Deck 11: One-Way Analysis of Variance Anova

Question 1

A researcher hypothesizes that people living in the Midwest are more in favor of tougher immigration laws than people who live on either the East or West Coast. In conducting a one-way ANOVA with this data, how can the null hypothesis (H₀) be stated?

A) H₀: Midwest < East Coast = West Coast
B) H₀: μMidwest = μEast Coast = μWest Coast
C) H₀: all μs are not equal
D) H₀: not all μs are equal

Answer 1

H₀: μMidwest = μEast Coast = μWest Coast

Question 2

A researcher hypothesizes that people living in the Midwest are more opposed to same-sex marriage than people living on either the West or East Coast (who do not differ from each other). In conducting a one-way ANOVA with this data, how should the alternative hypothesis (H₁) be stated?

A) H₁: μMidwest < μWest = μEast
B) H₁: all μs are equal
C) H₁: μMidwest ≠ μWest ≠ μEast
D) H₁: not all μs are equal

Answer 2

H₁: not all μs are equal

Question 3

A researcher hypothesizes Republicans are more opposed to abortion than Moderates, who in turn are more opposed than Democrats. In conducting a one-way ANOVA with these three groups, how should the alternative hypothesis (H₁) be stated?

A) H₁: Republicans > Moderates > Democrats
B) H₁: Republicans ≠ Moderates ≠ Democrats
C) H₁: all μs are not equal
D) H₁: not all μs are equal

Answer 3

H₁: not all μs are equal

Question 4

A researcher hypothesizes that people who currently own a Toyota automobile are less likely to believe Toyotas are dangerous than people who drive American made cars, who are in turn less likely to believe Toyotas are dangerous than people who do not drive. In conducting a one-way ANOVA with this data, how should the alternative hypothesis (H₁) be stated?

A) H₁: not all μs are equal
B) H₁: all μs are not equal
C) H₁: H₁: Toyota < American < Nondriver
D) H₁: Toyota ≠ American ≠ Nondriver

Question 5

A researcher hypothesizes that drug experimentation is higher with seniors than juniors, higher in juniors than sophomores, and higher in sophomores than in first year high school students. In conducting a one-way ANOVA with this data, how can the null hypothesis (H₀) be stated?

A) H₀: all μs are equal
B) H₀: all μs are different
C) H₀: not all μs are different
D) H₀: not all μs are equal

Question 6

A researcher hypothesizes that drug experimentation is higher with seniors than juniors, higher in juniors than sophomores, and higher in sophomores than in first year high school students. In conducting a one-way ANOVA with this data, how can the alternative hypothesis (H₁) be stated?

A) H₀: all μs are equal
B) H₀: all μs are different
C) H₀: not all μs are different
D) H₀: not all μs are equal

Question 7

A researcher hypothesizes that freshmen spend more time studying than sophomores, who spend more time studying than juniors, and so on. In conducting a one-way ANOVA with this data, how can the null hypothesis (H₀) be stated?

A) H₀: all μs are different
B) H₀: not all μs are different
C) H₀: all μs are equal
D) H₀: not all μs are equal

Question 8

The concept and calculation of 'variance' is primarily concerned with ______.

A) differences
B) central tendency
C) samples and populations
D) theoretical distributions

Question 9

A researcher hypothesizes people who don't smoke will be more in favor of laws banning smoking in public places than either people who smoke cigarettes or people who smoke cigars (the two groups of smokers do not differ in their beliefs). In conducting a one-way ANOVA with these three groups, how should the alternative hypothesis (H₁) be stated?

A) H₁: not all μs are equal
B) H₁: Nonsmoker ≠ Cigarettes ≠ Cigars
C) H₁: Nonsmoker > Cigarettes = Cigars
D) H₁: all μs are unequal

Question 10

A researcher hypothesizes that people with 'high' incomes will be more opposed to changes in the health care system than people with 'average' incomes, who in turn will be more opposed than people with 'low' incomes. In conducting a one-way ANOVA with this data, how could the null hypothesis (H₀) be stated?

A) H₀: High > Average > Low
B) H₀: not all μs are equal
C) H₀: all μs are equal
D) H₀: High ≠ Average ≠ Low

Question 11

A researcher hypothesizes people who smoke cigars are more likely to oppose laws banning smoking in public places than people who smoke cigarettes, who in turn are more opposed to these laws than people who do not smoke at all. In conducting a one-way ANOVA with these three groups, how should the alternative hypothesis (H₁) be stated?

