Deck 9: One-Way Between-Groups Anova

Question 1

An investigator determined the difference between two means to be statistically significant by using an ANOVA procedure. The F-ratio was 16. If the investigator had used a t-test procedure instead, what value would he have obtained for the t-ratio?

A) 4
B) 8
C) 16
D) No way to determine

Answer 1

A

Question 2

Using the following one-way ANOVA summary table, how many levels of the independent variable were in this study? $\begin{array}{|l|l|l|l|l|l|}\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } & \text { P } \\\hline \text { Between } & 200 & 4 & \text { B } & \text { D } & .01 \\\hline \text { Within } & \text { A } & 80 & \text { C } & & \\\hline \text { Total } & 1000 & & & & \\\hline\end{array}$

A) 4
B) 5
C) 3
D) Cannot determine

Answer 2

5

Question 3

Using the following one-way ANOVA summary table, what is the total number of subjects in this study? $\begin{array}{|l|l|l|l|l|l|}\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } & \text { P } \\\hline \text { Between } & 200 & 4 & \text { B } & \text { D } & .01 \\\hline \text { Within } & \text { A } & 80 & \text { C } & & \\\hline \text { Total } & 1000 & & & & \\\hline\end{array}$

A) 76
B) 80
C) 84
D) 85

Answer 3

85

Question 4

Using the following one-way ANOVA summary table, how many subjects were in each group, if the ns were equal? $\begin{array}{|l|l|l|l|l|l|}\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } & \text { P } \\\hline \text { Between } & 200 & 4 & \text { B } & \text { D } & .01 \\\hline \text { Within } & \text { A } & 80 & \text { C } & & \\\hline \text { Total } & 1000 & & & & \\\hline\end{array}$

A) 4
B) 17
C) 80
D) 84

Question 5

Using the following one-way ANOVA summary table, what is the value of SS_W (A in the source table)? $\begin{array}{|l|l|l|l|l|l|}\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } & \text { P } \\\hline \text { Between } & 200 & 4 & \text { B } & \text { D } & .01 \\\hline \text { Within } & \text { A } & 80 & \text { C } & & \\\hline \text { Total } & 1000 & & & & \\\hline\end{array}$

A) 400
B) 600
C) 800
D) 1200

Question 6

Using the following one-way ANOVA summary table, what is the value of MS_B (B in the source table)? $\begin{array}{|l|l|l|l|l|l|}\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } & \text { P } \\\hline \text { Between } & 200 & 4 & \text { B } & \text { D } & .01 \\\hline \text { Within } & \text { A } & 80 & \text { C } & & \\\hline \text { Total } & 1000 & & & & \\\hline\end{array}$

A) 40
B) 50
C) 84
D) 800

Question 7

Using the following one-way ANOVA summary table, what is the value of MS_W (C in the source table)? $\begin{array}{|l|l|l|l|l|l|}\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } & \text { P } \\\hline \text { Between } & 200 & 4 & \text { B } & \text { D } & .01 \\\hline \text { Within } & \text { A } & 80 & \text { C } & & \\\hline \text { Total } & 1000 & & & & \\\hline\end{array}$

A) 5
B) 7.5
C) 10
D) 15

Question 8

Using the following one-way ANOVA summary table, what is the value of the F-ratio (D in the source table)? $\begin{array}{|l|l|l|l|l|l|}\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } & \text { P } \\\hline \text { Between } & 200 & 4 & \text { B } & \text { D } & .01 \\\hline \text { Within } & \text { A } & 80 & \text { C } & & \\\hline \text { Total } & 1000 & & & & \\\hline\end{array}$

A) 1.5
B) 5.0
C) 10
D) 12

Question 9

Using the following one-way ANOVA summary table, what is the researcher's conclusion, and what possible error is attached to this decision? (? = .05) $\begin{array}{|l|l|l|l|l|l|}\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } & \text { P } \\\hline \text { Between } & 200 & 4 & \text { B } & \text { D } & .01 \\\hline \text { Within } & \text { A } & 80 & \text { C } & & \\\hline \text { Total } & 1000 & & & & \\\hline\end{array}$

A) Retain the null hypothesis, Type I error
B) Retain the null hypothesis, Type II error
C) Reject the null hypothesis, Type II error
D) Reject the null hypothesis, Type I error

Question 10

A multiple comparison technique with which of the following characteristics would be the most powerful?

A) Planned, contrast-based
B) Planned, family-based
C) Post hoc, contrast-based
D) Post hoc, family-based

Question 11

When would it be appropriate to use the Scheffé multiple comparison rather than the Tukey procedure?

A) When planned comparisons are desired
B) When a family-based comparison technique is desired
C) When complex comparisons are desired
D) When a more liberal technique is desired

Question 12

When would a multiple comparison procedure be required following a one-way ANOVA?

A) When there are two levels of the independent variable and F is significant
B) When there are three levels of the independent variable and F is not significant
C) When there are two levels of the independent variable and F is not significant
D) When there are three levels of the independent variable and F is significant

Question 13

From a one-way ANOVA, the following are known:
SS_T = 500
SS_W = 400
What percentage of the total variance is explained by the treatment effects?

