Deck 13: One-Way Within-Groups Anova

Question 1

What is the correct formula for subjects degrees of freedom in a one-way within-groups ANOVA?

A) N_groups - 1
B) n - 1
C) N_total - 1
D) n - 2

Answer 1

n - 1

Question 2

Buying jeans can be a challenge for women.A local shop owner wants to be selective in what brands of jeans she carries in her store.She gets six of her closest friends to try five different pairs of jeans, with the requirement that they wear each pair for two whole days, without washing, and they rate the jeans at the end of the second day.What research design should she use to analyze her data?

A) one-way between-groups ANOVA
B) independent-samples t tests
C) one-way within-groups ANOVA
D) paired-samples t tests

Answer 2

one-way within-groups ANOVA

Question 3

Which statement accurately captures why within-groups designs are preferred over between-groups designs?

A) Variability due to participants' differences is held constant across levels of the independent variable in the within-groups design, resulting in less within-groups variability.
B) Loss of participants has a more significant negative impact on between-groups designs as compared to within-groups designs.
C) Control of extraneous variables is easier when using between-groups designs than within-groups designs.
D) Within-groups designs take less time than between-groups designs.

Answer 3

Variability due to participants' differences is held constant across levels of the independent variable in the within-groups design, resulting in less within-groups variability.

Question 4

Order effects in a within-groups ANOVA can be resolved by using:

A) random sampling.
B) counterbalancing.
C) a larger sample size.
D) mean differences.

Question 5

A researcher wants to examine people's preference for pets by having 10 people act as "foster owners" for four different types of family pets: dogs, cats, birds, and fish.The participants will foster each type of pet for one week, and a scale measure will be used to assess preference.Which research design should be used?

A) one-way between-groups ANOVA
B) correlation
C) one-way within-groups ANOVA
D) paired-samples t tests

Question 6

A one-way within-groups ANOVA is used when there is(are) _____ independent variable(s) with at least _____ levels.

A) 1; 2
B) 2; 2
C) 1; 3
D) 2; 3

Question 7

What types of designs are normally preferred to reduce variability by reducing individual differences?

A) between-groups designs
B) post hoc designs
C) within-groups designs
D) correlational designs

Question 8

What is the correct formula for between-groups degrees of freedom?

A) N_groups - 1
B) n - 1
C) N_total - 1
D) n - 2

Question 9

Determine the critical cutoff for F at a p level of 0.05 if the following degrees of freedom were calculated for a one-way within-groups ANOVA: df_between = 4, df_subjects = 5, df_total = 29, df_within = 20.

A) 2.25
B) 2.87
C) 3.01
D) 5.19

Question 10

If using a within-groups design results in a larger F statistic, this also means:

A) there is less variability between groups.
B) it is easier to reject the null hypothesis with this design.
C) Type I errors are more likely.
D) power is decreased.

Question 11

_____ is(are) an additional assumption that must be evaluated in a within-groups ANOVA compared to a between-groups ANOVA.

A) Random sampling
B) Order effects
C) Sample size
D) Mean differences

Question 12

A paired-samples t test is used when there are _____ groups, and a within-groups ANOVA is used when there are at least _____ groups.

A) 3; 2
B) 2; 3
C) 1; 3
D) 1; 2

Question 13

The one-way within-groups design can be viewed as an extension of which other research design because of its ability to analyze data from more groups?

A) independent-samples t test
B) paired-samples t test
C) Tukey HSD test
D) between-groups ANOVA

Question 14

The benefits of the within-groups design are seen in the calculation of the F statistic, in that the:

A) numerator is larger, resulting in a larger F statistic.
B) numerator is smaller, resulting in a smaller F statistic.
C) denominator is smaller, resulting in a larger F statistic.
D) denominator is larger, resulting in a smaller F statistic.

Question 15

Which degrees of freedom value is unique to the one-way within-groups ANOVA?

