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Statistical Techniques I

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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  1. Statistical Techniques I EXST7005 Miscellaneous ANOVA Topics & Summary

  2. 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.

  3. 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.

  4. 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

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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

  10. 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

  11. 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.

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