Question 1

In a factorial ANOVA, the research hypothesis for the interaction might look like this:

Accepted Answer

In a factorial ANOVA, the research hypothesis for the interaction effect is that there is a difference in the means across the levels of the factors, indicating an interaction. Thus, the hypothesis would state that the means are not equal, as in choice D.

Question 2

In the factorial ANOVA, subjects are measured ______.

Accepted Answer

In factorial ANOVA, subjects are typically measured only once, as it is used to analyze the effects of two or more independent variables on a single dependent variable in a between-subjects design.

Question 3

In the main effect F₍₁,₁₂₎ = 5.25, p < .05, what is the number of 5.25?

Accepted Answer

The number 5.25 is the obtained value of the main effect F-test.

Question 4

In the main effect F₍₁,₉₎ = 1.67, p = .229, what is the obtained value?

Accepted Answer

The obtained value in the main effect F₁,₉ is the F-value which is 1.67. The p-value is .229, which indicates that the obtained F-value is not statistically significant. Therefore, the answer is (C) 1.67.

Question 5

What do we call the difference when results showed a difference between levels of a factor?

Accepted Answer

The difference between levels of a factor is called the main effect.

Question 6

In the main effect F₍₁,₁₂₎ = 5.25, p < .05, what does the symbol p stand for?

Accepted Answer

The symbol p stands for the probability level or the probability of obtaining the observed statistic (in this case F₍₁,₁₂₎) by chance, given that the null hypothesis is true. A significance level (e.g., .05) is often set to determine whether the obtained p-value is statistically significant or not. If p < .05, it means that there is less than a 5% chance of obtaining the result by chance, which is considered statistically significant.

Question 7

In a factorial ANOVA, the null hypothesis for the interaction might look like this:

Accepted Answer

This is the correct null hypothesis for a factorial ANOVA, where µ represents the population mean and subscripts indicate the different levels of each factor being tested. The null hypothesis states that there is no interaction between the two factors being tested, meaning that the effect of one factor on the outcome variable does not depend on the level of the other factor. The other answer choices either do not accurately represent the null hypothesis for a factorial ANOVA or provide alternative hypotheses (H₁) instead.

Question 8

If you wanted to examine whether television viewing through social learning differs based on students' grade in school (i.e., first, second, third, etc.), what is the independent variable of interest?

Accepted Answer

The independent variable of interest is grade level, as it is the variable that is being manipulated (i.e., different grade levels are being compared to see if there are differences in television viewing through social learning).

Question 9

You wish to examine the impact of three different types of wall paint colors (blue, green, and yellow) on how often toddlers cry.Which of the following tests is appropriate to use?

Accepted Answer

One-way ANOVA is appropriate in this case as we have one independent variable (wall paint color) and one dependent variable (frequency of toddler crying). The test will help compare the means of the different paint colors and their impact on toddler crying. Factorial ANOVA is used when there are two or more independent variables, while t-tests are used when comparing the means of two groups only (either dependent or independent samples).

Question 10

In the main effect F₍₁,₉₎ = 1.67, p = .229, what is the level of significance?

Accepted Answer

The level of significance is represented by the p-value, which in this case is .229. Since the p-value is greater than the usual criterion for significance of .05, we fail to reject the null hypothesis and conclude that there is not sufficient evidence to support a significant main effect.

Question 11

In what condition do you use the factorial ANOVA?

Accepted Answer

Factorial ANOVA is used when you have more than one independent variable to analyze the relationship between the independent variables and the dependent variable. It also allows you to examine the interaction between the independent variables on the dependent variable. Therefore, option B is the correct answer.

Question 12

Dr.Moo conducted a research project in which she compared the impact of two types of therapy (pizza therapy and chocolate therapy) and gender on college students' happiness.Which of the following can be confirmed by the table below? $$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Source } & \text { Surns of Squares } & \text { df } & \text { Mear square } & F & \text { Significance } \
\hline \text { Therapy } & \mathbf { 2 6 5 . 2 2 5 } & 1 & 265.225 & 2.444 & .127 \
\hline \text { Gender } & \mathbf { 2 0 7 . 0 2 5 } & 1 & 207.205 & 1.908 & 176 \
\hline \text { Therapy } \times \text { Gender } & 1,050.625 & 1 & 1,050.625 & 9.683 & .004 \
\hline \text { Error } & \mathbf { 3 , 9 0 6 . 1 0 0 } & \mathbf { 3 6 } & 108.503 & & \
\hline \text { Total } & \mathbf { 2 2 4 , 3 2 1 . 0 0 0 } & \mathbf { 3 9 } & & & \
\hline
\end{array}$$

Accepted Answer

The answer of Dr.Moo conducted a research project in which...

