Question 1

After you run an ANOVA you find levene's statistics is .08. From this you will assume that the group ________________ is ____________________.

Accepted Answer

Levene's statistic tests for homogeneity of variance across groups. A value of .08 indicates that the variances are not significantly different. Therefore, we can assume that the group variances are not significantly different.

Question 2

A ________________ is used to compare the means of two independent groups.

Accepted Answer

An independent t-test is used to compare the means of two independent groups. Option B is used when the same group is measured twice, option C compares more than two independent groups, and option D compares the means of three or more dependent groups.

Question 3

Repeating a t-test multiple times to compare more than two groups results in raising the chance of a ____________________.

Accepted Answer

Repeating a t-test multiple times increases the risk of a type I error, also known as a false positive. This occurs when the results show a significant difference between groups when there is actually no real difference. This can happen due to chance alone when multiple tests are performed.

Question 4

A group of researchers is interested in if there is a statistically significant difference in the average number of clients served in four different departments. To answer this question, what type of ANOVA should they use?

Accepted Answer

The researchers are interested in comparing the means of four different groups (departments) which is the aim of one-way ANOVA. Factorial ANOVA involves the comparison of the means of two or more independent variables, mixed design ANOVA involves the comparison of the means of both between-subjects and within-subjects factors, and repeated measures ANOVA involves the comparison of the means of the same group of participants across different time points.

Question 5

The ANOVA is known as a(n) _____________________ because it only indicates whether or not there is a significant difference between the groups, not between which groups the difference lies.

Accepted Answer

The ANOVA is an omnibus test because it tests for overall differences between groups but does not provide information about which specific groups differ from one another.

Question 6

An assumption of the ___________________ is that the observations are independent of one another.

Accepted Answer

One-way ANOVA assumes that the observations within each group are independent of one another. In contrast, paired samples t-test, paired samples ANOVA, and repeated measures ANOVA all involve dependent observations.

Question 7

A researcher conducts an ANOVA and finds a significant result, what should be done next?

Accepted Answer

When a researcher conducts an ANOVA and finds a significant result, the next step should be to perform a post-hoc test to determine which specific groups have significant differences. This test can help identify where the differences lie among the groups and provide more detailed information about the results. Beta and alpha tests are not relevant to this situation, and omnibus tests are already completed as part of the ANOVA.

Question 8

After Jim runs his ANOVA he finds that station 3 is significantly different from station 5. He then looks at the ______________ for each station to determine which station has significantly faster response times.

Accepted Answer

The mean response time for each station will allow Jim to determine which station has faster response times. The F-statistic and eta square indicate whether there are significant differences between groups, but they do not provide information on the specific differences in response times. The t-statistic would be appropriate if Jim were comparing two groups instead of multiple groups.

Question 9

What statistic does an ANOVA produce?

Accepted Answer

ANOVA produces the F-statistic, which measures the variation between group means compared to the variation within groups.

Question 10

For Jim's case, one of his hypotheses is: Station 1 mean response time=Station 2 mean response time= (etc.) = Station 8 mean response time. This is considered his ____________ hypothesis.

Accepted Answer

Jim's hypothesis that all stations have equal mean response times is his null hypothesis, which is the default assumption until proven otherwise through research.

Question 11

_______________________ is used when you are comparing more than two related groups.

Accepted Answer

Repeated measures ANOVA is used when comparing more than two related groups, as it accounts for the correlation between the repeated measures on the same subjects.

Question 12

In Emily's case she will be utilizing a ____________________ to evaluate the difference in cultural competence between departments.

Accepted Answer

A one-way ANOVA would be the best choice to evaluate the difference in cultural competence between departments, as it can compare the means of three or more groups. A repeated-measures ANOVA would be used if measuring the same variable at multiple time points, a paired samples t-test would be used for comparing two related samples (such as pre- and post-intervention), and an independent t-test would be used for comparing two independent groups.

Question 13

The dependent variable in a repeated measure ANOVA is what type of variable?

Accepted Answer

The dependent variable in a repeated measure ANOVA is typically a continuous variable, meaning it can take on any numerical value. This makes it possible to calculate means and variances, which are important for conducting statistical tests. Grouping variables (A) are independent variables that are used to divide participants into different categories, such as male and female, or experimental and control groups. Ordinal variables (C) are variables that can be ranked, but the differences between values are not necessarily meaningful. Nominal variables (D) are variables that are used only for labeling categories, and do not have any inherent numerical value.

Question 14

A _________________ is used when the researcher is interested in the effect of one or more grouping variables on one or more repeated measures.

Accepted Answer

A mixed design ANOVA is used when the researcher wants to examine the effect of both between-subjects variables (such as different groups of participants) and within-subjects variables (such as repeated measures over time) on a dependent variable. This design allows for testing both main effects and interactions between variables.

Question 15

What is the minimum recommended number of cases for each group in ANOVA?

Accepted Answer

The minimum recommended number of cases for each group in ANOVA is typically 15 to ensure adequate power and reliability of the results.

Question 16

Regardless of which ANOVA test is performed, there is an assumption that the data is __________________.

Accepted Answer

The assumption for any ANOVA test is that the data is normally distributed.

Question 17

___________________ is calculated as the between sum of squares divided by the combined between sum of squares and the within sum of squares.

Accepted Answer

Eta square is the measure of effect size in ANOVA, which is calculated as the between sum of squares divided by the combined between sum of squares and the within sum of squares.

Question 18

A graduate student is interested how her numerical grade is impacted based on in which department she is taking the course and the gender of the professor. What type of ANOVA would she have to run to answer this question?

Accepted Answer

A factorial ANOVA would allow the graduate student to analyze the impact of two independent variables (department and gender of professor) on her dependent variable (numerical grade). This would provide a more comprehensive understanding of the factors influencing her grade compared to a one-way ANOVA, which would only examine the impact of one independent variable. A mixed design ANOVA and a repeated measures ANOVA are not appropriate for this research question as they involve analyzing within-subjects factors, which are not applicable in this scenario.

Question 19

_______________________ is an indicator of magnitude of difference between groups.

Accepted Answer

Effect size is a measure of the magnitude of difference between groups and can provide a more informative understanding of the practical significance of the results. P-value is a measure of statistical significance and does not directly relate to the magnitude of difference between groups. F-statistic is used in ANOVA to test for differences between groups but does not provide a direct measure of effect size. Significance is a broad term that can refer to statistical or practical significance and is not a specific measure of effect size.

Question 20

Classroom A scores an average of 89 on an exam, classroom B scores an average of 85 on the exam, and classroom C scores an average of 94 on the exam. You run an ANOVA test and find a p-value of .50. What is the next step you would take?

Accepted Answer

Given the p-value of .50, which is significantly higher than the common alpha level of 0.05, there is not enough evidence to reject the null hypothesis. This suggests that any observed differences in exam scores among the classrooms are likely due to chance. Rejecting the research hypothesis is the appropriate step, as it implies accepting the null hypothesis that there are no significant differences between the groups.

Quiz 10: Comparing Means of More Than Two Groups

After you run an ANOVA you find levene's statistics is .08. From this you will assume that the group is ____.