Deck 10: Analysis of Variance Anova

Question 1

When we want to compare more than 2 groups, we should use an ANOVA instead of a t-test because ______.

A) you cannot compare the means between all groups simultaneously with t-tests
B) you cannot take into account the variability for all samples with t-tests
C) you increase the chance of making a Type I error
D) all of these

Answer 1

D

Question 2

When using an ANOVA to compare between groups ______.

A) you use variance between the groups to determine how much the means differ
B) you use mean differences between all groups to determine how much the means differ
C) you use mean difference between 2 groups at a time in all combinations to determine how much means differ
D) none of these

Answer 2

A

Question 3

The F ratio ______.

A) compares mean differences between groups to the variance between groups
B) compares the variance within groups to mean differences
C) compares the variance between groups to the variance within groups
D) compares mean differences between groups to the variance within groups

Answer 3

C

Question 4

If the F-ratio is close to 1 ______.

A) the variability between the groups is approximately equal to the variability within the groups
B) there is likely a statistically significant difference between the group means
C) the mean difference between the groups is very large
D) it is impossible to determine without additional information

Question 5

When calculating an ANOVA, you are most likely to see a significant difference between groups when ______.

A) your between groups variability is large and your within groups variability is small
B) your between groups variability is large and your within groups variability is large
C) your between groups variability is small and your within groups variability is large
D) your between groups variability is small and your within groups variability is small

Question 6

For which of the following scenarios would you be most likely to have a significant F-ratio?

A) SS_B = 10 and SS_W = 10
B) SS_B = 10 and SS_W = 1
C) SS_B = 1 and SS_W = 1
D) SS_B = 1 and SS_W = 10

Question 7

You collect data on the length sales calls from four departments within an organization. Which of the following would the appropriate representation of the null hypothesis:

A) μ₁ = μ₂ = μ₃
B) μ₁ = μ₂
C) μ₁ = μ₂ = μ₃ = μ₄
D) none of these

Question 8

You collect data on the length sales calls from four departments within an organization. Which of the following would the appropriate representation of the alternative hypothesis?

A) μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄
B) at least two means differ
C) all of the means differ
D) all of these

Question 9

You collect data on the length sales calls from four departments within an organization. For this scenario, what is k?

A) 2
B) 3
C) 4
D) impossible to determine without more information

Question 10

You collect data on the length sales calls from four departments within an organization. For this scenario, what is df_B?

A) 2
B) 3
C) 4
D) impossible to determine without more information

Question 11

If n = 10 and k = 3, what is df_B?

A) 2
B) 3
C) 9
D) 7

Question 12

If n = 12 and k = 4, what is df_W?

A) 3
B) 4
C) 8
D) 9

Question 13

If n = 25 and k = 5, what is F_crit when α = .05?

A) 4.10
B) 4.43
C) 2.87
D) 2.71

Question 14

A researcher reports a F-ratio from a one-way ANOVA with df 2,33. Which of the following is accurate for this scenario:

A) The study had 2 treatment conditions and 33 participants.
B) The study had 3 treatment conditions and 33 participants.
C) The study had 3 treatment conditions and 35 participants.
D) The study had 3 treatment conditions and 36 participants.

Question 15

A researcher reports the following information: F(3, 20) = 4.67. What is the correct decision?

A) Reject the null if α = .05 and retain the null if α = .01.
B) Retain the null if α = .05 and retain the null if α = .01.
C) Reject the null if α = .05 and reject the null if α = .01.
D) Retain the null if α = .05 and reject the null if α = .01.

Question 16

A mean square is ______.

A) the average variability per subject
B) the median variability per degree of freedom
C) the average variability per degree of freedom
D) the median variability per subject

Question 17

Sum of squares is ______.

A) the mean distance between each score and its mean
B) the total distance between each score and its mean
C) the mean squared distance between each score and its mean
D) the mean total distance between each score and its mean

Question 18

The statistical test for one-way ANOVA is ______.

A) right-tailed
B) left-tailed
C) non-directional
D) none of these

Question 19

A measure of overall effect size for one-way ANOVA is ______.

A) the F statistic
B) $\eta$ ²
C) Cohen's d
D) post hoc tests

Question 20

$\eta$ ² = .5 indicates that 50% of the ______.

A) total variability is explained by between-groups variability
B) total variability is explained by within-groups variability
C) within-groups variability is explained by between-groups variability
D) between-groups variability is explained by within-groups variability

Question 21

In one-way ANOVA, post hoc tests are used to determine ______.

A) if an F test is statistically significant
B) the overall effect size in one-way ANOVA
C) the critical mean difference
D) none of these

Question 22

A commonly used post-hoc test is ______.

A) Tukey's honestly significance difference test
B) the least significant difference test
C) Scheffe's test
D) all of these

Question 23

Sum of squares is related to variance in that variance is ______.

A) sum of squares divided by the number of subjects
B) sum of squares divided by degrees of freedom
C) the median sum of squares
D) none of these

Question 24

Which of these is an appropriate formal test of the null hypothesis for one-way ANOVA if df_W = 10, df_B = 3, F = 1.25, and your p-value is .6?