A) between-groups
B) subjects
C) within-groups
D) total

Question 16

Dr.Sanders was interested in investigating the effects of stress on memory.He exposed participants to public speaking stress and room temperature stress and gave them a memory measure immediately after exposure to the two stressors.Dr.Sanders also gave participants the memory measure at baseline, when they first entered the research laboratory.Dr.Sanders hypothesized that participants' memories would be most affected by the two stressors compared to the baseline condition.What statistical test should Dr.Sanders use to test her hypothesis?

A) between-groups ANOVA
B) independent samples t test
C) within-groups ANOVA
D) dependent samples t test

Question 17

Within-groups designs reduce error due to differences between the groups by using the same participants in each group.If differences are then observed between the groups, those differences are attributed to:

A) extraneous variables.
B) differences between participants.
C) failure to control other important variables.
D) the manipulation of the independent variable.

Question 18

_____ degrees of freedom must be calculated in a within-groups ANOVA.

A) Five
B) Two
C) Three
D) Four

Question 19

Determine the critical cutoff for F at a p level of 0.05 if the following degrees of freedom were calculated for a one-way within-groups ANOVA: df_between = 2, df_subjects = 9, df_total = 29, df_within = 18.

A) 6.01
B) 4.26
C) 3.74
D) 3.56

Question 20

A one-way within-groups ANOVA is also known as a _____ ANOVA.

A) between-groups
B) single samples
C) repeated-measures
D) multiple groups

Question 21

For the data in the source table, calculate the F statistic of interest to researchers. $$\begin{array} { l | c | c c | c | } \hline \text { Source } & S S & d f & M S & F \\\hline \text { Between-groups } & 10.1 & 2 & 5.05 & \\\hline \text { Subjects } & 7.4 & 4 & 1.85 & \\\hline \text { Within-groups } & 8.5 & 8 & 1.063 & \\\hline \text { Total } & 26 & 14 & & \\\hline\end{array}$$

A) 4.75
B) 2.73
C) 1.74
D) 0.21

Question 22

For the data in the source table, what is the effect size for this one-way within-groups ANOVA? $$\begin{array} { | l | c | c c | c | } \hline \text { Source } & \text { SS } & d f & M S & F \\\hline \text { Between-groups } & 12.159 & 3 & 4.053 & 2.98 \\\hline \text { Subjects } & 6.77 & 5 & 1.354 & 0.996 \\\hline \text { Within-groups } & 20.4 & 15 & 1.360 & \\\hline \text { Total } & 39.329 & 23 & & \\\hline\end{array}$$

A) 0.249
B) 0.373
C) 0.664
D) 2.678

Question 23

A one-way within-groups ANOVA on 2 and 22 degrees of freedom results in an F statistic of 3.64.What decision should be made about the hypothesis based on this statistic?

A) Fail to reject the null hypothesis because the F statistic does not exceed the critical cutoff.
B) Fail to reject the null hypothesis and conclude there is no effect of the independent variable.
C) Reject the null hypothesis and conclude there are differences among the levels of the independent variable.
D) Reject the null hypothesis and conclude the independent variable has no effect.

Question 24

Which formula for calculating the subjects sum of squares for a within-groups ANOVA is correct?

A) $\Sigma$ (M_participant - GM)²
B) $\Sigma$ (M_participant - X)²
C) $\Sigma$ (M)(n - 1)
D) $\Sigma$ (M_participant - GM)

Question 25

A one-way within-groups ANOVA on 3 and 18 degrees of freedom results in an F statistic of 3.12.What decision should be made about the hypothesis based on this statistic?

A) Fail to reject the null hypothesis because the F statistic does not exceed the critical cutoff.
B) Fail to reject the null hypothesis and conclude there is no effect of the independent variable.
C) Reject the null hypothesis and conclude there are differences among the levels of the independent variable.
D) Reject the null hypothesis and conclude the independent variable has no effect.

Question 26

The _____ sum of squares is unique to the within-subjects design.

