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Linear Contrasts and Multiple Comparisons

One-Way Layout Example. A study was performed to examine the effect of a new sleep inducing drug on a population of insommiacs. Three (3) treatments were used:Standard DrugNew DrugPlacebo (as a control). What is the role of the placebo in this study?What is a control in an experimental study

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Linear Contrasts and Multiple Comparisons

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    1. Linear Contrasts and Multiple Comparisons

    2. One-Way Layout Example

    3. Response:

    4. Excell Analysis Tool Output

    5. Multiple Comparisons

    6. Linear Comparisons

    7. Linear Contrast

    8. Orthogonal Contrasts

    10. Drug Comparisons

    11. Importance of Mutual Orthogonality

    12. Example of Linear Contrasts

    13. Q1

    15. Q2

    17. Q3

    19. Mutual Orthogonality

    20. Error Rates

    21. Multiple Comparison Procedures

    22. Fisher’s Least Significant Difference - Protected

    23. Tukey’s W Procedure

    24. Student Newman Keul Procedure

    25. Duncan’s New Multiple Range Test

    26. Waller-Duncan k-ratio MCP (Protected)

    27. Scheffé’s S Method

    28. Geometric Mean

    29. Comparisonwise error rates for different MCP

    30. Experimentwise error rates for different MCP

    31. Example

    32. Statistics and AOV Table

    34. Differences for all of the t(t-1)/2=15 possible pairs of level means

    35. Fisher’s Protected LSD

    36. Tukey’s W (Honestly Significant Difference)

    37. Student-Newman-Keul Procedure (SNK)

    38. SNK

    39. Duncan’s New Multiple Range Test

    40. Duncan’s Test Critical values

    42. Duncan’s MRT

    43. Waller-Duncan K-Ratio MCP (Protected)

    44. Waller-Duncan MRT Critical Values

    47. Waller Duncan Table K=500

    49. Scheffé’s S Method

    50. Scheffe’s S Method

    51. Grouping of Ranked Means

    52. Conclusions Multiple comparison procedures allow us to separate means after the analysis of variance test has identified that there are some differences to be found. Linear contrasts are defined before we “look” at the data and each can be tested with its own F test with nominal a=0.05 type I error probability.

    53. Closing Remarks The unprotected MCPs will sometimes identify statistically significant differences even when the overall ANOVA test is not significant.

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