Deck 14: Analysis of Variance

Question 1

Your research hypothesis is "In the population, the average number of days female unauthorized immigrants stay in the U.S. is longer than the average number of days male unauthorized immigrants stay in the U.S." What type of hypothesis test should be used?

A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Answer 1

independent-samples t test

Question 2

An author reports the following information about a one-way ANOVA: F = 0.95, df = 3 and 48, p = .231. Which of the following is true?

A) There were 3 groups being compared.
B) The null hypothesis was rejected
C) The sample results were not significant.
D) The post hoc multiple comparisons should be examined.

Answer 2

The sample results were not significant.

Question 3

You are doing a one-way ANOVA. What level of measurement is required on the two variables you are using? (Circle the letter of the correct answer.)

A) Both must be interval ratio.
B) Both can be any level.
C) The dependent variable can be any level, the factor variable must be interval/ratio.
D) The dependent variable must be interval/ratio, the factor variable can be any level.

Answer 3

The dependent variable must be interval/ratio, the factor variable can be any level.

Question 4

If race and gender have a significant interaction effect on years of schooling,

A) the effect of race on years of schooling varies by gender
B) the effect of gender on years of schooling varies by race
C) "a" and "b" are both true
D) none of the above are true

Question 5

Your research hypothesis is "In the population, there is a difference in the average number of work days per year lost due to injury among the following groups: secretaries, professors, police officers, and ministers." What type of hypothesis test should be used?

A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Question 6

Your one-way ANOVA research hypothesis was that average years of schooling (EDUC) differed between strong Republicans, Independents, and strong Democrats. On the basis of the following output, which pairs of groups significantly differ?
Multiple Comparisons
EDUC Tukey HSD
$\begin{array}{|ll|r|r|r|}\hline & & & & \\\text { (I) POLPARTY } & \text { (J) POLPARTY } & \begin{array}{c}\text { Mean } \\\text { Difference (1- } \\\mathrm{J}\end{array} & \text { Std. Error } & \text { Sig. } \\\hline 1 \text { strong Republican } & 4 \text { independent } & 1.647^{*} & .602 & .018 \\& 7 \text { strong Democrat } & -471 & .606 & .718 \\\hline 4 \text { independent } & 1 \text { strong Republican } & -1.647^{*} & .602 & .018 \\& 7 \text { strong Democrat } & -2.118^{*} & .511 & .000 \\\hline 7 \text { strong Democrat } & 1 \text { strong Republican } & 471 & .606 & .718 \\& 4 \text { independent } & 2.118^{*} & .511 & .000 \\\hline\end{array}$
$*$ . The mean difference is significant at the $0.05$ level.

A) no pairs significantly differ
B) (strong Republicans & strong Democrats)
C) (strong Republicans & Independents) and (Strong Democrats & Independents)
D) all pairs significantly differ

Question 7

On the basis of this output, which of the following is true?
Tests of Between-Subjects Effects
Dependent Variable:INCOME
$\begin{array}{|l|r|r|r|r|r|}\hline \text { Source } & {\begin{array}{c}\text { Type III Sum } \\\text { of Squares }\end{array}} & \text { df } & \text { Mean Square } & {\mathrm{F}} & {\text { Sig. }} \\\hline \text { Corrected Model } & 1.810 \mathrm{E} 10 & 5 & 3.619 \mathrm{E} 9 & 4.303 & .001 \\\text { Intercept } & 9.911 \mathrm{E} 10 & 1 & 9.911 \mathrm{E} 10 & 117.844 & .000 \\\text { MARRIED } & 6.674 \mathrm{E9} & 2 & 3.337 \mathrm{E9} & 3.967 & .021 \\\text { SEX } & 4.128 \mathrm{E9} & 1 & 4.128 \mathrm{E} 9 & 4.908 & .028 \\\text { MARRIED * SEX } & 1.308 \mathrm{E} 9 & 2 & 6.540 \mathrm{E} 8 & .778 & .461 \\\text { Error } & 1.354 \mathrm{E} 11 & 161 & 8.410 \mathrm{E} 8 & & \\\text { Total } & 3.156 \mathrm{E} 11 & 167 & & & \\\text { Corrected Total } & 1.535 \mathrm{E} 11 & 166 & & & \\\hline\end{array}$
a. R Squared $= .118 ($ Adjusted R Squared $= .090 )$

A) The overall model is not significant.
B) The interaction effect is not significant.
C) The main effect of MARRIED is not significant.
D) The main effect of SEX is not significant.

Question 8

You are doing a two-way ANOVA. What level of measurement is required for the dependent variable?