A) between-groups
B) within-groups
C) total
D) subjects

Question 27

Why is the subjects sum of squares calculated separately from the within-groups sum of squares?

A) to remove Type I error
B) to remove the variability between groups
C) to remove the variability within groups
D) to remove the variability due to participant differences

Question 28

To calculate the total sum of square for the one-way within-groups ANOVA, each score's deviation from the _____ is squared and summed.

A) mean
B) grand mean
C) cell mean
D) group mean

Question 29

Which F statistic represents a new calculation as part of the within-groups ANOVA?

A) F_between
B) F_within
C) F_subjects
D) F_total

Question 30

For the data in the source table, calculate the F statistic of interest to researchers. $$\begin{array} { l c c | c c } \hline \text { Source } & S S & d f & M S & F \\\hline \text { Between-groups } & 12.159 & 3 & 4.053 \\\hline \text { Subjects } & 6.77 & 5 & 1.354 \\\hline \text { Within-groups } & 20.4 & 15 & 1.360 \\\hline \text { Total } & 39.329 & 23 & \\\hline\end{array}$$

A) 0.34
B) 1.00
C) 2.98
D) 2.99

Question 31

For the data in the source table, what decision can be made about the hypotheses being tested? $$\begin{array} { l | c | c c | c | } \hline \text { Source } & S S & d f & M S & F \\\hline \text { Between-groups } & 39.52 & 2 & 19.76 & \\\hline \text { Subjects } & 6.45 & 5 & 1.29 & \\\hline \text { Within-groups } & 19.93 & 10 & 1.993 & \\\hline \text { Total } & 53 & 17 & & \\\hline\end{array}$$

A) Fail to reject the null hypothesis because the F statistic does not exceed the critical cutoff.
B) Fail to reject the null hypothesis and conclude there is no effect of the independent variable.
C) Reject the null hypothesis and conclude there are differences among the levels of the independent variable.
D) Reject the null hypothesis and conclude the independent variable has no effect.

Question 32

For the data in the source table, what is the effect size for this one-way within-groups ANOVA? $$\begin{array} { | l c | c | c | c | } \hline \text { Source } & S S & d f & M S & F \\\hline \text { Between-groups } & 10.1 & 2 & 5.05 & 4.751 \\\hline \text { Subjects } & 7.4 & 4 & 1.85 & 1.740 \\\hline \text { Within-groups } & 8.5 & 8 & 1.063 & \\\hline \text { Total } & 26 & 14 & & \\\hline\end{array}$$

A) 0.47
B) 0.54
C) 0.58
D) 1.84

Question 33

For the data in the source table, what is the effect size for this one-way within-groups ANOVA? $$\begin{array} { l | c | c c | c | } \hline \text { Source } & S S & d f & M S & F \\\hline \text { Between-groups } & 39.52 & 2 & 19.76 & \\\hline \text { Subjects } & 6.45 & 5 & 1.29 & \\\hline \text { Within-groups } & 19.93 & 10 & 1.993 & \\\hline \text { Total } & 53 & 17 & & \\\hline\end{array}$$

A) 0.837
B) 0.849
C) 1.178
D) 1.195

Question 34

_____ sums of squares must be calculated in a within-groups ANOVA.

A) Five
B) Two
C) Three
D) Four

Question 35

For the data in the source table, what decision can be made about the hypotheses being tested? $$\begin{array} {| l |c| c | c c |} \hline \text { Source } & S S & d f & M S & F \\\hline \text { Between-groups } & 10.1 & 2 &5.05 \\\hline \text { Subjects } & 7.4 & 4 & 1.85 \\\hline \text { Within-groups } & 8.5 & 8 & 1.036 \\\hline \text { Total } & 26 & 14 & \\\hline\end{array}$$

A) Fail to reject the null hypothesis because the F statistic does not exceed the critical cutoff.
B) Fail to reject the null hypothesis and conclude there is no effect of the independent variable.
C) Reject the null hypothesis and conclude there are differences among the levels of the independent variable.
D) Reject the null hypothesis and conclude the independent variable has no effect.

