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In Anova

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• ### In Anova

1. 1. (ANalysis Of VAriance) Daniel Heaton MBA 634 March 27, 2006 ANOVA
2. 2. What Will Be Covered <ul><li>What ANOVA is and where it comes from </li></ul><ul><li>How ANOVA can be used in Quality Management </li></ul><ul><li>The basic parts of ANOVA </li></ul><ul><li>How ANOVA works and how it can be performed using Excel </li></ul><ul><li>Example and Exercise for ANOVA Application </li></ul>
3. 3. What ANOVA is <ul><li>An ANOVA is a guide for determining whether or not an event was most likely due to the random chance of natural variation. </li></ul><ul><li>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. </li></ul>
4. 4. Where ANOVA Comes From <ul><li>Ronald Aylmer Fisher (1890-1962) </li></ul>
5. 5. Brainstorming Exercise <ul><li>Why would you want to know if the difference between data sets is statistically significant? </li></ul><ul><li>What kinds of data are used or collected in your organization that ANOVA would be useful for? </li></ul>
6. 6. The Different Types of ANOVA <ul><li>One-way between groups </li></ul><ul><li>You are looking at the differences between the groups. </li></ul><ul><li>There is only one factor (or result) which you are using to define the groups. </li></ul><ul><li>This is the simplest version of ANOVA. </li></ul><ul><li>This type of ANOVA can also be used to compare variables between different groups. </li></ul>
7. 7. The Different Types of ANOVA <ul><li>One-way repeated measures </li></ul><ul><li>A one way repeated measures ANOVA is used when you have a single group on which you have measured something a few times. </li></ul><ul><li>You would use a one-way repeated measures ANOVA to see if results changed significantly over time. </li></ul>
8. 8. The Different Types of ANOVA <ul><li>Two-way between groups </li></ul><ul><li>A two-way between groups ANOVA is used to look at complex groupings. </li></ul><ul><li>Examines the effects of two different factors and their interactions. </li></ul><ul><li>Each of the main effects are one-way tests. The interaction effect is simply asking &quot;is there any significant difference in performance when you consider two factors acting together&quot;. </li></ul>
9. 9. The Different Types of ANOVA <ul><li>Two-way repeated measures </li></ul><ul><li>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. </li></ul>
10. 10. The ANOVA Table
11. 11. The Basic Parts of ANOVA <ul><li>SS or Sum of Squares </li></ul><ul><li>This is the measure of the variation around the mean. There are usually three different values of SS calculated: </li></ul><ul><ul><li>SSG measures variation of the group means around the overall mean (Between Groups) </li></ul></ul><ul><ul><li>SSE measures the variation of each observation around its group mean (Within Groups) </li></ul></ul><ul><ul><li>SST measures variation of the data around the overall mean (Total) </li></ul></ul>
12. 12. The Basic Parts of ANOVA <ul><li>df or Degrees of Freedom </li></ul><ul><li>This is the factor that adjusts for how large the groups are and the number of groups being considered. They are calculated as follows: </li></ul><ul><ul><li>Number of Groups (j) – 1 for SSG </li></ul></ul><ul><ul><li>Sample Size (n) – Number of Groups (j) for SSE </li></ul></ul><ul><ul><li>Sample Size (n) - 1 for SST </li></ul></ul>
13. 13. The Basic Parts of ANOVA <ul><li>MS = Mean Square = SS/df </li></ul><ul><li>This is like a standard deviation. Its numerator is the sum of squared deviations (SS), divided by the appropriate number of degrees of freedom. </li></ul>
14. 14. The Basic Parts of ANOVA <ul><li>F (F-Statistic or F-Ratio) = MSG/MSE </li></ul><ul><li>This tells you the proportion of variation between the groups compared to the variation within the groups. </li></ul><ul><ul><li>In general, the larger this value is, the more likely the variation between the groups is significant. </li></ul></ul><ul><ul><li>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. </li></ul></ul>