A) It must be nominal.
B) It must be ordinal.
C) It must be interval/ratio.
D) It can be any level of measurement.

Question 9

Your research hypothesis is "In the population, the average number of days unauthorized immigrants stay in the United States is less than 450." What type of hypothesis test should be used?

A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Question 10

"The educational attainment difference between persons raised by a single parent and persons raised by two parents is larger for lower social class families than for upper social class families." This is a description of

A) an interaction effect involving type of household in which raised and social class
B) a main effect of educational attainment
C) a main effect of social class
D) a main effect of type of household in which raised

Question 11

You want to know if two variables significantly interact in their effect on some variable. Which would be an appropriate procedure to use?

A) Frequencies
B) One-Way ANOVA
C) Paired-Samples T Test
D) Univariate General Linear Model (Two-Way ANOVA)

Question 12

Your research hypothesis is "In the population, there is a difference in the average self-confidence among the following groups: Protestants, Catholics, Jews, other religionists, and atheists." What type of hypothesis test should be used?

A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Question 13

You want to know if there are any significant differences between the means of three groups, and, if so, between which groups. Which would be an appropriate procedure to use?

A) Frequencies
B) One Sample T Test
C) One-Way ANOVA
D) Paired-Samples T Test

Question 14

You are doing a one-way ANOVA and the sample results are consistent with the research hypothesis. On the basis of the following output, your results _____ significant and you _____ proceed to discuss the post-hoc multiple comparisons.
ANOVA
EDUC
$\begin{array}{|l|r|r|r|r|r|}\hline & {\begin{array}{c}\text { Sum of } \\\text { Squares }\end{array}} &{\mathrm{df}} & \text { Mean Square } & \mathrm{F} & \text { Sig. } \\\hline \text { Between Groups } & 203.047 & 2 & 101.523 & 9.209 & .000 \\\text { Within Groups } & 2348.171 & 213 & 11.024 & & \\\text { Total } & 2551.218 & 215 & & & \\\hline\end{array}$

A) are … should
B) are … should not
C) are not … should
D) are not … should not

Question 15

Why is one-way ANOVA better than repeated independent-sample t tests for comparing means for three or more groups?

A) one-way ANOVA allows for a nominal dependent variable
B) one-way ANOVA is more likely to find a significant difference
C) repeated independent-samples t tests increase the chance of a Type I error
D) repeated independent-samples t tests increase the chance of multicollinearity

Question 16

Your research hypothesis is "In the population, first stays in the U.S. by unauthorized immigrants are on average longer than second stays in the U.S. by these same immigrants." What type of hypothesis test should be used?

A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Question 17

Your research hypothesis is "In the population, the effect of occupation on number of work days per year lost due to injury varies by sex." What type of hypothesis test should be used?

A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Question 18

On the basis of this output, which of the following is true?
Tests of Between-Subjects Effects
Dependent Variable:KIDSBEST
$\begin{array}{|l|r|r|r|r|r|}\hline \text { Source } & \begin{array}{c}\text { Type III Sum } \\\text { of Squares }\end{array} & \text { df } & \text { Mean Square } & \text { F } & {\text { Sig. }} \\\hline \text { Corrected Model } & 4.238^{a} & 5 & .848 & 1.174 & .325 \\\text { Intercept } & 327.547 & 1 & 327.547 & 453.553 & .000 \\\text { MARRIED } & 3.631 & 2 & 1.816 & 2.514 & .085 \\\text { SEX } & .701 & 1 & .701 & .971 & .326 \\\text { MARRIED* SEX } & 1.790 & 2 & .895 & 1.239 & .293 \\\text { Error } & 96.050 & 133 & .722 & & \\\text { Total } & 879.000 & 139 & & & \\\text { Corrected Total } & 100.288 & 138 & & & \\\hline\end{array}$
a. R Squared $= .042 ($ Adjusted R Squared $= .006 )$

A) The overall model is not significant.
B) The interaction effect is significant.
C) The main effect of MARRIED is significant.
D) The main effect of SEX is significant.

Question 19

You are doing a one-way ANOVA. Your research hypothesis is that there is a difference in the mean knowledge about the Bible between Baptists, Catholics, and Methodists. What is your null hypothesis?

A) All three groups have different mean knowledge.
B) All three groups have the same mean knowledge.
C) At least two groups have the same mean knowledge.
D) Knowledge of the Bible and religious affiliation are related.

