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

Chapter 12 Inference on the Least-squares

Regression Line; ANOVA12.3

One-way Analysis of Variance

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

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.

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.

1990 1995 20002.50 2.52 2.502.50 2.54 2.482.49 2.50 2.492.53 2.48 2.502.46 2.52 2.482.50 2.50 2.522.47 2.49 2.512.53 2.53 2.492.51 2.48 2.512.49 2.55 2.502.48 2.49 2.52

Descriptive Statistics

Variable N Mean Median TrMean StDev SE Mean1990 11 2.4964 2.5000 2.4967 0.0220 0.00661995 11 2.5091 2.5000 2.5078 0.0243 0.00732000 11 2.5000 2.5000 2.5000 0.0141 0.0043

Variable Minimum Maximum Q1 Q31990 2.4600 2.5300 2.4800 2.51001995 2.4800 2.5500 2.4900 2.53002000 2.4800 2.5200 2.4900 2.5100

EXAMPLE ANOVA

One-way Analysis of Variance

Analysis of VarianceSource DF SS MS F PFactor 2 0.000945 0.000473 1.11 0.342Error 30 0.012745 0.000425Total 32 0.013691 Individual 95% CIs For Mean Based on Pooled StDevLevel 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

Test Statistic for One-Way ANOVA

EXAMPLE Computing the F Test Statistic

Compute the F test statistic for the penny data.