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(ANalysis Of VAriance)

(ANalysis Of VAriance). ANOVA. Daniel Heaton MBA 634 March 27, 2006. What Will Be Covered. What ANOVA is and where it comes from How ANOVA can be used in Quality Management The basic parts of ANOVA How ANOVA works and how it can be performed using Excel

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(ANalysis Of VAriance)

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  1. (ANalysis Of VAriance) ANOVA Daniel Heaton MBA 634 March 27, 2006

  2. What Will Be Covered • What ANOVA is and where it comes from • How ANOVA can be used in Quality Management • The basic parts of ANOVA • How ANOVA works and how it can be performed using Excel • Example and Exercise for ANOVA Application MBA 634

  3. What ANOVA is • An ANOVA is a guide for determining whether or not an event was most likely due to the random chance of natural variation. • Or, conversely, the same method provides guidance in saying with a specific level of confidence that a certain factor (X) or factors (X, Y, and/or Z) were the more likely reason for the event. MBA 634

  4. Where ANOVA Comes From Ronald Aylmer Fisher (1890-1962) MBA 634

  5. Brainstorming Exercise • Why would you want to know if the difference between data sets is statistically significant? • What kinds of data are used or collected in your organization that ANOVA would be useful for? MBA 634

  6. The Different Types of ANOVA One-way between groups • You are looking at the differences between the groups. • There is only one factor (or result) which you are using to define the groups. • This is the simplest version of ANOVA. • This type of ANOVA can also be used to compare variables between different groups. MBA 634

  7. The Different Types of ANOVA One-way repeated measures • A one way repeated measures ANOVA is used when you have a single group on which you have measured something a few times. • You would use a one-way repeated measures ANOVA to see if results changed significantly over time. MBA 634

  8. The Different Types of ANOVA Two-way between groups • A two-way between groups ANOVA is used to look at complex groupings. • Examines the effects of two different factors and their interactions. • Each of the main effects are one-way tests. The interaction effect is simply asking "is there any significant difference in performance when you consider two factors acting together". MBA 634

  9. The Different Types of ANOVA Two-way repeated measures • This version of ANOVA simple uses the repeated measures structure of the “One-way repeated measures” method and includes the interaction effect of the “Two-way between groups” method. MBA 634

  10. The ANOVA Table MBA 634

  11. The Basic Parts of ANOVA SS or Sum of Squares • This is the measure of the variation around the mean. There are usually three different values of SS calculated: • SSG measures variation of the group means around the overall mean (Between Groups) • SSE measures the variation of each observation around its group mean (Within Groups) • SST measures variation of the data around the overall mean (Total) MBA 634

  12. The Basic Parts of ANOVA df or Degrees of Freedom • This is the factor that adjusts for how large the groups are and the number of groups being considered. They are calculated as follows: • Number of Groups (j) – 1 for SSG • Sample Size (n) – Number of Groups (j) for SSE • Sample Size (n) - 1 for SST MBA 634

  13. The Basic Parts of ANOVA MS = Mean Square= SS/df • This is like a standard deviation. Its numerator is the sum of squared deviations (SS), divided by the appropriate number of degrees of freedom. MBA 634

  14. The Basic Parts of ANOVA F (F-Statistic or F-Ratio) = MSG/MSE • This tells you the proportion of variation between the groups compared to the variation within the groups. • In general, the larger this value is, the more likely the variation between the groups is significant. • The level of significance is determined by comparing it to the F-Critical value for the samples. If the F-Statistic is larger than F-Critical, then the variation between the groups is statistically significant. MBA 634

  15. How to Perform ANOVA Using Excel • Enter the data into Excel MBA 634

  16. How to Perform ANOVA Using Excel • Enter the data into excel • Access ANOVA function using: Tools > Data Analysis > ANOVA: Single Factor MBA 634

  17. How to Perform ANOVA Using Excel • Enter the data into excel • Access ANOVA function using: Tools > Data Analysis > ANOVA: Single Factor • Select Range of Cells where data is located for “Input Range” and select other options as appropriate and click “OK” MBA 634

  18. How to Perform ANOVA Using Excel Excel Output MBA 634

  19. A Real World Example • Three inspectors wanted to see how accurately they measure a dimension of parts they inspect. • They each measured the same 10 parts in random order multiple times and the measurements are recorded as follows. MBA 634

  20. A Real World Example MBA 634

  21. A Real World Example • Since they want to look at different parts and different operators with repeated measurements, they use the “Anova: Two-Factor With Replication” function. MBA 634

  22. A Real World Example Excel Results MBA 634

  23. A Real World Example Excel Results • The variation within the inspectors measurements, between the inspectors, and of interactions between the two were all not significant. • However, this data helps them to see that most of the variation is due to the gage and not the operator. MBA 634

  24. ANOVA Exercise • Three friends want to see who is the best bowler. • They each play a different number of games and record their scores. • Analyze the data and determine which one is the best bowler, and if the results are significant or by chance. MBA 634

  25. ANOVA Exercise Enter the following data into Excel and analyze it using the “Anova: Single Factor” function. MBA 634

  26. ANOVA Exercise Procedure • Select: Tools > Data Analysis > Anova: Single Factor • Select Input Range and other values as shown. MBA 634

  27. ANOVA Exercise Results • Joe has the highest average score • The results are statistically significant and not due to chance MBA 634

  28. Summary • ANOVA is a useful and powerful tool for determining if differences are statistically significant. • It can also be used to establish cause and effect relationships with a specific degree of certainty • Excel has three ANOVA functions that can be used fro basic analysis of variance. MBA 634

  29. Readings List • The basic concepts of ANOVA can be found in almost any statistics text book. MBA 634

  30. Readings List • Books • Damon, Richard A., Experimental design, ANOVA, and regression, New York, Harper & Row, 1987. • Miller, Rupert G., Beyond ANOVA, basics of applied statistics, New York, Wiley, 1986. • Rutherford, Andrew, Introducing Anova and Ancova : a GLM approach, Thousand Oaks, SAGE, 2001. • Weiss, David J., Analysis of variance and functional measurement : a practical guide, New York, Oxford University Press, 2006. MBA 634

  31. Readings List • Online Resources • http://www.isixsigma.com/library/content/c021111a.asp • http://www.uwsp.edu/psych/cw/statmanual/anovaterms.html • http://www.csse.monash.edu.au/~smarkham/resources/anova.htm • www.math.yorku.ca/SCS/StatResource.html • www.statsci.org/teaching.html • http://www.sportsci.org/resource/stats/index.html • http://www.uwsp.edu/psych/cw/statmanual/index.html MBA 634

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