Question 1

What is the main advantage of using a factorial design instead of doing separate studies of each variable?
A)Speed: with a factorial design you are able to carry out a study at twice the speed of other designs.
B)Effect size: with a factorial design you can increase the effect size by a factor of 2-4.
C)Efficiency: with a factorial design you study both variables at once without needing twice as many participants.
D)Both A and B.

Accepted Answer

Factorial designs allow for the efficient testing of multiple variables simultaneously without requiring a significantly larger sample size. This saves time, resources and minimises the chances of participant attrition, making it the most efficient choice.

Question 2

A consumer researcher is interested in the effects of Annual Income and Motivations to Shop on shopping patterns of consumers. If Annual Income (broken into two levels: High and Moderate)and Motivation to Shop (with three levels: Escape, Necessity, and Socializing)are considered in one study, how many cells will there be?
A)2
B)3
C)4
D)6

Accepted Answer

The study involves two factors: Annual Income with two levels and Motivation to Shop with three levels. To find the number of cells, multiply the levels of each factor: 2 (Annual Income levels) * 3 (Motivation to Shop levels) = 6 cells.

Question 3

A research article presented the results of an analysis of variance as "F(2,38)= 3.60, p < .05." How many groups were there in the study?
A)2
B)3
C)40
D)41

Accepted Answer

The number of groups in the study is indicated by the first number in the F statistic notation, which is one less than the number of groups. Therefore, F(2,38) means there were 3 groups.

Question 4

Before carrying out a study, a researcher can calculate approximate power for the .05 significance level for small, medium, and large effect sizes if one has access to a power table and knows the __________.
A)estimated effect size
B)outcome of the hypothesis-testing procedure
C)multiple correlation
D)degrees of freedom within

Accepted Answer

The estimated effect size is necessary for calculating approximate power for different significance levels.

Question 5

When carrying out an ANOVA, what is the approximate number of participants needed in each group (assuming equal sample sizes)for 80% power when you anticipate a medium effect size and have four groups in the study?
A)16
B)18
C)21
D)45

Accepted Answer

The answer of When carrying out an ANOVA, what is...

Question 6

All of the following are true about the creator of the analysis of variance EXCEPT:
A)his name was Karl Pearson
B)he supported the idea of eugenics
C)he wrote 300 papers and 7 books
D)his work was first popularized in agriculture

Accepted Answer

The creator of the analysis of variance was not Karl Pearson, but rather Ronald Fisher. Pearson was a contemporary statistician who did significant work in correlation and regression, but he did not develop the analysis of variance.

Question 7

In a two-way factorial design, you are testing:
A)one interaction and one main effect
B)one interaction and two main effects
C)two interactions and one main effect
D)two interactions and two main effects

Accepted Answer

In a two-way factorial design, there are two independent variables or factors, each with two or more levels. This allows for the testing of two main effects (the effects of each factor on the dependent variable) and one interaction effect (the combined effect of the two factors on the dependent variable). Choice B is the correct answer as it includes one interaction effect and two main effects.

Question 8

The main advantage of a factorial design is that it lets you study:
A)the correlation between two or more variables
B)the predictive validity of several variables
C)the effects of combining two or more variables
D)nominal variables with parametric tests

Accepted Answer

A factorial design allows researchers to study the effects of combining two or more variables, which can provide insights into how variables interact and influence one another. This is particularly useful in fields like psychology and social sciences, where complex human behaviors and attitudes are being studied. The other answer choices are not accurate descriptions of the advantages of a factorial design.

Question 9

What is the approximate level of power for a study using ANOVA at the .05 significance level with four groups of 30 participants each (expected effect size is medium).
A) .13
B) .61
C) .96
D) .55

Accepted Answer

Based on power calculations, a study with four groups of 30 participants each and a medium effect size (f = 0.25) would have a power of approximately 0.61 at an alpha level of 0.05. Therefore, the correct answer is B.

Question 10

A research article reports the following: "The mean performance scores for the Normal Sleep, Reduced Sleep, and No Sleep groups were 18.0, 16.6, and 15.6, respectively, F(2,36)= 2.95, p < .05." Based on this information, which conclusion is most accurate?
A)People who get no sleep perform significantly worse than people who sleep a reduced amount.
B)People who sleep a reduced amount perform significantly worse than people who sleep a normal amount.
C)The three groups do not all come from populations with the same mean, although it is not clear which population means are different.
D)This null hypothesis cannot be rejected.

Accepted Answer

The F statistic and p-value indicate that there is a significant difference among the group means, but without post-hoc comparisons, it's unclear which specific groups differ from each other.

Question 11

__________ is a way of organizing a study in which the effect of two or more variables is examined at once by making groupings of every combination of the variables.
A)Factorial research design
B)Repeated measures research design
C)Multiple research design
D)Influential research design

Accepted Answer

A factorial research design allows researchers to examine the effects of two or more variables by creating groupings of every possible combination of the variables. This approach allows for the identification of potential interactions between variables and can help to better understand complex phenomena.

Question 12

An interaction effect in a two-way factorial research design:
A)is the effect of one variable, ignoring the influence of other variables
B)occurs when the influence of one variable changes according to the level of another variable
C)almost never occurs when more than one variable is considered at a time
D)is rare in a well-designed study, and usually indicates some error in computation

Accepted Answer

An interaction effect occurs when the influence of one variable changes according to the level of another variable. This means that the two variables are not operating independently of each other and there is a complex relationship between them. It is common in a two-way factorial research design and is not indicative of an error in computation.

