Deck 13: One-Way Analysis of Variance

Question 1

If a researcher wants to compare more than two groups, she could use

A) a three-sample t test.
B) an ANOVA test.
C) two-sample t tests to compare two groups at a time.
D) either "a" or "c" above.

Answer 1

B

Question 2

The problem with conducting multiple t tests is

A) the accumulated probability of a Type I error.
B) the accumulated probability of a Type II error.
C) too much sample variability.
D) the increased risk of calculation errors.

Answer 2

A

Question 3

Analysis of variance allows for comparison between several different groups using only one

A) hypothesis.
B) mean.
C) df.
D) alpha level.

Answer 3

D

Question 4

One-way analysis of variance involves manipulating only one

A) set of scores.
B) source of variance.
C) independent variable.
D) dependent variable.

Question 5

Within treatment variance in a one-way ANOVA is made up of

A) individual differences.
B) experimental error.
C) the effects of treatment.
D) both "a" and "b" above.

Question 6

Treatment variance is made up of

A) individual differences.
B) experimental error.
C) the effects of treatment.
D) all of the above.

Question 7

Examples of within-treatment variance include all of the following, except

A) body weight.
B) the effects of treatment.
C) motivation.
D) tolerance for discomfort.

Question 8

Examples of experimental error include all of the following, except

A) poorly written questions on the assessment instrument.
B) background noises.
C) body chemistry.
D) the researcher falling asleep during measurement.

Question 9

In conducting a one-way ANOVA, if there are no treatment effects, then

A) between-treatments variance and within-treatment variance would be approximately equal.
B) between-treatments variance would be larger than within-treatment variance.
C) within-treatment variance would be larger than between-treatments variance.
D) between-treatments variance would be 0.

Question 10

The F-statistic is the result of conducting a

A) one-sample t test.
B) independent samples t test.
C) repeated measures t test.
D) one-way ANOVA.

Question 11

Experiment-wise alpha level

A) is the accumulated probability of a Type I error.
B) is the accumulated probability of a Type II error.
C) involves changing the alpha level for each group comparison.
D) is the decision by the experimenter to use the most reasonable alpha level.

Question 12

Within-treatment variance

A) is considered to be the result of random error.
B) is the result of treatment.
C) involves treating participants between groups differently.
D) involves treating participants within each group differently.

Question 13

Which of the following is a correct representation of the F-statistic?

A) within-treatment variance/between-treatments variance
B) treatment-variance/error variance
C) error variance/treatment variance
D) MS_wi/MS_bet

Question 14

Which of the following is a correct representation of the F-statistic?

A) within-treatment variance/between-treatments variance
B) MS_wi/MS_bet
C) MS_bet/MS_wi
D) error variance/treatment-variance

Question 15

The value predicted by the F-statistic if treatment is not effective is

A) 0
B) 1
C) 2
D) 100

Question 16

The F-value predicted by the null hypothesis is

A) 0
B) 1
C) 2
D) 100

Question 17

For a one-way ANOVA, the null hypothesis

A) predicts the value of F to be 1.
B) asserts that treatment had no effect.
C) attributes any differences between means to random error.
D) All of the above are true.

Question 18

Which of the following is a correctly stated alternative hypothesis for a one-way ANOVA?

A) μ₁ = μ₂ = μ₃
B) μ₁ ≤ μ₂ ≤ μ₃
C) M₁ ≠ M₂ ≠ M₃
D) some μs are not equal.

Question 19

If you fail to reject the null hypothesis for a one-way ANOVA, then

A) your obtained F-value was lower that F_crit.
B) there were significant differences between means.
C) the alternative hypothesis has been supported.
D) your obtained F-value was higher that F_crit.

Question 20

Which of the following statements is true regarding a one-way ANOVA?

A) Three df values are required to determine F_crit.
B) There are no two-tailed tests.
C) Obtained F-values can be either positive or negative.
D) If H₀ is true, F_obt will be 0.

Question 21

Which of the following calculations is not required for conducting a one-way ANOVA?

A) F-statistic
B) sum of squares values
C) standard error of difference between the means
D) mean square values

Question 22

In a one-way ANOVA, k represents

A) the number of subjects.
B) the number of groups.
C) the number of levels of the independent variable.
D) both "b" and "c" above.

Question 23

The number of groups in a one-way ANOVA is represented by

A) k
B) N
C) t
D) ∑X_tot

Question 24

Given a sample size of n = 6 in each of 4 groups and an α = .01 for a one-way ANOVA, what is F_crit?

A) 3.92
B) 3.10
C) 4.94
D) 4.87

Question 25

Given N = 12, k = 3, and α = .05 for a one-way ANOVA, what is F_crit?

A) 4.26
B) 8.02
C) 3.86
D) 3.49

Question 26

To determine df_wi for a one-way ANOVA, use _________.

A) k - N
B) N - 1
C) k - 1
D) N - k

Question 27

To determine df_bet for a one-way ANOVA, use _________.

