1 / 96

Comparison of Several Multivariate Means

Comparison of Several Multivariate Means. Shyh-Kang Jeng Department of Electrical Engineering/ Graduate Institute of Communication/ Graduate Institute of Networking and Multimedia. Paired Comparisons. Measurements are recorded under different sets of conditions

rstumpf
Download Presentation

Comparison of Several Multivariate Means

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Comparison of Several Multivariate Means Shyh-Kang Jeng Department of Electrical Engineering/ Graduate Institute of Communication/ Graduate Institute of Networking and Multimedia

  2. Paired Comparisons • Measurements are recorded under different sets of conditions • See if the responses differ significantly over these sets • Two or more treatments can be administered to the same or similar experimental units • Compare responses to assess the effects of the treatments

  3. Example 6.1: Effluent Data from Two Labs

  4. Single Response (Univariate) Case

  5. Multivariate Extension: Notations

  6. Result 6.1

  7. Test of Hypotheses and Confidence Regions

  8. Example 6.1: Check Measurements from Two Labs

  9. Experiment Design for Paired Comparisons 1 2 3 n . . . . . . Treatments 1 and 2 assigned at random Treatments 1 and 2 assigned at random Treatments 1 and 2 assigned at random Treatments 1 and 2 assigned at random

  10. Alternative View

  11. Repeated Measures Design for Comparing Measurements • q treatments are compared with respect to a single response variable • Each subject or experimental unit receives each treatment once over successive periods of time

  12. 3 4 2 1 Example 6.2: Treatments in an Anesthetics Experiment • 19 dogs were initially given the drug pentobarbitol followed by four treatments Present Halothane Absent Low High CO2 pressure

  13. Example 6.2: Sleeping-Dog Data

  14. Contrast Matrix

  15. Test for Equality of Treatments in a Repeated Measures Design

  16. Example 6.2: Contrast Matrix

  17. Example 6.2: Test of Hypotheses

  18. Example 6.2: Simultaneous Confidence Intervals

  19. Comparing Mean Vectors from Two Populations • Populations: Sets of experiment settings • Without explicitly controlling for unit-to-unit variability, as in the paired comparison case • Experimental units are randomly assigned to populations • Applicable to a more general collection of experimental units

  20. Assumptions Concerning the Structure of Data

  21. Pooled Estimate of Population Covariance Matrix

  22. Result 6.2

  23. Proof of Result 6.2

  24. Wishart Distribution

  25. Test of Hypothesis

  26. Example 6.3: Comparison of Soaps Manufactured in Two Ways

  27. Example 6.3

  28. Result 6.3: Simultaneous Confidence Intervals

  29. Example 6.4: Electrical Usage of Homeowners with and without ACs

  30. Example 6.4: Electrical Usage of Homeowners with and without ACs

  31. Example 6.4: 95% Confidence Ellipse

  32. Bonferroni Simultaneous Confidence Intervals

  33. Result 6.4

  34. Proof of Result 6.4

  35. Remark

  36. Example 6.5

  37. Example 6.9: Nursing Home Data • Nursing homes can be classified by the owners: private (271), non-profit (138), government (107) • Costs: nursing labor, dietary labor, plant operation and maintenance labor, housekeeping and laundry labor • To investigate the effects of ownership on costs

  38. One-Way MANOVA

  39. Assumptions about the Data

  40. Univariate ANOVA

  41. Univariate ANOVA

  42. Univariate ANOVA

  43. Univariate ANOVA

  44. Concept of Degrees of Freedom

  45. Concept of Degrees of Freedom

  46. Examples 6.6 & 6.7

  47. MANOVA

  48. MANOVA

  49. MANOVA

  50. Distribution of Wilk’s Lambda

More Related