Question 36

Compared to a one-way between-groups ANOVA, the effect size calculation for the one-way ANOVA differs in:

A) Cohen's guidelines for interpreting the effect size values.
B) that variability due to subjects is removed from total variability in the denominator.
C) its ease of computation.
D) the content of the numerator.

Question 37

For the data in the source table, what decision can be made about the hypotheses being tested? $$\begin{array} { | l c | c c | c | } \hline \text { Source } & \text { SS } & d f & M S & F \\\hline \text { Between-groups } & 12.159 & 3 & 4.053 & \\\hline \text { Subjects } & 6.77 & 5 & 1.354 & \\\hline \text { Within-groups } & 20.4 & 15 & 1.360 & \\\hline \text { Total } & 39.329 & 23 & & \\\hline\end{array}$$

A) Fail to reject the null hypothesis because the F statistic does not exceed the critical cutoff.
B) Fail to reject the null hypothesis and conclude there is no effect of the independent variable.
C) Reject the null hypothesis and conclude there are differences among the levels of the independent variable.
D) Reject the null hypothesis and conclude the independent variable has no effect.

Question 38

In addition to hypothesis testing, effect size calculations are recommended as a way to assess:

A) the power of the statistical analysis.
B) the number of subjects needed to correctly reject the null hypothesis.
C) where the significant differences exist among groups.
D) whether the significant differences found are large enough to matter.

Question 39

For the data in the source table, what is the F statistic of interest to researchers? $$\begin{array} { l | c | c c | c | } \hline \text { Source } & S S & d f & M S & F \\\hline \text { Between-groups } & 39.52 & 2 & 19.76 & \\\hline \text { Subjects } & 6.45 & 5 & 1.29 & \\\hline \text { Within-groups } & 19.93 & 10 & 1.993 & \\\hline \text { Total } & 53 & 17 & & \\\hline\end{array}$$

A) 0.10
B) 0.65
C) 9.91
D) 15.32

Question 40

In addition to hypothesis testing, post hoc tests are required as a way to assess:

A) the power of the statistical analysis.
B) the number of subjects needed to correctly reject the null hypothesis.
C) where the significant differences exist among groups.
D) whether the significant differences found are large enough to matter.

Question 41

A researcher studying weight loss among overweight teenage girls wants to use a matched groups design to assess the effectiveness of three different diets.On which variable is it MOST important to match the participants?

A) month of birth
B) favorite junk food
C) level of commitment to the study
D) percent of body fat

Question 42

A researcher wants to take advantage of the strengths of a within-groups design but does not want to have each participant experience all levels of the independent variable.She can accomplish this through what other design option?

A) a series of independent-samples t tests
B) counterbalancing
C) matched groups
D) a series of Tukey HSD post hoc tests

Question 43

The one-way within-groups ANOVA is the multiple-group equivalent of a paired-samples t test.

Question 44

Pet preference was compared for four different types of animals (dogs, cats, birds, and fish), using a one-way within-groups ANOVA with nine participants.The standard error was calculated as 0.19.What are the critical cutoffs for the two-tailed Tukey HSD tests for these data, assuming a p level of 0.05, given the following groups' means: Dogs M = 4.43, Cats M = 4.18, Birds M = 2.73, Fish M = 4.07?

A) -4.0 and 4.0
B) -3.90 and 3.90
C) 3.90
D) 4.0

Question 45

For the data in the source table, what is the effect size for this one-way within-groups ANOVA? $$\begin{array} { | l c | c | c | c | } \hline \text { Source } & S S & d f & M S & F \\\hline \text { Between-groups } & 10.1 & 2 & 5.05 & 4.751 \\\hline \text { Subjects } & 7.4 & 4 & 1.85 & 1.740 \\\hline \text { Within-groups } & 8.5 & 8 & 1.063 & \\\hline \text { Total } & 26 & 14 & & \\\hline\end{array}$$

A) small
B) medium
C) large
D) very large

Question 46

Pet preference was compared for four different types of animals (dogs, cats, birds, and fish), using a one-way within-groups ANOVA with nine participants.The standard error was calculated as 0.19.Where are the significant effects for preference among these groups, given the following means for preference: Dogs M = 4.43, Cats M = 4.18, Birds M = 2.73, Fish M = 4.07?

