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ANOVA: Examples

ANOVA: Examples. Do five different brands of gasoline have an effect on automobile efficiency? Does the type of sugar solution (glucose, sucrose, fructose, mixture) have an effect on bacterial growth?

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ANOVA: Examples

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  1. ANOVA: Examples • Do five different brands of gasoline have an effect on automobile efficiency? • Does the type of sugar solution (glucose, sucrose, fructose, mixture) have an effect on bacterial growth? • Does the hardwood concentration in pulp (%) have an effect on tensile strength of bags made from the pulp? • Does the resulting color density of a fabric depend on the amount of dye used?

  2. ANOVA: Graphical

  3. ANOVA test statistic

  4. ANOVA test

  5. F Distribution http://www.vosesoftware.com/ModelRiskHelp/index.htm#Distributions/ Continuous_distributions/F_distribution.htm

  6. F curve and critical value http://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

  7. Table A.9Critical Values for F Distribution (first page)

  8. ANOVA Table: Formulas

  9. ANOVA Hypothesis test: Summary H0: μ1 = μ2 =  = μI Ha: At least one i is different Test statistic: Rejection Region: F ≥ F,dfm,dfe

  10. ANOVA: Example An experiment was carried out to compare five different brands of automobile oil filters with respect to their ability to capture foreign material. A sample of nine filters of each brand was used. Do the filters capture the same amount of foreign material at a 0.05 significance level?

  11. ANOVA: Example (cont) • H0: 1 = 2 = 3 = 4= 5 The true mean amount of foreign material is the same for all of the filters HA: at least one of the i is different The true mean amount of foreign material caught is not the same for all of the filters

  12. ANOVA: Example (cont)

  13. Example: ANOVA (cont) The data does provide strong support to the claim that the mean amount of foreign material caught is not the same for all of the filters.

  14. Problem with Multiple t tests

  15. Overall Risk of Type I Error in Using Repeated t Tests at  = 0.05

  16. Table A.10: Studentized Range

  17. ANOVA: Example (Tukey) An experiment was carried out to compare five different brands of automobile oil filters with respect to their ability to capture foreign material. A sample of nine filters of each brand was used. Do the filters capture the same amount of foreign material at a 0.05 significance level? Which one(s) of the filters is best? x̅1.= 14.5 x̅2.= 13.8 x̅3.= 13.3 x̅4.= 14.3 x̅5.= 13.1

  18. Example: Tukey (cont)

  19. Example: Tukey (cont)

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