A) H₁: all μs are not equal
B) H₁: Cigars ≠ Cigarettes ≠ Nonsmoker
C) H₁: Cigars > Cigarettes > Nonsmoker
D) None of these

Question 12

A researcher hypothesizes that Democrats and Independents are equally in favor of gun control, and both are more in favor of gun control than Republicans. In conducting a one-way ANOVA with these three groups, how should the alternative hypothesis (H₁) be stated?

A) H₁: Democrats = Independents > Republicans
B) H₁: Republicans < Democrats = Independents
C) H₁: Democrats ≠ Independents ≠ Republicans
D) None of these

Question 13

The formula for the ______ of the t-test and F-ratio concerns ______ and involves group ______.

A) numerator; differences between groups; means
B) denominator; differences between groups; standard deviations
C) numerator; differences within groups; standard deviations
D) denominator; differences within groups; means

Question 14

A researcher hypothesizes that freshmen spend more time studying than sophomores, who spend more time studying than juniors, who spend more time studying than seniors. In conducting a one-way ANOVA with this data, how could the null hypothesis (H₀) be stated?

A) H₀: Freshman > Sophomore > Junior > Senior
B) H₀: μFreshman = μSophomore = μJunior = μSenior
C) H₀: all μs are not equal
D) H₀: μFreshman ≠ μSophomore ≠ μJunior ≠ μSenior

Question 15

______ variability may also be thought of as ______.

A) Between-group; 'error'
B) Within-group; 'effect'
C) Between-group; 'effect'
D) Unexplained; 'effect'

Question 16

A researcher hypothesizes Democrats are more in favor of gun control than Moderates, who in turn are more favor of gun control than Republicans. In conducting a one-way ANOVA with these three groups, how should the alternative hypothesis (H₁) be stated?

A) H₁: Democrats > Moderates > Republicans
B) H₁: Democrats ≠ Moderates ≠ Republicans
C) H₁: all μs are not equal
D) None of these

Question 17

The concept and calculation of 'variance' is primarily concerned with ______.

A) squared deviations from a mean
B) summing scores
C) hypothesis testing
D) normal distributions

Question 18

A research study hypothesized that people who drive hybrid cars are less likely to smoke than people who drive minivans or SUVs (who do not differ from each other). In conducting a one-way ANOVA with this data, how could the null hypothesis (H₀) be stated?

A) H₀: Hybrid < Minivan = SUV
B) H₀: μHybrid = μMinivan = μSUV
C) H₀: all μs are not equal
D) H₀: Hybrid ≠ Minivan = SUV

Question 19

A researcher hypothesizes that voters who identify themselves as being part of the 'Tea Party' are more likely to believe people have the right to wear guns in public places than will voters who consider themselves to be either 'Conservative' or 'Moderate' (whose beliefs do not differ from each other). In conducting a one-way ANOVA with this data, how could the null hypothesis (H₀) be stated?

A) H₀: Tea Party > Conservative = Moderate
B) H₀: not all μs are equal
C) H₀: all μs are equal
D) H₀: Tea Party ≠ Conservative = Moderate

Question 20

______ variability may also be thought of as ______.

A) Between-group; 'error'
B) Within-group; 'error'
C) Between-group; 'significant'
D) Within-group; 'effect'

Question 21

The F-ratio is calculated by ______.

A) dividing between-group variance by within-group variance
B) subtracting within-group variance from between-group variance
C) multiplying between-group variance and within-group variance
D) dividing between-group variance by total variance

Question 22

A researcher collects data from five groups and eventually calculates a value of 16.95 for MSBG. What is the value for SSBG?

A) 4
B) 16.95
C) 67.80
D) 84.75

Question 23

The theoretical distribution of ______ is represented by ______ because ______. Figure A Figure B

A) F-ratios; Figure A; they can only be positive
B) t-tests; Figure A; they can be both positive or negative
C) F-ratios; Figure B; they can be both positive or negative
D) t-tests; Figure B; they can only be positive

Question 24

Arnold compares the means of three groups and calculates a value of -2.01 for the F-ratio. This implies ______.

A) the mean of the first group is the highest of the three groups
B) the mean of the third group is the highest of the three groups
C) the differences between the means are statistically significant
D) he has made an error in his calculations

Question 25

A researcher collects data from six groups and eventually calculates a value of 6.75 for MSBG. What is the value for SSBG?

A) 5
B) 6.75
C) 33.75
D) Cannot be calculated with information provided

Question 26

The ______ of the F-ratio (______ variability) may also be thought of as ______.

A) denominator; within-group; 'error'
B) numerator; within-group; 'effect'
C) denominator; between-group; 'effect'
D) numerator; between-group; 'error'

Question 27

A researcher collects data from four groups and eventually calculates a value of 2.79 for MSBG. What is the value for SSBG?