A) F(3,10) = 1.25, p > .05
B) F(10,3) = 1.25, p > .05
C) F(3,10) = 1.25, p < .05
D) F(10,3) = 1.25, p < .05

Question 25

Scheffe's test is a conservative post-hoc test and LSD is not a very conservative post-hoc test. This means ______ with Scheffe's test than with an LSD test.

A) you are more likely to find statistical significance
B) you are less likely to find statistical significance
C) you are more likely to find large effect sizes
D) you are less likely to find large effect sizes

Question 26

In post-hoc tests, the critical mean difference is used to determine if ______.

A) the F statistic is statistically significant
B) the post hoc test is practically significant
C) the post hoc test is statistically significant
D) all of these

Question 27

When identifying homogeneous subgroups, a larger critical mean difference would be most likely to result in ______.

A) more homogeneous subgroups
B) fewer homogeneous subgroups
C) the same number of homogeneous subgroups
D) none of these

Question 28

You conduct a one-way ANOVA and find that managers and salespeople are in one homogeneous subgroup, whereas salespeople and warehouse employees are in a second homogeneous subgroup. This means that salespeople ______.

A) are the same as both managers and warehouse employees
B) cannot be distinguished from managers or warehouse employees
C) are different from managers and warehouse employees
D) none of these

Question 29

If you want to determine differences due to both department (managers, sales, warehouse) and gender (male, female) on one outcome, you should conduct a ______.

A) one-way ANOVA
B) n-way ANOVA
C) independent-samples t-test
D) none of these

Question 30

An interaction ______.

A) describes when a unique combination of two variables results in a joint effect we would not expect given the effect of each variable individually
B) is a possible outcome of n-way ANOVA
C) is most typically depicted with multiple lines on a line graph
D) all of these

Question 31

An ANOVA is a hypothesis test where the variance of group means is compared to variance within those groups.

Question 32

Within groups variability estimates the degree to which group means vary from one another within ANOVA.

Question 33

Between groups variability is the degree to which members of a group vary from one another within ANOVA.

Question 34

F-ratios can be negative.

Question 35

F-ratios can be less than 1.

Question 36

One-way ANOVA can be used to compare any number of groups on one outcome variable.

Question 37

One-way ANOVA can be both directional and non-directional.

Question 38

The alternative hypothesis for an ANOVA where k = 3 can be written as μ₁ ≠ μ₂ ≠ μ_3.

Question 39

Degrees of freedom in one-way ANOVA must always be positive.

Question 40

There are 4 treatment conditions in one-way ANOVA when k = 5.

Question 41

Mean square is the average sum of squares per degree of freedom.

Question 42

For one-way ANOVA, when $\alpha$ = .05, the critical value when df_B = 3 and df_W = 10 is 8.79.

Question 43

For one-way ANOVA, when $\alpha$ = .05, the critical value when k = 3 and df_w = 10 is 4.10.

Question 44

For one-way ANOVA, when $\alpha$ = .01, the critical value when df_B = 3 and n = 20 is 5.29.

Question 45

For one-way ANOVA, if $\eta$ ² = .6, 6% of the variability in the outcome is attributable to group membership.

Question 46

Scheffe's test is the best post-hoc to use after a statistically significant one-way ANOVA.

Question 47

The critical F used in Scheffe's test after a one-way ANOVA is the same critical F used in to determine overall significance for one-way ANOVA.

Question 48

If two groups are in the same homogeneous subgroup, they are significantly different from each other.

Question 49

An n-way ANOVA should be used instead of one-way ANOVA when you have more than one outcome variable.

Question 50

An interaction is the unique combined effect of two variables that you would not expect from the effect of each variable alone.

Question 51

Why should you use an ANOVA instead of multiple independent-samples t-tests?

Question 52

Why is it possible to get a negative value for t but not for F?

Question 53

Describe the purpose of a post hoc test and when one should be used.

Question 54

When is appropriate to use an n-way ANOVA instead of a one-way ANOVA? Provide an example of a business setting where n-way ANOVA might be used.

Question 55

$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Survey }$
$\begin{array}{|c|c|c|c|}\hline \text { Sales } & \text { Service } & \text { Warehouse } & \text { Management } \\\hline 3 & 2 & 2 & 4 \\\hline 1 & 3 & 4 & 3 \\\hline 3 & 4 & 2 & 4 \\\hline 2 & 4 & 2 & 4 \\\hline 2 & 3 & 2 & 3 \\\hline\end{array}$ You would like to compare employees in each of the four departments of your organization: the sales department, the service department, the warehouse, and management. Specifically, you want to know if job satisfaction survey scores are different due to Department.
1) What is the research question?
2) What are the hypotheses?
3) What are the degrees of freedom?
4) What is the critical value for this test?
5) Create an ANOVA summary table.
6) State the formal results of the test.
7) Should you compute a measure of the overall effect size? How do you know? If so, calculate this effect size.
8) What is the critical mean difference for Scheffe's test?
9) Should you conduct post-hoc tests? Why or why not?
10) Which groups are significantly different from one another?
11) State all appropriate conclusions.