Question 13

What is the two-way analysis of variance?

Accepted Answer

The two-way analysis of variance (ANOVA) is also known as a factorial ANOVA, which looks at the effects of two independent variables on one dependent variable. It is called "two-way" because there are two factors or variables that are being analyzed. The simple ANOVA (C) only looks at the effect of one independent variable on one dependent variable, while the complex ANOVA (D) refers to ANOVA designs with more than two independent variables. The one-way ANOVA (A) is not the same as the two-way ANOVA as it only involves one independent variable.

Question 14

If you wanted to examine whether television viewing through social learning differs based on students' grade in school (i.e., first, second, third, etc.), what is the dependent variable of interest?

Accepted Answer

The dependent variable of interest is the television viewing behavior, as that is what is being measured and compared based on the independent variable (grade level). The independent variable in this case is grade level (A), and the other options (C and D) are not relevant to this research question.

Question 15

In a factorial ANOVA, one of the null hypotheses for a main effect might look like this:
A)
B)
C)
D)

Accepted Answer

The answer of In a factorial ANOVA, one of the...

Question 16

You wish to examine the impact of two different types of music (pop music and jazz music) and pet food served (wet food and dry food) on how often cats glare at their owners.Which of the following tests is appropriate to use?

Accepted Answer

A factorial ANOVA would be appropriate in this scenario because it allows for analyzing the effects of multiple independent variables (type of music and type of pet food) on a dependent variable (frequency of cats glaring). This will help determine if there is a significant main effect of music type, pet food type, or if there is an interaction effect between the two.

Question 17

Dr.Moo conducted a research project in which she compared the impact of two types of therapy (pizza therapy and chocolate therapy) and gender on college students' happiness.What is the following table called? $$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Source } & \text { Surns of Squares } & d f & \text { Mean square } & F & \text { Significance } \
\hline \text { Therapy } & 265.225 & 1 & 265.225 & 2.444 & .127 \
\hline \text { Gender } & 207.025 & 1 & 207.205 & 1.908 & 176 \
\hline \text { Therapy } \times \text { Gender } & 1,050.625 & 1 & 1,050.625 & 9.683 & .004 \
\hline \text { Error } & \mathbf { 3 , 9 0 6 . 1 0 0 } & \mathbf { 3 6 } & 108.503 & & \
\hline \text { Total } & \mathbf { 2 2 4 , 3 2 1 . 0 0 0 } & \mathbf { 3 9 } & & & \
\hline
\end{array}$$

Accepted Answer

This table is called a source table, which is used in ANOVA (Analysis of Variance) to display the sources of variance, sums of squares, degrees of freedom, mean squares, F-values, and significance levels.

Question 18

The factorial ANOVA is used when you have multiple independent variables.

Accepted Answer

The factorial ANOVA is used when there are two or more independent variables that are crossed or combined to form conditions.

Question 19

A researcher wants to create an intervention to improve the well-being of graduate students in a counseling program, so she gives one group of students specific doses of rocky road ice cream, the second group of students specific doses of licorice, and the third group of students specific doses of chewy fruit-flavored candies for their treatments.As a second factor, she includes students in their first semester of their first year of graduate school as one cohort and students in the first semester of their second year of graduate school as the other cohort.To analyze the differences in well-being between the students in the three different "treatments" and two cohorts, she would use a(n) _______.

Accepted Answer

A factorial analysis of variance is appropriate for analyzing the effects of two independent variables (in this case, "treatment" and "cohort") on a dependent variable (well-being). This will allow the researcher to determine whether there are significant main effects of treatment, cohort, or an interaction between the two.

Question 20

A researcher wants to create an intervention to improve the well-being of graduate students in a counseling program, so she gives one group of students specific doses of rocky road ice cream, the second group of students specific doses of licorice, and the third group of students specific doses of chewy fruit-flavored candies for their treatments.As a second factor, she includes students in their first semester of their first year of graduate school as one cohort and students in the first semester of their second year of graduate school as the other cohort.The first factor in this intervention would be _______, the second factor would be _______, and the dependent variable would be _______.

Accepted Answer

The first factor in this intervention would be the type of treatment (rocky road ice cream, licorice, or fruit-flavored candies). 
The second factor would be the cohort (first-year students vs second-year students). 
The dependent variable would be well-being, as the researcher's goal is to improve the well-being of graduate students in the counseling program.

Quiz 14: Two Too Many Factors: Factorial Analysis of Variancea Brief Introduction