1. Section 15.2 One-Way Analysis of Variance
AP Statistics

2. One-Way Analysis of Variance
Which of four advertising offers mailed to sample households produces the highest sales in dollars?
Which of ten brands of automobile tires wears longest?
How long do cancer patients live under each of three therapies for their cancer?

3. One-Way Analysis of Variance
Which of four advertising offers mailed to sample households produces the highest sales in dollars?
Which of ten brands of automobile tires wears longest?
How long do cancer patients live under each of three therapies for their cancer?

4. One-Way Analysis of Variance
One-Way Analysis of Variance (ANOVA) is good at comparing more than two treatments against each other.
When comparing two means, we would typically 2-sample z-test or 2-sample t-test.
When comparing more than 2 means, use ANOVA.

5. Example
Pickup trucks and four-wheel-drive sport utility vehicles are replacing cars in American driveways. Do trucks and SUVs have lower gas mileage than cars? We have data on the highway gas mileage (in miles per gallon) for 28 midsize cars, 8 standard size pickup trucks, and 26 SUVs.

8. Sure, the means are different, but are they significantly so?

9. The problem with doing multiple comparisions
We could do 3 2-sample t-tests, but this is cumbersome.
Instead, we will do one test determine whether there any differences amongst the three groups.
If there is a difference, then follow up with pair-wise analysis

12. One-way ANOVA: Midsize, Pickup, SUV
Source DF SS MS F P
Factor
Error
Total
S = R-Sq = 57.63% R-Sq(adj) = 56.19%
Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev
Midsize (---*----)
Pickup ( *------)
SUV (----*---)
Pooled StDev = 2.749

14. One-way ANOVA: Midsize, Pickup, SUV
Source DF SS MS F P
Factor
Error
Total
S = R-Sq = 57.63% R-Sq(adj) = 56.19%
Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev
Midsize (---*----)
Pickup ( *------)
SUV (----*---)
Pooled StDev = 2.749

15. The idea of analysis of variance
Here is the main idea for comparing means: what matters is not how far apart the sample means are but how far apart they are relative to the variability of individual observations.

16. Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev
Midsize (---*----)
Pickup ( *------)
SUV (----*---)
Pooled StDev = 2.749

17. Same means, different variances

18. The analysis of variance idea
Analysis of variance compares the variation due to specific sources with the variation among individuals who should be similar.
In particular, ANOVA tests whether several populations have the same mean by comparing how far apart the sample means are with how much variation there is within the samples.

19. Degree of freedom for ANOVA

20. Assignment
odd
15.30