ANOVA

1) In one-way ANOVA, how many groups or treatments are compared?

• Two

• Three or more

• Only one

• None of the above

3) What does the F-statistic represent in ANOVA?

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

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

• The difference between means of two groups

• The difference between variances of two groups

4) How do you interpret a significant F-statistic in ANOVA?

• There is a difference between the largest and smallest group means

• There is no difference between any of the group means

• There is a difference between at least two group means

• There is no interpretation for a significant F-statistic

5) Which assumption of ANOVA states that the population variances are equal across all groups?

• Normality

• Homogeneity of variances

• Independence

• Random sampling

6) What is the post hoc test commonly used after ANOVA to determine which specific groups differ significantly from each other?

• Independent t-test

• Paired t-test

• Tukey's HSD

• Pearson correlation

8) In a two-way ANOVA, what does a significant interaction effect suggest?

• The two factors have independent effects on the dependent variable

• There is no relationship between the factors and the dependent variable

• The two factors are correlated with each other

• The two factors have a combined effect on the dependent variable

7) What is the purpose of conducting a two-way ANOVA instead of two separate one-way ANOVAs?

• It provides more information about the data

• It is computationally simpler

• There is no difference between the two approaches

• It reduces the likelihood of Type I error

Answer explanation

Type I error occurs when a null hypothesis that is actually true is incorrectly rejected.

In the context of ANOVA, this would mean incorrectly concluding that there is a significant difference between groups when there isn't one in reality.

When performing multiple hypothesis tests (such as conducting separate one-way ANOVAs for each factor in a two-way ANOVA), the chance of making at least one Type I error increases with each test.

2) In a two-way ANOVA, what are the two main factors that are examined?

• Time and space

• Gender and age

• Treatment and time

• Two independent variables or factors

1. 9) What does an ANOVA table show?

• • A summary of descriptive statistics for each group.

• • The F-statistic, its p-value, and degrees of freedom.

• • A visualization of the data distribution for each group.

• • The estimated mean and standard deviation for the overall data.

10) An educational psychologist wants to assess the effectiveness of three different study techniques on exam scores. Students are randomly assigned to one of the three groups and complete an exam after implementing the assigned technique. What could be concluded from a significant F-statistic in a one-way ANOVA?

• • All three study techniques are equally effective for all students.

• • Individual differences in learning styles prevent any technique from being universally effective.

• • At least one study technique leads to significantly different average exam scores compared to others.

• • The specific study technique with the highest average score is automatically the best for everyone.