A) k - N
B) N - k
C) N - 1
D) k - 1

Question 28

In a one-way ANOVA, mean square is equivalent to

A) a standard deviation.
B) variance.
C) SS.
D) standard error of difference between the means.

Question 29

For a one-way ANOVA, if F_crit = 4.29 and F_obt = 4.28, you should

A) reject H₀ at α = .01, but fail to reject H₀ at α = .05.
B) reject H₀ at α = .05, but fail to reject H₀ at α = .01.
C) reject H₀.
D) fail to reject H₀.

Question 30

Given the summary values for a one-way ANOVA: SS_wi = 78, k = 4, and n = 8 for each group, what is MS_wi?

A) 2.79
B) 19.5
C) 11.14
D) 26

Question 31

Given the summary values for a one-way ANOVA: SS_bet = 105, k = 4, and n = 7 for each group, what is MS_bet?

A) 1.28
B) 4.38
C) 35
D) 26.25

Question 32

If SS_bet = 120 and SS_tot = 220, what is SS_wi?

A) .5455
B) 100
C) 120
D) 340

Question 33

If df_tot = 16 and df_bet = 4 for a one-way ANOVA, what is df_wi?

A) 64
B) 4
C) 20
D) 12

Question 34

Given the summary values for a one-way ANOVA: SS_bet = 63, SS_wi = 48, df_bet = 3, and df_wi = 16, what is F_obt?

A) 3
B) 21
C) 7
D) 1.31

Question 35

Given the summary values for a one-way ANOVA: SS_bet = 34, SS_wi = 27, MS_bet = 17, and MS_wi = 3, what is F_obt?

A) 5.67
B) 2
C) .1765
D) .5

Question 36

Eta squared tells us the proportion of the total variability in a one-way ANOVA that is accounted for by _______________.

A) chance
B) treatment
C) individual differences
D) experimental error

Question 37

The correct symbolic notation for eta squared is

A) r²
B) σ²
C) α²
D) η²

Question 38

which is the correct formula for eta squared?

A) SS_bet/SS_tot
B) SS_tot/SS_bet
C) SS_wi/SS_tot
D) SS_tot/SS_wi

Question 39

Which of the following is NOT true regarding Tukey's HSD test?

A) It is used to determine which means differ significantly.
B) It is a post hoc test.
C) To use this test, the sample size must be different for each group.
D) It has built-in safeguards to minimize the risk of a Type I error.

Question 40

You have conducted an ANOVA test using several different groups and H₀ was rejected. How can you best determine which groups differed significantly?

A) Conduct t tests for two groups at a time.
B) Use Tukey's HSD.
C) Use eta squared.
D) Use chi-square.

Question 41

The Studentized Range Statistic, needed to calculate Tukey's HSD, is symbolized as

A) π
B) σ
C) η
D) q

Question 42

Which of the following is NOT an assumption for a one-way ANOVA?

A) independent and random selection of subjects
B) interval or ratio scores for the dependent variable
C) normal distribution of scores in the population
D) unequal variances in the population

Question 43

Why is it inappropriate to use multiple t tests to examine the differences between the means of several different groups?

Question 44

What is experiment-wise alpha level?

Question 45

What are the sources that contribute to within-treatment variance?

Question 46

What are the sources that contribute to between-treatments variance?

Question 47

What are the two types of variance in a one-way ANOVA and what are the factors that cause scores to vary with each type?

Question 48

What obtained F-value is predicted by the null hypothesis? Explain the reason for this by describing the variance components that make up the F-statistic.

Question 49

In a one-way ANOVA, if df_bet = 3 and df_wi = 24, how many groups were involved in the study and how many subjects participated?

Question 50

When is a post hoc test conducted and what is its purpose?

Question 51

List the assumptions for a one-way ANOVA.

Question 52

The summary table below includes partial values for the results of a one-way ANOVA. Complete the rest of the table where indicated with a blank line.

Question 53

Given the information below, determine F_crit and decide if H₀ should be rejected.

Question 54

For the following scores from three different groups, calculate SS_tot, SS_wi, and SS_bet.

Question 55

Conduct a one-way ANOVA for the scores below using an α = .05. If appropriate, follow up with Tukey's HSD.

Question 56

A pharmaceutical research company is studying a new non-addictive sleep medication. Participants who suffered from insomnia for over a year were randomly assigned to one of three groups. Group 1 is given a placebo, Group 2 is given 10 mg of the medication, and Group 3 is given 20 mg of the medication. The scores below represent the nightly average number of hours that the participants slept for a one-week period of time during the study. Conduct a one-way ANOVA using an α = .01. If appropriate, follow up with a measure of effect size and Tukey's HSD.

Question 57

A manufacturing company has developed a new specialized hand operated can opener which can only be assembled manually. However, there are different methods for assembling the opener. The CEO of the company hires a research consultant to determine which of four methods is the fastest. Twenty employees were randomly assigned to a different method. After one hour, the average number of can openers assembled was recorded for each method. The mean number of openers that were assembled for each method are shown below along with other summary values. Conduct a one-way ANOVA with an α = .05. If appropriate, follow up with Tukey's HSD.