Question 20

Your research hypothesis is that there is a difference between Protestants, Catholics, and Jews in average reported ideal number of children (KIDSBEST) for a family. Your sample results are consistent with the _____ and you should proceed to _____.
Descriptives
KIDSBEST
$\begin{array}{|l|r|r|r|r|}\hline & & & & \\& {\mathrm{N}} & \text { Mean } & \text { Std. Deviation } & \text { Std. Error } \\\hline \text { 1 Protestant } & 147 & 2.71 & 1.034 & .085 \\\text { 2 Catholic } & 44 & 2.59 & .996 & .150 \\\text { 3 Jewish } & 20 & 2.45 & .887 & .198 \\\text { Total } & 211 & 2.66 & 1.012 & .070 \\\hline\end{array}$

A) null hypothesis … Step 3 (check significance level)
B) null hypothesis … Step 4 (state conclusion)
C) research hypothesis … Step 3 (check significance level)
D) research hypothesis … Step 4 (state conclusion)

Question 21

Your research hypothesis is "In the population, the average number of work days per year lost due to injury is 3." What type of hypothesis test should be used?

A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Question 22

Which of the following is NOT a possible stopping point in a two-way ANOVA problem?

A) If the overall model is not significant.
B) If the interaction effect is significant.
C) If the first main effect you examine is not significant.
D) If the second main effect is significant.

Question 23

When are post hoc multiple-comparison results examined and when are they not examined?

Question 24

Your research hypothesis is "In the population, the effect of type of school attended on SAT score varies by social class." What type of hypothesis test should be used?

A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Question 25

The F ratio for a one-way ANOVA is reported to have 5 and 171 degrees of freedom. That means _____ groups were being compared and there were _____ cases included in the analysis.

A) 4 … 176
B) 5 … 171
C) 6 … 177
D) 176 … 4

Question 26

What is a main effect?

Question 27

You are doing a one-way ANOVA. Your sample size is 500. Your factor (independent) variable has six categories. How many degrees of freedom will your F-ratio have?
__________ and __________ degrees of freedom

Question 28

What kinds of questions can you answer using a two-way analysis of variance?

Question 29

What kinds of questions can you answer using a one-way analysis of variance?

Question 30

Your research hypothesis is "In the population, college graduates have a higher average self-confidence than those same persons had when they were just high school graduates." What type of hypothesis test should be used?

A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Question 31

Your research hypothesis is "In the population, there is a difference between men and women in the average number of work days per year lost due to injury." What type of hypothesis test should be used?

A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Question 32

You are doing a one-way ANOVA and the sample results are consistent with the research hypothesis. On the basis of the following output, your results _____ significant and you _____ proceed to discuss the post-hoc multiple comparisons.
ANOVA
KIDSBEST
$\begin{array}{|l|r|r|r|r|r|}\hline &{\begin{array}{c}\text { Sum of } \\\text { Squares }\end{array}} & \mathrm{df} & \text { Mean Square } & {\mathrm{F}} & \text { Sig. } \\\hline \text { Between Groups } & 1.523 & 2 & .761 & .741 & .478 \\\text { Within Groups } & 213.586 & 208 & 1.027 & & \\\text { Total } & 215.109 & 210 & & & \\\hline\end{array}$

A) are … should
B) are … should not
C) are not … should
D) are not … should not

Question 33

There is almost always an interaction effect present in the sample data, so why isn't there almost always a significant interaction effect?

Question 34

What is an interaction effect?

Question 35

You are doing a one-way ANOVA. Your sample size is 1,000. Your factor (independent) variable has four categories. How many degrees of freedom will your F-ratio have?
__________ and __________ degrees of freedom

Question 36

On the basis of this output, which of the following is true?
Tests of Between-Subjects Effects
Dependent Variable:ABORTOK
$\begin{array}{|l|r|r|r|r|r|}\hline \text { Source } & {\begin{array}{c}\text { Type III Sum } \\\text { of Squares }\end{array}} & \text { df } & \text { Mean Square } &{\text { F }} & {\text { Sig. }} \\\hline \text { Corrected Model } & 214.225^{a} & 11 & 19.475 & 5.594 & .000 \\\text { Intercept } & 1451.930 & 1 & 1451.930 & 417.071 & .000 \\\text { MARRIED } & 21.421 & 2 & 10.710 & 3.077 & .049 \\\text { RELINTEN } & 51.237 & 3 & 17.079 & 4.906 & .003 \\\text { MARRIED * RELINTEN } & 24.451 & 6 & 4.075 & 1.171 & .326 \\\text { Error } & 459.525 & 132 & 3.481 & & \\\text { Total } & 3326.000 & 144 & & & \\\text { Corrected Total } & 673.750 & 143 & & & \\\hline\end{array}$
a. $\mathrm { R }$ Squared $= .318$ (Adjusted R Squared $= .261$ )

A) The overall model is significant.
B) The interaction effect is significant.
C) Discussion of the main effect of MARRIED would be skipped.
D) Discussion of the main effect of RELINTEN would be skipped.

