Guide to Using Minitab 14 For Basic Statistical Applications To Accompany Business Statistics: A Decision Making Approach, 6th Ed. Chapter 12: Analysis of Variance By Groebner, Shannon, Fry, & Smith Prentice-Hall Publishing Company Copyright, 2008

Chapter 12 Minitab Examples Analysis of Variance Hydronics Corporation Digitron Inc. Randomized Block Analysis of Variance Citizens State Bank Two Factor Analysis of Variance with replications – Fly High Airlines

Analysis of Variance - Hydronics Corporation Issue: The company wants to compare two weight loss supplements with a placebo. Objective: Use Minitab to help test a hypothesis about the mean weight loss associated with three groups. Data file is Hydronics.MTW

Analysis of Variance – Hydronics Corp. Open File Hydronics.MTW

Analysis of Variance – Hydronics Corp. First click on Stat, then ANOVA and finally on One-Way

Analysis of Variance – Hydronics Corp. Identify the columns containing the variables to be analyzed (Loss) Then identify the column containing the Factor (Program) Click on OK

Analysis of Variance – Hydronics Corp. The Minitab output shows we should reject the hypothesis of equal means. The p-value is less than alpha and F is greater than F critical. Minitab also determines confidence intervals for all variables

One-Way ANOVA Digitron Issue: Digitron is interested in testing whether there is a difference in the mean stopping distance for four brake types Objective: Use Minitab to test the hypothesis there is no difference in average stopping distance. Data file is Digitron.MTW

Analysis of Variance – Digitron. Open File Digitron.MTW

Analysis of Variance – Digitron First click on Stat, then ANOVA and finally on One-Way

Analysis of Variance – Digitron Identify the columns containing the variables to be analyzed (Distance) Then identify the column containing the Factor (Brake) Click on OK

Analysis of Variance – Digitron The Minitab output shows we should reject the hypothesis of equal means. The p-value is less than alpha and F is greater than F critical. Minitab also determines confidence intervals for all variables’ means

Randomized Block ANOVA Citizens State Bank Issue: Bank managers wish to test the hypothesis that there is no difference in the average house appraisal by three different appraising companies. Objective: Use Minitab to test the hypothesis there is no difference in average appraisal price. Data file is Citizens.MTW

Randomized Block ANOVA – Citizens State Bank Open File Citizens.MTW File contains appraisal values for 5 houses by each appraiser.

Randomized Block ANOVA – Citizens State Bank First click on Stat, then ANOVA and finally on Two-way.

Randomized Block ANOVA – Citizens State Bank Identify the columns containing the response variable to be analyzed (Appraisal), the column containing the house identifier (Company) and the company identifier (Property).

Randomized Block ANOVA – Citizens State Bank The F and P-values indicate both the blocking and main effects are significant.

Two Factor ANOVA With Replications - Fly High Airlines Issue: The airline is interested in determining the effect of redemption offers on the number of miles that would be redeemed. Objective: Use Minitab to test the hypothesis there is no difference in average redemption rate. Data file is Fly-High.MTW

Two Factor ANOVA With Replications – Fly High Airlines Open file Fly-High.MTW

Two Factor ANOVA With Replications – Fly High Airlines First click on Stat, then ANOVA and finally on Two-way.

Two Factor ANOVA With Replications – Fly High Airlines Identify the columns containing the response variable to be analyzed (Value), the Row Factor (Redemption Option) and the Column Factor (Age Group)

Two Factor ANOVA With Replications – Fly High Airlines This is last part of the Minitab output. All the F values are small and all P-values are large. No interaction – and fail to reject hypothesis that factor means are equal.