A) 2.79
B) 8.37
C) 11.16
D) Cannot be calculated with information provided

Question 28

Instead of being a bell-curve shape, the F-ratio distribution is ______.

A) positively skewed
B) negatively skewed
C) normally distributed
D) flat

Question 29

The theoretical distribution of F-ratios is ______.

A) bimodal
B) normal
C) asymmetric
D) unknown

Question 30

The F-ratio is calculated by ______ different types of variability.

A) adding
B) subtracting
C) multiplying
D) dividing

Question 31

The ______ of the formula for the F-ratio concerns ______ and involves group ______.

A) denominator; differences within groups; means
B) numerator; differences within groups; standard deviations
C) denominator; differences between groups; standard deviations
D) numerator; differences between groups; means

Question 32

The theoretical distribution of F-ratios is ______ because ______.

A) bell-curve shaped; there are an infinite number of F-ratios
B) skewed; F-ratios are based on squared deviations
C) normal; F-ratios can be either positive or negative
D) asymmetrical; you can only support rather than prove research hypotheses

Question 33

The ______ of the F-ratio concerns ______ and may also be thought of as ______.

A) denominator; differences between groups; 'error'
B) numerator; differences between groups; 'effect'
C) denominator; differences within groups; 'effect'
D) numerator; differences within groups; 'error'

Question 34

A researcher collects data from four groups (each of whom consists of 5 respondents). Eventually the researcher calculates a value of 4.56 MSBG. What is the value for SSBG?

A) 13.68
B) 18.24
C) 22.80
D) 86.64

Question 35

The theoretical distribution of F-ratios is ______ because ______. Figure A Figure B

A) bell-curve shaped; there are an infinite number of F-ratios
B) skewed; F-ratios are based on variances
C) normal; F-ratios can be either positive or negative
D) asymmetrical; research hypotheses are directional

Question 36

The shape of the theoretical distribution of F-ratios is ______.

A) symmetrical
B) skewed
C) normal
D) flat

Question 37

The ______ of the t-test and F-ratio involves ______, which may also be defined as ______ variability.

A) numerator; differences among group means; within-group
B) denominator ; differences among group means; between-group
C) numerator; group standard deviations; between-group
D) denominator; group standard deviations; within-group

Question 38

The degrees of freedom ______ indicates ______.

A) dfBG; the number of dependent variable
B) dfWG; number of scores in each group
C) dfBG; the size of the sample
D) dfWG; the directionality of the alternative hypothesis

Question 39

A researcher collects data from three groups and eventually calculates a value of 9.78 for MSBG. What is the value for SSBG?

A) 4.89
B) 19.56
C) 29.34
D) 39.12

Question 40

The degrees of freedom ______ indicates ______.

A) dfBG; the number of levels of the independent variable
B) dfWG; between-group variability
C) dfBG; the size of the sample
D) dfWG; the directionality of the alternative hypothesis

Question 41

A study reports the F-ratio F(4,15) = 1.16. This means that the study consisted of ______ groups with ______ participants in each group.

A) 4; 4
B) 4; 15
C) 5; 4
D) 5; 15

Question 42

Sarah conducts a one-way ANOVA comparing four groups, each of which consists of 6 participants (N = 6). In evaluating the F-ratio for this analysis, what is the critical value for α = .05?

A) 2.78
B) 3.01
C) 3.05
D) 3.10

Question 43

I calculate an F-ratio of 3.11. If this F ratio is ______ the critical value, I will ______ the null hypothesis because the probability of this F-ratio is ______ .05.

A) greater than; not reject; less than
B) greater than; not reject; greater than
C) greater than; reject; greater than
D) less than; not reject; greater than

Question 44

A researcher conducts a one-way ANOVA comparing four groups, each of which consists of 20 participants (N = 20). In evaluating the F-ratio for this analysis, what is the critical value for α = .05?

A) 2.76
B) 2.70
C) 2.53
D) 2.46

Question 45

A study reports the F-ratio F(2,15) = 2.32. The TOTAL sample size (combining the different groups) was ______.

A) 17
B) 18
C) 30
D) cannot be calculated with information provided

Question 46

A study reports the F-ratio F(3,24) = 3.91. The TOTAL sample size (combining the different groups) is ______.

A) 24
B) 25
C) 27
D) 28

Question 47

A study reports the following statistic: F(2,33) = 1.16. What is N (the number of participants in each group)?

A) 2
B) 3
C) 12
D) 33

Question 48

A study reports the F-ratio F(3,20) = 1.16. This means that the study consisted of ______ groups with ______ participants in each group.