Question 37

What are the three rounds for analyzing a two-way ANOVA?

Question 38

When is an independent-samples t test used to compare group means and when is a one-way ANOVA used?

Question 39

Does the one-way ANOVA research hypothesis claim that in the population, every group's mean differs from every other group's mean? Explain.

Question 40

You want to know if, on average, participants weigh significantly less at the end of a weight-loss program than they did at the start of the program. Which would be an appropriate procedure to use?

A) Frequencies
B) One-Way ANOVA
C) Paired-Samples T Test
D) Univariate General Linear Model (Two-Way ANOVA)

Question 41

Answer the questions that follow this SPSS output:


Your research hypothesis is "In the population, there is a difference in the average earnings of 1^st born children, middle-born children, and last-born children."

A) What is your null hypothesis?
B) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
C) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
D) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
E) Are your results statistically significant? (yes / no)
F) Is it appropriate to discuss the results of the post hoc multiple comparisons tests? (yes / no)
G) If it is appropriate to discuss the post hoc multiple comparison tests, which pairs of groups are probably different from one another in the population? If it is not appropriate, explain why it is not appropriate.

Question 42

A researcher reports that her one-way ANOVA results were not significant. The following statistics are reported (F = 1.78, df = 7 and 1000, p = .13). How many groups were being compared and how big was the sample?

A) # of groups being compared ___________
B) # of cases in the sample ___________

Question 43

You are reading a research article and you come across the following information: F = 26.94, df = 3 and 450, p = .001)

A) How many groups are being compared? __________
B) How many cases are included in the analysis? __________

Question 44

Answer the questions that follow this SPSS output:


You have done a two-way analysis of variance with earnings (EARNIN04) as the dependent variable and RACE and FEMALE as the factor variables.

A) Is the overall model statistically significant? (yes / no)
B) Is the interaction effect statistically significant? (yes / no / skipped) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.)
C) Is the main effect of RACE statistically significant? (yes / no / skipped) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.)
D) Is the main effect of gender(FEMALE) statistically significant? (yes / no / skipped) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.)

Question 45

Answer the questions that follow this SPSS output:


Your research hypothesis is "In the population, there is a difference in the average income among the following groups: those with less than a high school degree, those with just a high school degree, and those with at least a junior college degree."

A) What is your null hypothesis?
B) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
C) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
D) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
E) Are your results statistically significant? (yes / no)
F) Is it appropriate to discuss the results of the post hoc multiple comparisons tests? (yes / no)
G) If it is appropriate to discuss the post hoc multiple comparison tests, which pairs of groups are probably different from one another in the population? If it is not appropriate, explain why it is not appropriate.

Question 46

Answer the questions that follow this SPSS output:


Your research hypothesis is "In the population, there is a difference in the average SAT scores among the following groups: students from Harris County, students from Travis County, and students from Nacogdoches County."

A) What is your null hypothesis?
B) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
C) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
D) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
E) Are your results statistically significant? (yes / no)
F) Is it appropriate to discuss the results of the post hoc multiple comparisons tests? (yes / no)
G) If it is appropriate to discuss the post hoc multiple comparison tests, which pairs of groups are probably different from one another in the population? If it is not appropriate, explain why it is not appropriate.

Question 47

Answer the questions that follow this SPSS output:

You have done a two-way analysis of variance with number of children (CHILDS) as the dependent variable and SEX and CLASS as the factor variables.

A) Is the overall model statistically significant? (yes / no)
B) Is the interaction effect statistically significant? (yes / no ) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.)
C) Is the main effect of SEX statistically significant? (yes / no) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.)
D) Is the main effect of CLASS statistically significant? (yes / no) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.)

Question 48

Describe the interaction effect shown in this plot.

Question 49

Answer the questions that follow this SPSS output:

You have done a two-way analysis of variance with age at birth of first child (AGEKDBRN) as the dependent variable and CLASS and SEX as the factor variables.

A) Is the overall model statistically significant? (yes / no)
B) Is the interaction effect statistically significant? (yes / no / skipped) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.)
C) Is the main effect of CLASS statistically significant? (yes / no / skipped) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.)
D) Is the main effect of SEX statistically significant? (yes / no / skipped) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.)