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Analysis of Treatment Means

Analysis of Treatment Means. KNNL – Chapter 17. Cell Means Model – Sampling Distributions and Graphs. Inference for Individual Treatment Means. Comparing Two Treatment Means. Contrasts among Treatment Means. Simultaneous Comparisons.

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Analysis of Treatment Means

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  1. Analysis of Treatment Means KNNL – Chapter 17

  2. Cell Means Model – Sampling Distributions and Graphs

  3. Inference for Individual Treatment Means

  4. Comparing Two Treatment Means

  5. Contrasts among Treatment Means

  6. Simultaneous Comparisons • Confidence Coefficient (1-a) applies to only one estimate or comparison, not several comparisons simultaneously. Confidence Coefficient for a “family” of tests/intervals will be smaller than confidence coefficient for “individual” tests/intervals • If we construct five independent confidence intervals, each with confidence level = 0.95, Pr{All Correct} = (0.95)5 = 0.774 • Confidence Coefficient (1-a) applies to only pre-planned comparisons, not those suggested by observed samples (referred to as “data snooping”). • If we wait until after observing the data, then decide to test whether most extreme means are different, actual a too high

  7. Tukey’s Honest Significant Difference (HSD) - I

  8. Tukey’s Honest Significant Difference (HSD) - II

  9. Scheffe’s Method for Multiple Comparisons

  10. Bonferroni’s Method for Multiple Comparisons

  11. SNK Method for All Pairwise Comparisons • Controls False Discovery Rate at e • Uses Different Critical Values for different ranges of means

  12. Duncan’s Method for All Pairwise Comparisons • More powerful than SNK method, at cost of increasing e for longer stretches (does not control experimentwise error rate) • Uses Different Critical Values for different ranges of means

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