A) Preference for birds is significantly lower than for the other three groups, and there are no other differences among the mean preferences.
B) Dogs and cats are preferred over birds and fish, but there are no differences between the other groups.
C) Birds and fish are less preferred than dogs and cats, but there are no other differences present.
D) All post hoc tests were significant at the 0.05 level.

Question 47

Each participant experiences all levels of the dependent variable in a within-groups design.

Question 48

Pet preference was compared for four different types of animals (dogs, cats, birds, and fish), using a one-way within-groups ANOVA with nine participants.The standard error was calculated as 0.19.What is the Tukey HSD value when comparing data for birds and fish given the following means for preference: Dogs M = 4.43, Cats M = 4.18, Birds M = 2.73, Fish M = 4.07?

A) 0.14
B) 6.38
C) -6.38
D) -7.05

Question 49

Pet preference was compared for four different types of animals (dogs, cats, birds, and fish), using a one-way within-groups ANOVA with nine participants.The standard error was calculated as 0.19.What is the Tukey HSD value when comparing data for dogs and birds given the following means for preference: Dogs M = 4.43, Cats M = 4.18, Birds M = 2.73, Fish M = 4.07?

A) 8.95
B) 8.10
C) 0.19
D) 0.11

Question 50

According to Cohen's conventions, an effect size of 0.012 for a one-way within-groups ANOVA is considered to be:

A) small.
B) medium.
C) medium to large.
D) large.

Question 51

The one-way within-groups ANOVA is the multiple-group equivalent of an independent-samples t test.

Question 52

For the data in the source table, what is the effect size for this one-way within-groups ANOVA? $$\begin{array} { l | c | c c | c | } \hline \text { Source } & S S & d f & M S & F \\\hline \text { Between-groups } & 39.52 & 2 & 19.76 & \\\hline \text { Subjects } & 6.45 & 5 & 1.29 & \\\hline \text { Within-groups } & 19.93 & 10 & 1.993 & \\\hline \text { Total } & 53 & 17 & & \\\hline\end{array}$$

A) small
B) medium
C) large
D) very large

Question 53

Pet preference was compared for four different types of animals (dogs, cats, birds, and fish), using a one-way within-groups ANOVA with nine participants.The standard error was calculated as 0.19.A significant F test indicates that there are differences between the groups.What post hoc tests are you most interested in performing given these group means: Dogs M = 4.43, Cats M = 4.18, Birds M = 2.73, Fish M = 4.07?

A) comparisons of preference for dogs with the other animals because of their popularity
B) computing all between-group comparisons
C) comparisons of preference for birds with the other groups, because the mean is noticeably lower
D) any comparison of preference for birds and fish because of their low popularity

Question 54

Pet preference was compared for four different types of animals (dogs, cats, birds, and fish), using a one-way within-groups ANOVA with nine participants.The standard error was calculated as 0.19.What is the Tukey HSD value when comparing data for cats and birds, given the following means for preference: Dogs M = 4.43, Cats M = 4.18, Birds M = 2.73, Fish M = 4.07?

A) 7.63
B) 6.90
C) 0.13
D) -7.63

Question 55

According to Cohen's conventions, an effect size of 0.16 for a one-way within-groups ANOVA is considered to be:

A) small.
B) medium.
C) medium to large.
D) large.

Question 56

Pet preference was compared for four different types of animals (dogs, cats, birds, and fish), using a one-way within-groups ANOVA with nine participants.The standard error was calculated as 0.19.What is the Tukey HSD value when comparing data for dogs and cats given the following means for preference: Dogs M = 4.43, Cats M = 4.18, Birds M = 2.73, Fish M = 4.07?

