These slides are about ANOVA

1. Introduction to Analysis of
Variance (ANOVA)
Course: Probability and Statistics
Instructor: Dr. Umara Zahid
Fall 2021

2. Outline
• Introduction
• Different Types of ANOVA
• Assumptions of ANOVA
• Hypotheses in ANOVA
• Main Effects/ Interaction Effects
• Post Hoc Tests
• The F Distribution

3. Introduction
• ANOVA is a statistical method used to compare the means of two or
more groups
• Factors (Variables)
• Levels
• Factor: ‘Dosage’
• Levels: 0mg, 50mg, 100mg

4. One Way ANOVA
• One factor with at least two levels, levels are independent

5. Repeated Measures ANOVA
• One factor with at least two levels, levels are dependent

6. Factorial ANOVA
• Two or more factors (each of which with at least two levels), levels
can be independent, dependent or mixed

7. Assumptions in ANOVA
1. Normality of sampling distribution of means
2. Independence of errors
• Errors between cases is independent of one another
3. Absence of Outliers
• Outliers must be removed from the dataset
4. Homogeneity of Variances

8. Hypotheses in ANOVA
• ANOVA with one factor (“A” three levels)
• ANOVA with two factors (“A” and “B” each with three levels)

9. Post Hoc Analysis
• If we reject the null hypothesis, all we know is there is difference
among groups
• Post hoc test determine where the difference lie

10. The F distribution in ANOVA
• When doing ANOVA, we calculate an “F” statistic. It is similar to other
statistics such as “z” and “t”
• If there are no treatment differences (If there is no actual effect), we
expect F to be 1. If there are treatment differences, we expect F to be
greater than 1.
• The F statistic has its own one-tailed distribution, much like ‘t’ and ‘z’

11. One-Way ANOVA
• One factor with at least two levels,
levels are independent
• Researchers want to test a new anti-
anxiety medication. They split
participants into three conditions
(0mg, 50mg, 100mg), then ask them
to rate their anxiety level on a scale
of 1-10. Are there any differences
between the three conditions using
alpha=0.05?
• We have to follow the same 7 steps

12. One way ANOVA
• Define Hypotheses
• Alpha= 0.05

13. State Decision Rule
• To look up the critical value, we need to use two different degrees of
freedom

14. F table for 0.05

15. Calculate Test Statistics
• Consider the following table:

16. Calculate Test Statistics