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Multiple Comparison

Multiple Comparison. Type I Error Rates. = error rate of any comparison. I. Per Comparison. = # of comparisons. II. Per Experiment (frequency). if = 10 and = 0.05 per experiment = 0.5. (frequency). III. Familywise (for independent comparisons).

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Multiple Comparison

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  1. Multiple Comparison Type I Error Rates = error rate of any comparison I. Per Comparison = # of comparisons II. Per Experiment (frequency) if = 10 and = 0.05 per experiment = 0.5 (frequency) III. Familywise (for independent comparisons) probability of at least one Type I error. Per Comparison Familywise Per Experiment

  2. Complete vs. Restricted H0 Independent Samples Treatments =141 MSTreat MSerror Complete H0

  3. Restricted H0 e.g., A Priori Comparisons Post Hoc Comparisons The role of overall F - might NOT pick up - changes Familywise

  4. A Priori Comparisons Multiple t tests (compare two conditions) - replace individual or with MSerror - test t with dferror Comparing Treatments 1 and 3 n.s.

  5. Linear Contrasts Compare:  two conditions  a set of conditions and a condition  two sets of conditions Let for equal n’s

  6. (1) Contrasting Treatments 1 & 3 again = = = = SScontrast = SSerror = MScontrast = always = 1 MSerror = MScontrast SScontrast = = MSerror = (Look at t- test) F(1,12) =

  7. (2) Contrasting Treatments 1 & 2 with 3 = = = = = = = SScontrast = SSerror = MScontrast = MScontrast = F(1,12) =

  8. (3) Contrasting Treatments 1 & 3 with 2 = = = = = = SScontrast = SSerror = MScontrast = MScontrast = F(1,12) =

  9. Orthogonal Contrasts = = if n’s are equal # of comparisons = dfTreat dfTreat = 2 in our example contrasts = 1 and 2 = = = 2 and 3 = = = 1 and 3 = = SScontrast1 = SScontrast3 = = SSTreat

  10. Bonferroni’s Control for FW error rate () use  = 0.01 Bonferroni Inequality e.g.: if, per comparison  = 0.05 and if, 4 comparisons are made then, the FW CANNOT exceed p = 0.02 EW or FW  c(PC) c = # of comparisons Thus, we can set the FW or the per experiment  to a desired level (e.g., 0.05) and adjust the PC If we desire a FW = 0.05 then: 0.05 = PC (4) 0.0125 = PC

  11. Bonferroni’s (comparing 2 means) using t2 = F and moving terms This allows us to contrast groups of means. (linear contrasts) if

  12. Multistage Procedures Bonferroni: divides  into equal parts Multistage (Holm): divides  into different size portions if or heterogenous S2’s

  13. Multistage 1. calculate all s 2. arrange in order of magnitude 3. compare largest s to critical value (Dunn’s Tables) C = total # of contrasts to be made ONLY if significant 4. compare next largest to critical value C = C-1 5. and so on FW is kept at 0.05 ()

  14. Linear Contrast Subject X Treatment Design I Weight each observation by its assigned condition weight II Compute Di for each subject III Sum Di across subjects IV Compute SScontrast Compute SScontrast V Compute SSSsXC(error)

  15. Treatments Contrast 1 with 3 Di Di2 MScon = SScon = MSSsXcon = SSSsXcon = df = 4 F(1,4) = 23.14

  16. Treatments Contrast 1 & 3with 2 Di Di2 MScon = SScon = MSSsXcon = SSSsXcon = F(1,4) = 36

  17. SScon1 = SScon2 = = SSTreat Total = Orthogonal Contrasts Error term could be SSres or error SSSsXcon1 + SSSsXcon2 = ? 5.6 + 1.2 = 6.8 ?? dfcon1 + dfcon2 = dfTreat = 1 + 2 dfSsXcon1 + dfSsXcon2 = df ? 4 + 4 = 8

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