), above
D) none of the above

Question 11

If the treatment has no effect, we would expect

A) group population means to be equal
B) group sample means to be equal
C) group sample means to vary
D) none of the above

Question 12

Variability of group means about the grand mean affords an indication of

A) inherent variation
B) variation attributable to treatment effect, when present
C) a combination of (a) and (b) above
D) none of the above

Question 13

The use of the single symbol
to represent inherent variance for all groups follows logically from

A) the general form of a variance estimate
B) the mathematical properties associated with variance
C) the independence of inherent variation and differential treatment effects
D) the assumption of homogeneity of variance

Question 14

leads to an estimate of

A) within-group variation
B) between-group variation
C) total variation
D) none of the above

Question 15

leads to an estimate of

A) within-group variation
B) between-group variation
C) total variation
D) none of the above

Question 16

In an analysis of variance problem, the total number of degrees of freedom is

A) n_total
B)
C) n-k
D) n_total - 1

Question 17

If we divide a sum of squared deviation scores by the associated degrees of freedom we have

A) inherent variation
B) variance estimate
C) within-groups variation
D) population variance

Question 18

The denominator of any variance estimate consists of

A) sums of squared deviations
B) within-groups variation
C) degrees of freedom
D) inherent variation

Question 19

In a one-way ANOVA, the following results are obtained:

A) 186.3
B) 18.9
C) 51.3
D) none of the above

Question 20

The following are the scores from two groups of two cases each:
Group 1: 2, 4
Group 2: 4, 6,
SS_W=

A) 3
B) 4
C) 6
D) 8

Question 21

The following are the scores from two groups of two cases each:
Group 1: 2, 4
Group 2: 4, 6
SS_total =

A) 3
B) 4
C) 6
D) 8

Question 22

The within-groups variance estimate is calculated by dividing the appropriate sum of squares by

A)
B) n _total
C) n_total - K
D) n_total - 1

Question 23

If there are n scores in each group and k groups, the between-groups variance estimate is calculated by dividing the appropriate sum of squares by

A)
B)
C)
D)

Question 24

If there are three groups and
then

A) 30
B) 29
C) 24
D) cannot be determined from the above information

Question 25

If there are three groups of 10 cases each, then

A) 30
B) 29
C) 27
D) 10

Question 26

In analysis of variance, which of the following is normally not computed?

A) s_total
B) df_total
C) SS_total
D) all of the above are computed

Question 27

is a variance estimate that reflects

A) inherent variation
B) variation attributable to treatment effect, when present
C) a combination of (a) and (b) above
D) none of the above

Question 28

is a variance estimate that reflects

A) inherent variation
B) variation attributable to treatment effect, when present
C) a combination of (a) and (b) above
D) none of the above

Question 29

Which of the following is incorrect

A)
B)
C)
D)

Question 30

F is formed by

A) the difference between two variance estimates
B) the ratio between two variance estimates
C) the difference between two standard deviation estimates
D) the ratio between two population variances

Question 31

The F distribution is like the t distribution in that

A) its mean is zero
B) it is symmetrical
C) it is actually a family of distributions
D) both positive and negative values are possible

Question 32

In analysis of variance, if the group sample means were all equal, the calculated value of F would be

A) negative
B) zero
C) +1.00
D) greater than +1.00

Question 33

In the analysis of variance F test, when the null hypothesis is false, we would expect most calculated values of F to

A) be zero
B) be between zero and +1.00
C) exceed +1.00
D) +1.96 when

Question 34

In the analysis of variance F test, the quantity that reflects the treatment effect

A) is always placed in the numerator
B) is always placed in the denominator
C) is sometimes placed in the numerator and sometimes in the denominator
D) is excluded from F

Question 35

The calculated value of F may be expected to follow the distribution of tabled F when there is

A) a positive treatment effect
B) a negative treatment effect
C) a treatment effect of any kind
D) no treatment effect

Question 36

Which, if any, is not a characteristic necessary for F to be distributed according to its tabled values?

A) sampling is random
B) group populations are normally distributed
C) the numerator and denominator estimates are independent
D) sample group means are equal

Question 37

The assumption of homogeneity of variance means that

A) within-group variance should be the same as between-group variance
B) within-group variance should be the same as total variance
C) between-group variance should be the same as total variance
D) group population variance should be the same for all groups

Question 38

In analysis of variance, nonnormality of the distribution of group scores

A) is not a problem
B) is not likely to be a problem if sample size is large
C) is not likely to be a problem if samples are drawn from different populations
D) is likely to be a problem only when the number of degrees of freedom for the denominator of F is large

Question 39

In analysis of variance, problems that tend to be created by nonhomogeneity of variance are

A) minimized when group sample size is equal for all groups
B) minimized when group sample size is large
C) minimized by both (a) and (b)
D) unaffected by sample size

Question 40

In the two-sample, independent-groups design,

A) 2t
B) t/2
C) 2t²
D) t²

Question 41

Which of the following, obtained for each group separately, are the basic quantities from which all other computations flow when performing a one-way ANOVA?

A)
B)
C)
D)

Question 42

If study of the outcome of a one-way ANOVA suggests examination of a particular comparison, it would be better to study it as

A) a planned comparison
B) a post hoc comparison
C) an orthogonal comparison
D) a dependent comparison

Question 43

In analysis of variance, a comparison could compare

A) a control condition with the average of several experimental conditions
B) an experimental condition with a control condition
C) the average of two experimental conditions with the average of two control conditions
D) any of the above

Question 44

A planned comparison is one that was planned

A) before the study was completed
B) before the study was completed but after the major comparisons were made
C) after the outcome of the study was inspected
D) any of the above situations

Question 45

Planned comparisons should be

A) specified in advance of collecting the data
B) as few as possible
C) as independent of each other as possible
D) all of the above

Question 46

An orthogonal comparison is most nearly

A) an independent comparison
B) a post hoc comparison
C) a planned comparison
D) any of the above

Question 47

One difference between a planned comparison and Tukey's HSD test is that with the latter

A) a larger difference is required to be declared significant
B) a smaller difference is required to be declared significant
C) HSD comparisons must be specified in advance
D) planned comparisons should be specified after the outcome of the data is known

Question 48

In ANOVA for repeated measures, SS_W is partitioned into

A) SS_bet and SS_subjects
B) SS_bet and SS_resid
C) SS_subj and SS_total
D) SS_subj and SS_resid

Question 49

In ANOVA for repeated measures, to determine if there is a treatment effect the F ratio is

A) s²_resid/s²_bet
B) s²_bet/s²_total
C) s²_bet/s²_resid
D) s²_bet/s²_w