Practice Exercise: One -way Analysis of Variance (ANOVA)

1. When is it appropriate to use a one-way ANOVA to analyze data?

2. What letter is use the designate the test statistic used in the one-way ANOVA?

3. What are the two types of variance that are examined when conducting an analysis of variance?

4. Which type of variance is related to the effect of a treatment?

5. Does the analysis of variance test differences between two specific groups?

Use the One-way ANOVA function in SPSS to answer the questions based on the following scenario. (Assume a critical level of significance of .05).

A researcher is interested in determining if participation in extracurricular activities affects academic performance. High school students are randomly assigned to one of three conditions: no activities, some activities, many activities. The data from the final exam scores are as follows:

No activities: 75 74 66 79 62 68 59 73 76 69
Some activities: 78 85 85 77 81 76 90 85 73 80
Many activities: 58 70 58 59 62 55 58 63 67 59

6. Write an appropriate null hypothesis for this analysis.

7. What is the observed or computed value of F?

8. How would you explain the procedure for determining the degrees of freedom for the Between Groups variance (numerator)?

9. How would you explain the procedure for determining the degrees of freedom for the Within Groups variance (denominator)?

10. What is the value of the Between Groups degrees of freedom?

11. What are the value for the Within Groups degrees of freedom?

12. What is the reported level of significance?

13. Based on the reported level of significance, would you reject the null hypothesis?

14. Based on the reported level of significance, would you conclude that there was a statistically significant difference among the three groups?

15. Write a statement as it might appear in an article that reports the results of the one-way ANOVA.

Practice Exercise: One -way Analysis of Variance (ANOVA)

Use the One-way ANOVA function in SPSS to answer the questions based on the following scenario. Select Descriptives from the Options menu to obtain the means and standard deviations. (Assume a critical level of significance of .05).

Researchers are interested in determining if the type of medication influences the number of days it takes for symptoms to cease. Thirty-six patients are randomly assigned to receive Brand X, Brand Y, or Brand Z medication. The number of days before symptoms ceased are reported below.

Brand X: 20 30 26 15 13 24 28 19 23 29 17 25
Brand Y: 15 5 23 15 22 23 18 24 19 16 10 6
Brand Z: 14 15 16 20 21 24 14 23 17 11 14 22

1. Write an appropriate null hypothesis for this analysis.

2. What is the mean number of days it takes for symptoms to cease for each brand?

3. What is the standard deviation of the number of days it takes for symptoms to cease for each brand?

4. What is the observed or computed value of F?

5. What is the value for the Between Groups degrees of freedom?

6. What is the value for the Within Groups degrees of freedom?

7. What is the reported level of significance?

8. Based on the reported level of significance, would you reject the null hypothesis?

9. Based on the reported level of significance, would you conclude that there was a statistically significant difference among the three groups?

10. Write a statement as it might appear in an article that reports the results of the one-way ANOVA.