A) 20%
B) 44%
C) 56%
D) 80%

Question 14

In addition to R², what other statistic is sometimes calculated to examine the practical value of a significant F-ratio?

A) Chi squared
B) Eta squared
C) Omega squared
D) t squared

Question 15

Student-Newman-Keuls is a multiple comparison technique that employs a contrast-based approach. Arrange Tukey(T), Scheffé(S), and Student-Newman-Keuls (SNK) in order from most conservative to most liberal.

A) T, S, SNK
B) SNK, T, S
C) S, T, SNK
D) S, SNK, T

Question 16

Which of the following is a mistake?

A) F = .82
B) r = 1.25
C) t = -36
D) z = -3.16

Question 17

Who developed the statistical procedure known as analysis of variance?

A) Ronald Fisher
B) William Gossett
C) Charles Spearman
D) Karl Pearson

Question 18

What is the SS_T for the following data? 5, 8, 10, 12, 15

A) 11.6
B) 14.5
C) 50.0
D) 58.0

Question 19

On what aspect do Tukey and Scheffé differ?

A) Planned versus post hoc
B) Simple versus complex
C) Family-based versus contrast-based
D) Multiple comparison versus significant F

Question 20

Compared to Tukey, Scheffé is more or less conservative?

A) More conservative and more likely to result in Type I errors
B) Less conservative and less likely to result in Type I errors
C) More conservative and less likely to result in Type I errors
D) Less conservative and more likely to result in Type I errors

Question 21

In an ANOVA, the main effect for factor A, which had two levels, was found to be statistically significant. What multiple comparison technique should be used?

A) Tukey
B) Scheffé
C) Either Tukey or Scheffé
D) None

Question 22

In a one-way ANOVA, the SS_B was 68 and the unexplained variance was 60% of the total variance. What is the SS_T?

A) 68
B) 102
C) 170
D) 230

Question 23

Which of the following is an inferential statistic?

A) Mode
B) F-ratio
C) Standard deviation
D) Range

Question 24

Consider the statistic F (1,75) = 5.5, p<0.05. What does (1,75) indicate?

A) The probability of a Type 1 error is rejected
B) The degrees of freedom
C) The calculated value of F
D) The significance level (alpha)

Question 25

What name is given to an experimental design with different subjects in each level of the independent variable?

A) Between groups
B) Repeated measures
C) Mixed
D) Longitudinal

Question 26

What happens to the F-ratio when there are significant differences between the means?

A) F will have a value greater than 1.0.
B) F will be equal to 1.0.
C) F will have a value less than 1.0.
D) It depends on the number of levels of the independent variable.

Question 27

The F-ratio is associated with which inferential test?

A) t-test
B) PPM
C) ANOVA
D) Spearman rho

Question 28

A one-way ANOVA is appropriate to analyze data from which of the following experiments?

A) One with more than one independent variable and more than one dependent variable
B) One with one independent variable and more than one dependent variable
C) One with two independent variables and one dependent variable
D) One with one independent variable and one dependent variable

Question 29

Which of the following is a multiple comparison test?

A) Pearson's R
B) Scheffé
C) ANOVA
D) Gossett's

Question 30

Which of the following results in an omnibus inferential test?

A) Tukey
B) ANOVA
C) Scheffé
D) Student-Newman-Keuls

Question 31

Which of the following inferential statistical tests can be used for examining differences among means? (Assume the data are interval or ratio.)

A) One-way ANOVA
B) t-test
C) Both A and B
D) Neither A nor B
E) Insufficient information is provided.

Question 32

What conclusion is justified if an F-ratio of .93 is obtained in a one-way ANOVA?

A) The null hypothesis is accepted, with the chance of this conclusion being wrong equal to the α level selected.
B) Since the numerator and the denominator of the F-ratio both estimate the same value, a result of less than 1 is not possible; hence, a mathematical error must have occurred.
C) There is no significant difference among treatment means, and sampling error caused the F-ratio to be less than 1.
D) Acceptance of the null hypothesis is called for, but the F-ratio of less than 1 suggests a probable Type II error.

Question 33

The population means for each of four populations is 100, and the variance for each of the four populations is 16. The four ns for samples drawn from each population all equal 50. (When you answer the question, do not calculate-just think.) In a one-way ANOVA, what is the expected value of MS_B?

A) 0
B) 4
C) 16
D) 100

Question 34

The population means for each of four populations is 100, and the variance for each of the four populations is 16. The four ns for samples drawn from each population all equal 50. (When you answer the question, do not calculate-just think.) In a one-way ANOVA, what is the expected value of MS_W?

A) 0
B) 4
C) 16
D) 100

Question 35

The population means for each of four populations is 100, and the variance for each of the four populations is 16. The four ns for samples drawn from each population all equal 50. (When you answer the question, do not calculate-just think.) In a one-way ANOVA, what is the expected F-ratio?

