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Comparing and Contrasting Treatment Means Analysis

Discover the intricate world of treatment means analysis, including KNNL, cell means model, sampling distributions, and inference methods. Learn how to compare individual treatment means, contrasts among treatment means, and conduct simultaneous comparisons. Explore confidence coefficients and multiple comparison methods like Tukey's HSD, Scheffe's method, Bonferroni's method, and SNK method. Understand Duncan's method for pairwise comparisons and controlling false discovery rates. Enhance your statistical analysis skills with this comprehensive guide.

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Comparing and Contrasting Treatment Means Analysis

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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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