Analysis of Variance (ANOVA): Comparing Group Means - Data Analysis PhD

Question 1

A one-way ANOVA is used to compare means between:

Accepted Answer

Two or more groups

Answer

One group at two or more time points

Answer

Two groups on two or more variables

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Three or more groups on one variable with repeated measures

Question 2

The F-statistic in ANOVA represents:

Accepted Answer

The ratio of between-group variance to within-group variance

Answer

The probability of obtaining the observed results by chance

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The number of groups in the study

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The degrees of freedom for the within-group variance

Question 3

Which post-hoc test is used to compare all possible pairs of means in an ANOVA?

Accepted Answer

Tukey's Honestly Significant Difference (HSD) test

Answer

Bonferroni test

Answer

Scheffé test

Answer

Games-Howell test

Question 4

Which of the following is a violation of the normality assumption of ANOVA?

Accepted Answer

Skewness or kurtosis in the distribution of residuals

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Outliers in the data

Answer

Unequal sample sizes

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Non-independence of observations

Question 5

The main effect of an independent variable in a two-way ANOVA is:

Accepted Answer

The effect of the variable on the dependent variable, averaged across all levels of the other variable

Answer

The effect of the variable on the dependent variable, controlling for the effect of the other variable

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The effect of the variable on the dependent variable, ignoring the effect of the other variable

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The effect of the dependent variable on the independent variable

Question 6

In a one-way ANOVA, what is the null hypothesis?

Accepted Answer

The means of all groups are equal

Answer

The means of at least two groups are different

Answer

The standard deviations of all groups are equal

Answer

The residuals are normally distributed

Question 7

In a two-way ANOVA, what effect represents the combined effect of the two factors?

Accepted Answer

Interaction effect

Answer

Main effect of factor A

Answer

Main effect of factor B

Answer

Residual effect

Question 8

In a two-way ANOVA, what is the effect called when the effect of one factor changes the effect of the other factor?

Accepted Answer

Interaction effect

Answer

Main effect

Answer

Crossover effect

Answer

Residual effect

Question 9

What is the purpose of the F-test in an ANOVA?

Accepted Answer

To determine whether the means of two or more groups differ significantly.

Answer

To determine whether the variance of two or more groups differ significantly.

Answer

To determine whether the mean of a group differs significantly from a specified value.

Answer

To determine whether the correlation between two variables is significant.

Question 10

How does increasing the sample size affect the power of an ANOVA?

Accepted Answer

It increases the power.

Answer

It decreases the power.

Answer

It has no effect on the power.

Answer

It depends on the effect size.

Question 11

Describe the key difference between parametric and non-parametric tests.

Accepted Answer

Parametric tests assume that the data is normally distributed, while non-parametric tests do not.

Answer

Non-parametric tests assume that the data is normally distributed, while parametric tests do not.

Answer

Parametric tests are more powerful than non-parametric tests.

Answer

Non-parametric tests are more powerful than parametric tests.

Question 12

Within the context of ANOVA, what is the main purpose of effect size?

Accepted Answer

To gauge the practical significance of the observed differences between groups.

Answer

To establish the statistical significance of the ANOVA findings.

Answer

To pinpoint the specific groups that differ from one another.

Question 13

What is the purpose of the F-test in ANOVA?

Accepted Answer

To determine if one or more population means are different

Answer

To test the significance of individual means

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To estimate the variance of a population

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To determine the probability of making a Type I error

Question 14

What is the difference between a main effect and an interaction effect in ANOVA?

Accepted Answer

A main effect is the effect of a single independent variable, while an interaction effect is the combined effect of two or more independent variables

Answer

A main effect can only occur in a one-way ANOVA, while an interaction effect can only occur in a two-way ANOVA

Answer

A main effect is the effect of a qualitative variable, while an interaction effect is the effect of a quantitative variable

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A main effect is always significant, while an interaction effect is not

Question 15

What is the purpose of post-hoc tests in ANOVA?

Accepted Answer

To compare the means of specific groups after a significant ANOVA result

Answer

To adjust the results of ANOVA for multiple comparisons

Answer

To test the assumptions of ANOVA

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To calculate the effect size of ANOVA

Question 16

What is the advantage of using a mixed-design ANOVA?

Accepted Answer

It can handle both within-subjects and between-subjects factors in the same analysis

Answer

It is not affected by violations of the assumption of independence

Answer

It is easier to interpret than a two-way ANOVA

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It is more powerful than a one-way ANOVA

Question 17

In ANOVA, the F-test is primarily used to:

Accepted Answer

Test for statistically significant differences between the means of multiple groups.

Answer

Estimate the variance of the error term

Answer

Determine the effect size of the independent variable

Question 18

Which of the following is a common type of ANOVA?

Accepted Answer

One-way ANOVA

Answer

Regression analysis

Answer

Factor analysis

Answer

Discriminant analysis

Question 19

In a one-way ANOVA, the null hypothesis typically states that:

Accepted Answer

The means of all groups being compared are equal.

Answer

The data is normally distributed

Answer

The effect size of the independent variable is zero

Answer

The variance of the groups being compared is equal

Question 20

Which of the following is an example of a post-hoc test used after ANOVA?

Accepted Answer

Tukey's Honestly Significant Difference (HSD) test

Answer

Chi-square test

Answer

t-test

Answer

F-test

Question 21

What is the measure of effect size commonly reported for ANOVA?

Accepted Answer

Eta squared

Answer

Cohen's d

Answer

Omega squared

Answer

R-squared

Question 22

Which of the following is considered a limitation of ANOVA?

Accepted Answer

It does not account for potential interactions between independent variables.

Answer

It can only be used with normally distributed data

Answer

It requires a very large sample size

Question 23

What is the fundamental difference between a one-way and two-way ANOVA?

Accepted Answer

One-way ANOVA compares means between multiple groups on a single independent variable, while two-way ANOVA compares means on two independent variables.

Answer

One-way ANOVA is parametric, while two-way ANOVA is non-parametric

Question 24

How is the p-value related to the F-test in ANOVA?

Accepted Answer

The p-value represents the probability of observing an F-value as large or larger than the calculated F-value, assuming the null hypothesis is true.

Answer

The F-value is the ratio of the error sum of squares to the treatment sum of squares