1. Meead Saberi K., Portland State University
Analysis of Variance
ANOVA
Meead Saberi K., Portland State University
CE507 Introduction to Transportation Research Methods, Dr. Chris Monsere

2. Generate Research Hypothesis
Does rainfall affect traffic speed?

3. What is ANOVA?
To analyze the effects of one or more factors on a dependent variable
To test the difference in population means 3

4. Assumptions or Requirements
Dependent Variable (Y)
(Quantitative)
Independent Variable (X)
(Quantitative or Qualitative)
Rainfall in different levels
SPEED
Mean Speed
Rainfall level 27
No rain 30
Very light
23.5
Light
Moderate 4

5. Are the populations normally distributed?
Assumptions or Requirements
Are the populations normally distributed? 5

6. Are the populations normally distributed?
Assumptions or Requirements
Are the populations normally distributed? 6

7. Are the populations normally distributed?
Assumptions or Requirements
Are the populations normally distributed? 7

8. Are the populations normally distributed?
Assumptions or Requirements
Are the populations normally distributed? 8

9. Are the populations normally distributed?
Assumptions or Requirements
Are the populations normally distributed? 9

10. Assumptions or Requirements
Are the populations normally distributed?
No, they are not. So?
Use non-parametric Kruskall Wallis test 10

11. Are the populations variances equal?
Assumptions or Requirements
Are the populations variances equal?
Rainfall level
Variance of Speed
No rain
226
Very light rain
213
Light rain
211
Moderate rain
144 11

12. Assumptions or Requirements
Are the populations variances equal?
No, they are not. So?
Use non-parametric Kruskall Wallis test 12

13. F-Ratio Test (SPSS) Speed df F Sig. Between Groups 3 1.382 0.247
If the difference between the means is due only to chance, F value would be 1.
The larger this value, the greater the likelihood that the differences between the means are due to something other than chance alone, namely real effects.
α = 0.05
α = 0.25 13

14. Conclusions
Statistical results of ANOVA may not provide definitive conclusions as to the underlying processes. They merely provide clues to support or refute an engineering claim.
No amount of statistics can replace logic and critical thinking about a process.
Use the non-parametric Kruskall Wallis test if the requirements were not met. 14

15. Questions?
Thanks