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Chapter 5 Anova2009

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Sumit Prajapati
Sumit Prajapati
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Analysis of Variance Yuantao Hao 26th,Oct. 2009 Chapter5
Review: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
main steps: ,[object Object],[object Object],[object Object]
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P value ,[object Object]
[object Object]
Question: ,[object Object],[object Object],[object Object],[object Object]
An alysis o f va riance (ANOVA) : ,[object Object],[object Object]
5.1 One-Way ANOVA for the Completely Random Design ,[object Object],[object Object]
[object Object],[object Object]
12 11 10 9 8 7 6 5 4 3 2 1 Unit number 60 36 72 92 08 89 82 66 00 22 90 39 Random number 6 4 8 12 2 10 9 7 1 3 11 5 Rank (R) 2 1 2 3 1 3 3 2 1 1 3 2 Grouping result
 
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[object Object]
 
 
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Two assumptions on analysis of variance: ,[object Object],[object Object]
Bartlett’s test : are not all equal : :
Example 5.2 (cont.) ,[object Object],P >0.10
Test for normality and transformations:
5.2 Multiple comparisons ,[object Object],[object Object]
LSD- t test ,[object Object],H 0 is rejected if ：
SNK- q test ,[object Object]
[object Object],[object Object],[object Object],[object Object]
 
H 0 is rejected if ：
 
5.3 Two-Way ANOVA for the Randomized Complete-Block Design ,[object Object]
[object Object]
 
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[object Object]
 
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[object Object]
5
 
0.532
Summary: ,[object Object],[object Object],[object Object],[object Object]
THE END ,[object Object]

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Chapter 5 Anova2009

Editor's Notes

  1. Sort all the random numbers and rank them from 1-12.
  2. One factor: anticoagulant; three level: A, B, C
  3. The alternative hypothesis is that at least two of the group means are not the same.
  4. The squared deviations are summed over all observations over all groups. Partitioning the sum of squares.
  5. The results from the analysis of variance are typically displayed in an ANOVA table.
  6. The ANOVA test lets us detect when at least two groups have different underlying means, but it does not let us state which of the groups have means that differ from each other. The usual practice is to perform the overall F test . If H0 is rejected, then specific groups are compared, as discussed in this section.
  7. Df is the degree of freedom of MSE.
  8. Gene, heredity; same breed. Same race