A) 3; 20
B) 3; 8
C) 4; 6
D) 4; 20

Question 49

Boop conducts a one-way ANOVA comparing four groups, each of which consists of 6 participants (N = 6). In evaluating the F-ratio for this analysis, what is the critical value for α = .05?

A) 2.78
B) 2.87
C) 3.01
D) 3.10

Question 50

Betty conducts a one-way ANOVA comparing five groups, each of which consists of 10 participants (N = 10). In this situation, what is dfWG?

A) 4
B) 5
C) 45
D) 50

Question 51

Michelle conducts a one-way ANOVA comparing six groups, each of which consists of 4 participants (N = 4). In evaluating the F-ratio for this analysis, what is the critical value for α = .05?

A) 2.77
B) 2.66
C) 2.51
D) Cannot be calculated with information provided

Question 52

The degrees of freedom ______ indicates ______.

A) dfBG; the size of the sample
B) dfWG; the number of groups being compared
C) dfBG; within-group variability
D) dfWG; the size of the sample

Question 53

Fred conducts a one-way ANOVA comparing six groups, each of which consists of 5 participants (N = 5). In evaluating the F-ratio for this analysis, what is the critical value for α = .05?

A) 2.53
B) 2.62
C) 4.95
D) 5.05

Question 54

Betty conducts a one-way ANOVA comparing four groups, each of which consists of 10 participants (N = 10). In this situation, what is dfWG?

A) 3
B) 9
C) 36
D) 40

Question 55

Fred conducts a one-way ANOVA comparing five groups, each of which consists of 5 participants (N = 5). In evaluating the F-ratio for this analysis, what is the critical value for α = .05?

A) 2.69
B) 2.78
C) 2.87
D) 5.05

Question 56

Fred conducts a one-way ANOVA comparing three groups, each of which consists of 18 participants (N = 18). In evaluating the F-ratio for this analysis, what is the critical value for α = .05?

A) 2.76
B) 2.84
C) 3.23
D) 3.59

Question 57

The degrees of freedom ______ provides an indication of ______.

A) dfBG; the size of the sample
B) dfBG; the number of groups being compared
C) dfWG; the independent variable
D) dfWG; whether the F-ratio will be large or small

Question 58

A one-way ANOVA is conducted comparing 6 groups, each with 10 participants. For this sample the dfBG _is ______ and the dfWG is ______ with a total sample size of ______.

A) 6; 10; 60
B) 5; 59; 60
C) 6; 9; 60
D) 5; 54; 60

Question 59

Barney conducts a one-way ANOVA comparing the means of six groups, each of which consists of 4 scores (N = 4). In this situation, what is dfBG?

A) 4
B) 5
C) 6
D) 18

Question 60

A one-way ANOVA is conducted comparing 4 groups, each with 5 participants. For this sample the dfBG _is ______ and the dfWG is ______ with a total sample size of ______.

A) 3; 5; 20
B) 4; 5; 20
C) 3; 16; 20
D) 4; 20; 20

Question 61

Analytical comparisons are calculated ______.

A) when the null hypothesis for the F-ratio is statistically insignificant
B) when the null hypothesis for the F-ratio is rejected
C) when the null hypothesis for the F-ratio is not rejected
D) whenever a research feels like it

Question 62

Which type of analytic comparisons is made in the absence of a specific hypothesis regarding which groups should be included?

A) planned comparisons
B) unplanned comparisons
C) a priori comparisons
D) complex comparisons

Question 63

If my value of the F ratio falls between the critical values for α = .05 and α = .01, I will ______ the null hypothesis and conclude ______.

A) not reject; p < .05
B) not reject; p < .01
C) reject; p > .01
D) reject; p < .05

Question 64

Imagine the value of an F-ratio is less than the critical value for $\alpha$ = .05 and less than the critical value for α = .01. Which is the most appropriate way to report the level of significance?

A) p < .01
B) p > .01
C) p < .05
D) p > .05

Question 65

If an F ratio is ______ the critical value, I will ______ the null hypothesis and conclude that ______.

A) less than; not reject; the groups are not all equal to each other
B) greater than; reject; the groups are not all equal to each other
C) less than; reject; the groups do not differ significantly from each other
D) greater than; reject; all of the groups are different from each other

Question 66

Which type of analytical comparisons is not built into the research design prior to data collection?

A) a priori comparisons
B) planned comparisons
C) unplanned comparisons
D) simple comparisons

Question 67

A researcher hypothesizes that people, on average, spend more money a week on gasoline than on food or clothing. She conducts a one-way ANOVA involving Gasoline (M = $51.40), Food (M = $24.57) and Clothing (M = $18.29). If she makes the decision to reject the null hypothesis, what is the MOST specific conclusion she can draw?

