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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.

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slide1
Statistical Techniques I

EXST7005

Miscellaneous ANOVA Topics & Summary

slide2
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.
slide3
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.
slide4

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

slide5

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

slide6
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.
slide7
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.
slide8
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.
slide9
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
slide10
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
slide11
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.