15. 15. How to Perform ANOVA Using Excel <ul><li>Enter the data into Excel </li></ul>
16. 16. How to Perform ANOVA Using Excel <ul><li>Enter the data into excel </li></ul><ul><li>Access ANOVA function using: Tools > Data Analysis > ANOVA: Single Factor </li></ul>
17. 17. How to Perform ANOVA Using Excel <ul><li>Enter the data into excel </li></ul><ul><li>Access ANOVA function using: Tools > Data Analysis > ANOVA: Single Factor </li></ul><ul><li>Select Range of Cells where data is located for “Input Range” and select other options as appropriate and click “OK” </li></ul>
18. 18. How to Perform ANOVA Using Excel <ul><li>Excel Output </li></ul>
19. 19. A Real World Example <ul><li>Three inspectors wanted to see how accurately they measure a dimension of parts they inspect. </li></ul><ul><li>They each measured the same 10 parts in random order multiple times and the measurements are recorded as follows. </li></ul>
20. 20. A Real World Example
21. 21. <ul><li>Since they want to look at different parts and different operators with repeated measurements, they use the “Anova: Two-Factor With Replication” function. </li></ul>A Real World Example
22. 22. A Real World Example <ul><li>Excel Results </li></ul>
23. 23. A Real World Example <ul><li>Excel Results </li></ul><ul><li>The variation within the inspectors measurements, between the inspectors, and of interactions between the two were all not significant. </li></ul><ul><li>However, this data helps them to see that most of the variation is due to the gage and not the operator. </li></ul>
24. 24. ANOVA Exercise <ul><li>Three friends want to see who is the best bowler. </li></ul><ul><li>They each play a different number of games and record their scores. </li></ul><ul><li>Analyze the data and determine which one is the best bowler, and if the results are significant or by chance. </li></ul>
25. 25. ANOVA Exercise <ul><li>Enter the following data into Excel and analyze it using the “Anova: Single Factor” function. </li></ul>
26. 26. ANOVA Exercise <ul><li>Procedure </li></ul><ul><li>Select: Tools > Data Analysis > Anova: Single Factor </li></ul><ul><li>Select Input Range and other values as shown. </li></ul>
27. 27. ANOVA Exercise <ul><li>Results </li></ul><ul><li>Joe has the highest average score </li></ul><ul><li>The results are statistically significant and not due to chance </li></ul>
28. 28. Summary <ul><li>ANOVA is a useful and powerful tool for determining if differences are statistically significant. </li></ul><ul><li>It can also be used to establish cause and effect relationships with a specific degree of certainty </li></ul><ul><li>Excel has three ANOVA functions that can be used fro basic analysis of variance. </li></ul>
29. 29. Readings List <ul><li>The basic concepts of ANOVA can be found in almost any statistics text book. </li></ul>
30. 30. Readings List <ul><li>Books </li></ul><ul><ul><li>Damon, Richard A., Experimental design, ANOVA, and regression, New York, Harper & Row, 1987. </li></ul></ul><ul><ul><li>Miller, Rupert G., Beyond ANOVA, basics of applied statistics , New York, Wiley, 1986. </li></ul></ul><ul><ul><li>Rutherford, Andrew, Introducing Anova and Ancova : a GLM approach, Thousand Oaks, SAGE, 2001. </li></ul></ul><ul><ul><li>Weiss, David J., Analysis of variance and functional measurement : a practical guide, New York, Oxford University Press, 2006. </li></ul></ul>
31. 31. Readings List <ul><li>Online Resources </li></ul><ul><ul><li>http://www.isixsigma.com/library/content/c021111a.asp </li></ul></ul><ul><ul><li>http://www.uwsp.edu/psych/cw/statmanual/anovaterms.html </li></ul></ul><ul><ul><li>http://www.csse.monash.edu.au/~smarkham/resources/anova.htm </li></ul></ul><ul><ul><li>www.math.yorku.ca/SCS/StatResource.html </li></ul></ul><ul><ul><li>www.statsci.org/teaching.html </li></ul></ul><ul><ul><li>http://www.sportsci.org/resource/stats/index.html </li></ul></ul><ul><ul><li>http://www.uwsp.edu/psych/cw/statmanual/index.html </li></ul></ul>