1. Chapter 12 Inference on the Least-squares Regression Line; ANOVA 12.3 One-way Analysis of Variance

2. Analysis of Variance (ANOVA) is an inferential method that is used to test the equality of three or more population means

5. Verifying the Requirement of Equal Population Variances The one-way ANOVA procedures may be used provided the largest sample standard deviation is no more than 2 times larger than the smallest sample standard deviation.

6. EXAMPLE Verifying the Requirements of ANOVA The following data represent the weight (in grams) of pennies minted at the Denver mint in 1990, 1995, and 2000. Verify that the requirements in order to perform a one-way ANOVA are satisfied.

7. 1990 19952000 2.50 2.522.50 2.50 2.542.48 2.49 2.502.49 2.53 2.482.50 2.46 2.522.48 2.50 2.502.52 2.47 2.492.51 2.53 2.532.49 2.51 2.482.51 2.49 2.552.50 2.48 2.492.52

11. Descriptive Statistics Variable N Mean Median TrMean StDev SE Mean 1990 11 2.4964 2.5000 2.4967 0.0220 0.0066 1995 11 2.5091 2.5000 2.5078 0.0243 0.0073 2000 11 2.5000 2.5000 2.5000 0.0141 0.0043 Variable Minimum Maximum Q1 Q3 1990 2.4600 2.5300 2.4800 2.5100 1995 2.4800 2.5500 2.4900 2.5300 2000 2.4800 2.5200 2.4900 2.5100

13. EXAMPLE ANOVA

14. One-way Analysis of Variance Analysis of Variance Source DF SS MS F P Factor 2 0.000945 0.000473 1.11 0.342 Error 30 0.012745 0.000425 Total 32 0.013691 Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev -+---------+---------+---------+----- 1990 11 2.4964 0.0220 (---------*----------) 1995 11 2.5091 0.0243 (----------*---------) 2000 11 2.5000 0.0141 (---------*----------) -+---------+---------+---------+----- Pooled StDev = 0.0206 2.484 2.496 2.508 2.520

17. Test Statistic for One-Way ANOVA

21. EXAMPLE Computing the F Test Statistic Compute the F test statistic for the penny data.