A) 0
B) 1
C) 4
D) 16

Question 36

Using the following ANOVA summary table, what is the sum of squares for total for these data? $\begin{array}{|l|l|l|l|l|}\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } \\\hline \text { Between } & 270 & 9 & & \\\hline \text { Within } & 5600 & 560 & & \\\hline \text { Total } & & & & \\\hline\end{array}$

A) SS_T = SS_B- SS_W = 5330
B) SS_T = SS_B + SS_W = 5870
C) SS_T = grand x?² - (?x?)²/N= 5670
D) Cannot determine from information given.

Question 37

Using the following ANOVA summary table, what F-ratio is obtained for these data, and is it significant at the .05 alpha level? $\begin{array}{|l|l|l|l|l|}\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } \\\hline \text { Between } & 270 & 9 & & \\\hline \text { Within } & 5600 & 560 & & \\\hline \text { Total } & & & & \\\hline\end{array}$

A) 1.0, not significant
B) 2.0, not significant
C) 3.0, significant
D) 4.0, significant

Question 38

Using the following ANOVA summary table, how many means are being compared, and how many subjects were included in each treatment? (Assume equal ns.) $\begin{array}{|l|l|l|l|l|}\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } \\\hline \text { Between } & 270 & 9 & & \\\hline \text { Within } & 5600 & 560 & & \\\hline \text { Total } & & & & \\\hline\end{array}$

A) 9 means, 56 subjects
B) 9 means, 57 subjects
C) 10 means, 56 subjects
D) 10 means, 57 subjects

Question 39

Using the following ANOVA summary table, which of the following conditions is NOT an assumption for this statistical test? $\begin{array}{|l|l|l|l|l|}\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } \\\hline \text { Between } & 270 & 9 & & \\\hline \text { Within } & 5600 & 560 & & \\\hline \text { Total } & & & & \\\hline\end{array}$

A) The dependent variable is normally distributed in the treatment populations.
B) The subjects are randomly assigned to treatments.
C) The same number of subjects is assigned to each treatment.
D) The variances in the populations from which the samples are drawn are equal.

Question 40

What element is usually manipulated by the researcher to achieve a specified amount of power in an ANOVA?

A) The actual falsity of the null hypothesis
B) The number of subjects
C) The alpha level
D) The error variance

Question 41

In a one-way ANOVA with three levels, the resulting means were x̄₁=25, x̄₂=25, and x̄₃=25. What would SS_T equal?

A) SS_W
B) SS_B
C) 0.0
D) Cannot determine from information given.

Question 42

Select the pair of multiple comparison techniques where both are of the contrast-based type, but one in the pair is planned and the other is post hoc.

A) Tukey and Dunnett
B) Student-Newman-Keuls and POC
C) Scheffé and Student-Newman-Keuls
D) Scheffé and Tukey

Question 43

When we apply the Student-Newman-Keuls procedure, the difference between which pair of means is evaluated first?

A) The two largest means
B) The largest and the smallest mean
C) The means from the groups with the largest ns
D) The two smallest means

Question 44

Which post hoc multiple comparison technique requires the largest effect size to indicate significance?

A) Dunnett
B) Student-Newman-Keuls
C) Scheffé
D) Tukey

Question 45

Which of the following is a contrast-based multiple comparison technique?

A) Scheffé
B) Dunnett
C) Student-Newman-Keuls
D) Tukey

Question 46

Using the following information from a between-groups one-way ANOVA, what is the F-ratio, and is it significant? (? = .05)
Group 1 mean = 45 n = 10
Group 2 mean = 40 n = 10
Group 3 mean = 35 n = 10
Group 4 mean = 30 n = 10
Group 5 mean = 25 n = 10
$\begin{array}{|l|l|l|l|l|}\hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & \text { F } \\\hline \text { Between } & 2400 & & & \\\hline \text { Within } & 9000 & & & \\\hline\end{array}$

A) 3.0, yes
B) 3.0, no
C) 2.4, yes
D) 2.4, no

Question 47

Using the following information from a one-way ANOVA, in the Student-Newman-Keuls procedure, what value would be multiplied by the appropriate q value?
Group 1 mean = 45 n = 10
Group 2 mean = 40 n = 10
Group 3 mean = 35 n = 10
Group 4 mean = 30 n = 10
Group 5 mean = 25 n = 10
$\begin{array}{|l|l|l|l|l|}\hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & \text { F } \\\hline \text { Between } & 2400 & & & \\\hline \text { Within } & 9000 & & & \\\hline\end{array}$

A) 3.00
B) 3.74
C) 4.47
D) 7.74

Question 48

Using the following information from a one-way ANOVA, in the Student-Newman-Keuls procedure, is there a significant difference between the means for Groups 2 and 5, and what is the q value used? (? = .05)
Group 1 mean = 45 n = 10
Group 2 mean = 40 n = 10
Group 3 mean = 35 n = 10
Group 4 mean = 30 n = 10
Group 5 mean = 25 n = 10
$\begin{array}{|l|l|l|l|l|}\hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & \text { F } \\\hline \text { Between } & 2400 & & & \\\hline \text { Within } & 9000 & & & \\\hline\end{array}$

A) Yes, 3.84
B) No, 3.84
C) Yes, 3.36
D) No, 3.36