Question 13

A two-way factorial design:
A)is "two-way" because the influence of two separate variables is being studied
B)varies only in name from a one-way analysis of variance
C)considers two levels of a single variable
D)considers a single level of two variables

Accepted Answer

A two-way factorial design involves examining the influence of two separate variables, hence the term "two-way." It is distinct from a one-way analysis of variance, which only considers one variable. Additionally, a factorial design can consider multiple levels of each variable, not just a single level.

Question 14

Which of the following would be most likely to appear in a research article?
A)F(22)= 3.40, significant
B)F(2,55)< .05
C)F(2,44)= 3.4, p < .05
D)F = 3.40, p < .05

Accepted Answer

In research articles, statistical results are usually presented in the form of an F-statistic, degrees of freedom, and p-value. Option A does not provide degrees of freedom or p-value, option B only provides an inequality and not the actual F-statistic value or p-value, and option D does not provide degrees of freedom. Option C provides all the necessary information.

Question 15

Which of the following shows how the results of an analysis of variance would usually be reported in a research article?
A)F < p(.01)
B)F(3,50)= 4.33, p < .01
C)F(4.33)= p(.01)
D)F = 4.33, significant

Accepted Answer

The correct way to report the results of an analysis of variance is to provide the F-value, the degrees of freedom for the numerator and denominator (in parentheses), and the p-value for the significance test. Option A only provides the p-value, while Option C has the F-value and the p-value but not the degrees of freedom. Option D is too vague and does not provide any statistical information.

Question 16

Suppose you are planning a study involving five groups and you expect a medium effect size (and will use the .05 level). For 80% power, how many participants will you need in each group?
A)240
B)52
C)16
D)39

Accepted Answer

For a medium effect size with 80% power and a significance level of 0.05, approximately 39 participants per group are needed in a study involving five groups.

Question 17

According to the effect size conventions for ANOVA, .14 is considered to be a __________ effect.
A)very small
B)small
C)medium
D)large

Accepted Answer

According to Cohen's conventions for effect size in ANOVA, an effect size (eta squared) of .14 is considered to be large.

Question 18

Ronald A. Fisher was noted for:
A)the creation of the t test for independent means
B)his charming personality, which inadvertently helped popularize various statistical tests
C)the creation of the analysis of variance
D)his overcoming of great physical disabilities

Accepted Answer

Ronald A. Fisher is known for his work in creating the analysis of variance, which is a statistical tool used to analyze differences among group means. While he did make significant contributions to other statistical tests, such as the t test, it is the creation of ANOVA that he is most noted for. His personality and personal struggles are not relevant to his contributions to statistics.

Question 19

You conduct an ANOVA in which you expect a small effect size. What is your approximate level of power if you plan to use five groups with 20 participants in each group?
A) .01
B) .10
C) .13
D) .17

Accepted Answer

The answer of You conduct an ANOVA in which you...

Question 20

Suppose you are planning a study involving three groups and you expect a large effect size (and will use the .05 level). For 80% power, how many participants will you need in total?
A)52
B)18
C)63
D)156

Accepted Answer

For a study with three groups, expecting a large effect size, and aiming for 80% power at the .05 significance level, a total of 63 participants is typically needed. This calculation is based on standard power analysis methods for comparing means across groups, taking into account the desired power level, effect size, and alpha level.

Quiz 10: Introduction to the Analysis of Variance

What is the main advantage of using a factorial design instead of doing separate studies of each variable?

A research article presented the results of an analysis of variance as "F(2,38) = 3.60, p < .05." How many groups were there in the study?

Before carrying out a study, a researcher can calculate approximate power for the .05 significance level for small, medium, and large effect sizes if one has access to a power table and knows the __________.

When carrying out an ANOVA, what is the approximate number of participants needed in each group (assuming equal sample sizes) for 80% power when you anticipate a medium effect size and have four groups in the study?

All of the following are true about the creator of the analysis of variance EXCEPT:

In a two-way factorial design, you are testing:

The main advantage of a factorial design is that it lets you study:

What is the approximate level of power for a study using ANOVA at the .05 significance level with four groups of 30 participants each (expected effect size is medium) .

A research article reports the following: "The mean performance scores for the Normal Sleep, Reduced Sleep, and No Sleep groups were 18.0, 16.6, and 15.6, respectively, F(2,36) = 2.95, p < .05." Based on this information, which conclusion is most accurate?

__________ is a way of organizing a study in which the effect of two or more variables is examined at once by making groupings of every combination of the variables.

An interaction effect in a two-way factorial research design:

A two-way factorial design:

Which of the following would be most likely to appear in a research article?

Which of the following shows how the results of an analysis of variance would usually be reported in a research article?

Suppose you are planning a study involving five groups and you expect a medium effect size (and will use the .05 level) . For 80% power, how many participants will you need in each group?

According to the effect size conventions for ANOVA, .14 is considered to be a __________ effect.

Ronald A. Fisher was noted for:

You conduct an ANOVA in which you expect a small effect size. What is your approximate level of power if you plan to use five groups with 20 participants in each group?

Suppose you are planning a study involving three groups and you expect a large effect size (and will use the .05 level) . For 80% power, how many participants will you need in total?