A) 0.198
B) 0.760
C) 1.190
D) 1.316

Question 57

There are some problems with a matched groups design, including that:

A) we might over-control variables that threaten the research.
B) participant drop-out means data are discarded.
C) power is reduced due to within-group variability.
D) participants can benefit from exposure to other treatment conditions.

Question 58

When using matched groups for a one-way within-groups ANOVA, a researcher should "match" participants on:

A) how many levels of the independent variable they experience.
B) all of the variables that the researcher wants to control.
C) their previous research experience.
D) the timing of their participation so that they meet the same people each time.

Question 59

According to Cohen's conventions, an effect size of 0.062 for a one-way within-groups ANOVA is considered to be:

A) small.
B) medium.
C) medium to large.
D) large.

Question 60

For the data in the source table, what is the effect size for this one-way within-groups ANOVA? $$\begin{array} { | l | c | c c | c | } \hline \text { Source } & \text { SS } & d f & M S & F \\\hline \text { Between-groups } & 12.159 & 3 & 4.053 & 2.98 \\\hline \text { Subjects } & 6.77 & 5 & 1.354 & 0.996 \\\hline \text { Within-groups } & 20.4 & 15 & 1.360 & \\\hline \text { Total } & 39.329 & 23 & & \\\hline\end{array}$$

A) small
B) medium
C) large
D) very large

Question 61

The effect size measure for the one-way within-groups ANOVA is Cohen's d.

Question 62

When conducting the one-way within-groups ANOVA, two F statistics are calculated, but only the between-groups F statistic is of interest.

Question 63

Order effects likely have been addressed if counterbalancing has occurred in the research.

Question 64

A researcher interested in the impact of "dress-down Fridays" on work performance decides to study the impact of attire at work.She randomly selects 35 people at a large company to participate.Over the course of three weeks, she has all 35 participants experience working under three different levels of work attire: casual, dress-casual, and formal attire.What statistical analysis would be appropriate for her design?

A) one-way within-groups ANOVA
B) one-way between-groups ANOVA
C) independent-samples t tests
D) paired-samples t tests

Question 65

When conducting the one-way within-groups ANOVA, two F statistics are calculated, but only one is of primary interest.

Question 66

Because the same participants are used in each condition, post hoc tests are not necessary when conducting a within-groups ANOVA.

Question 67

All of the assumptions for the one-way within-groups ANOVA are the same as those for the one-way between-groups ANOVA.

Question 68

The multiple-group equivalent of a paired-samples t test is the:

A) one-way between-groups ANOVA.
B) one-way within-groups ANOVA.
C) mixed design ANOVA.
D) matched groups design.

Question 69

The Tukey HSD test helps us determine which means are statistically significantly different from each other in a within-groups ANOVA.

Question 70

Effect sizes help us determine whether the differences observed are large enough to matter in a within-groups ANOVA.

Question 71

The primary benefit of the within-groups design is that within-groups variability is reduced.

Question 72

Effect sizes help us determine which means are statistically significantly different from each other in a within-groups ANOVA.

Question 73

Each participant experiences all levels of the independent variable in a within-groups design.

Question 74

A between-groups hypothesis test is preferred over a within-groups hypothesis test.

Question 75

When conducting the one-way within-groups ANOVA, two F statistics are calculated, but only the subjects F statistic is of interest.

Question 76

Matched groups require participants who are similar on all the variables that the researcher wants to control.

Question 77

The primary benefit of the within-groups design is that between-groups variability is reduced.

Question 78

The effect size measure for the one-way within-groups ANOVA is R².

Question 79

All within-groups designs require that the same people experience each level of the independent variable.

Question 80

When calculating effect size for one-way within-groups ANOVA, variability between means is considered relative to total variability after removing the variability that can be accounted for by the participants.