A) Money spent varies as a function of type of expense.
B) Money spent on gasoline is greater than food or clothing.
C) The money spent on the three expenses are all different from each other.
D) The analysis supports the research hypothesis.

Question 68

Which type of analytic comparisons is made when the researcher has a specific hypothesis regarding which groups should be included?

A) planned comparisons
B) unplanned comparisons
C) simple comparisons
D) post hoc comparisons

Question 69

For the same set of data, the relationship between the t-test and the F-ratio may be characterized as ______.

A) t = F
B) t² = F
C) F² = t
D) none of these

Question 70

George calculates the F-ratio for a one-way ANOVA comparing the means of three groups: Group A (M = 4.12), Group B (M = 7.37) and Group C (M = 8.92). If he makes the decision to reject the null hypothesis, what is the most specific and appropriate conclusion he can make?

A) The groups are all different from each other.
B) The groups are not all equal to each other.
C) Group A ≠ Group B ≠ Group C
D) Group A < Group B < Group C

Question 71

A study compares the attitudes of 9 Seniors, 9 Juniors, 9 Sophomores, and 9 First-year students and obtains a value of 2.98 for the F-ratio. Which of the following is the correct way to present this analysis?

A) F(4,36) = 2.98, p < .05
B) F(4,36) = 2.98, p > .05
C) F(3,32) = 2.98, p < .05
D) F(3,35) = 2.98, p < .05

Question 72

A researcher calculates an F-ratio comparing the GPAs of three different SJSU majors: Major A (M = 2.70), Major B (M = 2.87) and Major C (M = 3.01). If she makes the decision to NOT reject the null hypothesis, what is the most specific and appropriate conclusion she can draw?

A) The SAT scores for the three groups are all different from each other.
B) The analysis supports the research hypothesis.
C) The GPAs of the three majors are not significantly different.
D) No conclusion can be determined without conducting further analyses.

Question 73

A researcher calculates an F-ratio comparing the GPAs of three different SJSU majors: Major A (M = 2.40), Major B (M = 2.16) and Major C (M = 3.05). If she makes the decision to reject the null hypothesis, what is the most specific and appropriate conclusion she can draw?

A) GPAs vary as a function of major.
B) The GPAs for the three majors are not different from each other.
C) The GPAs for the three majors are all different from each other.
D) The analysis supports the research hypothesis.

Question 74

Barry calculates an F-ratio for a one-way ANOVA comparing the incomes of graduates of three different SJSU majors and rejects the null hypothesis. Which of the following is the most appropriate conclusion he could draw?

A) The income levels for the three majors are all different from each other.
B) The income levels for the three majors do not differ from each other.
C) Income levels vary as a function of major.
D) The analysis supports the research hypothesis.

Question 75

If an F ratio is ______ the critical value, I will ______ the null hypothesis and conclude that ______.

A) greater than; not reject; the groups are not all equal to each other
B) greater than; reject; all of the groups are different from each other
C) less than; not reject; the groups do not differ significantly from each other
D) less than; reject; the groups are all equal to each other

Question 76

______ are analytical comparisons researchers build into the research design prior to the data collection process.

A) Planned comparisons
B) Unplanned comparisons
C) Simple comparisons
D) Post hoc comparisons

Question 77

Barry calculates an F-ratio involving the SAT scores of three groups and does NOT reject the null hypothesis. Which of the following is the MOST appropriate conclusion he could draw?

A) The SAT scores for the three groups are all different from each other.
B) The SAT scores for the three groups are all equal to each other.
C) The SAT scores for the three groups are not significantly different.
D) No conclusion can be determined without conducting further analyses.

Question 78

When researchers have a plan regarding the comparisons between groups needed to test their research hypotheses, these comparisons are known as ______.

A) planned comparisons
B) unplanned comparisons
C) post hoc comparisons
D) complex comparisons

Question 79

If an F ratio is ______ the critical value, I will ______ the null hypothesis because ______.

A) greater than; not reject; p < .05
B) greater than; reject; p > .05
C) less than; not reject; p > .05
D) less than; reject; p > .05

Question 80

A study compares the attitudes of 6 Democrats, 6 Republicans, and 6 Independents and obtains a value of 3.80 for the F-ratio. Which of the following is the correct way to present this analysis?

A) F(2,15) = 3.80, p < .05
B) F(2,15) = 3.80, p > .05
C) F(2,18) = 3.80, p < .05
D) F(3,18) = 3.80, p < .05