Statistical Techniques I

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# Statistical Techniques I - PowerPoint PPT Presentation

Statistical Techniques I. EXST7005. Miscellaneous ANOVA Topics & Summary. LSMeans calculation. The calculations of LSMeans is different. For a balanced design, the results will be the same. However, for unbalanced designs the results will often differ.

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## Statistical Techniques I

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Statistical Techniques I

EXST7005

Miscellaneous ANOVA Topics & Summary

LSMeans calculation
• The calculations of LSMeans is different. For a balanced design, the results will be the same. However, for unbalanced designs the results will often differ.
• The MEANS statement in SAS calculates a simple mean of all available observations in the treatment cells.
• The LSMeans statement will calculate the mean of the treatment cell means.
LSMeans calculation (continued)
• Example:
• The MEAN of 4 treatments, where the observations are 3,4,8 for a1, 3,5,6,7,9 for a2, 7,8,6,7 for a3 and 3,5,7 for a4 is 5.8667.
• The individual cells means are 5, 6, 7 and 5 for a1, a2, a3 and a4 respectively. The mean of these 4 values is 5.75. This would be the LSMean.

Raw means

Treatments

a1

a2

a3

Means

b1

5

6

9

7

8

6.5

4

b2

7

5

5

9

7

6.6

Means

7

5.75

7

LSMeans means

a1

a2

a3

Means

Treatments

b1

6

6

9

7

b2

8

5

6

6.33

Means

7

5.5

7.5

Treatments

a1

a2

a3

Means

b1

6.5

b2

6.6

Means

7

5.75

7

Confidence Intervals on Treatments
• Like all confidence intervals on normally distributed estimates, this will employ a t value and will be of the form Mean ± ta/2(S`Y)
• The treatment mean can be obtained from a means (or LSMeans) statement, but the standard deviation provided is not the correct standard error for the interval.
Confidence Intervals on Treatments (continued)
• The standard error is the square root of MSE/n, where n is the number of observations used in calculating the mean.
• The degrees of freedom for the tabular t value is the d.f. from the MSE used to calculate the standard error.
Confidence Intervals on Treatments (continued)
• If there are several error terms (e.g. experimental error and sampling error) use the one that is appropriate for testing the treatments.
Exam Coverage
• ANOVA (one-way and two-way) will be covered.
• Be aware of similarities and differences with the t-test.
• HOV tests and tests of normality will be included
• Factorial treatment arrangement (two-way) with interpretation interactions will be covered
Exam Coverage (continued)
• RBD will be covered only as the concepts. How is the linear model different, why do we block, what is a block, etc. No SAS output on RBD.
• Be able to interpret and discuss Post-ANOVA tests
• contrasts
• range tests
Exam Coverage (continued)
• Be able to place a confidence interval on a treatment mean.
• Recognize designs and treatment arrangements from a described problem.
• be able to determine the experimental unit, sampling unit, and get the d.f. error.
• Answers to questions will be on the net.
• Good Luck.