Robust Between Groups Factorial and Robust RM

Brief examples

Robustitude

• As in most statistical situations there would be a more robust method for going about factorial anova

• Instead of using means, we might prefer trimmed means or medians so as to have tests based on estimates not so heavily influenced by outliers.

• And, there’s nothing to it.

Between subjects factorial using trimmed means

Main effects

Interaction

Robustitude

• Or using R you type in something along the lines of – t2way(A, B, x, grp=c(1:p), tr=.2, alpha=.05)*

• Again, don’t be afraid to try robust methods as they are often easily implemented with appropriate software.

Robust Repeated Measure

Robust RM

• One can perform robust procedures for repeated measures designs

• Consider our previous dataset regarding stress and test taking

• I changed the values for the first subject to create an outlier case– This person was stressed before

and after but not the week of the exam

Before During After36.00 15.00 35.0034.00 33.00 22.0026.00 28.00 25.0030.00 33.00 17.0035.00 33.00 30.0016.00 31.00 23.0027.00 28.00 28.0028.00 33.00 18.0028.00 34.00 27.0025.00 27.00 25.00

Compare results

• SPSS output for this data

Not significant

Tests of Within-Subjects Effects

Measure: MEASURE_1

99.800 2 49.900 1.394 .274

99.800 1.602 62.292 1.394 .274

99.800 1.895 52.656 1.394 .274

99.800 1.000 99.800 1.394 .268

644.200 18 35.789

644.200 14.419 44.677

644.200 17.058 37.766

644.200 9.000 71.578

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sourcefactor1

Error(factor1)

Type III Sumof Squares df Mean Square F Sig.

Compare results

• Wilcox’s libraries provide a simple way to perform an RM analysis for trimmed means

• TITLE: Function rmanova

• USAGE: rmanova(x, tr, grp)

• x refers to the dataset, tr the amount of trimming, and grp can be used to test a subset of the variables

R output• rmanova(stressdata, tr=.2)

– 20% off both ends

• Results (generalized Hunyh-Feldt correction, provides the epsilon used)

• Trimmed means (non-trimmed in parentheses):– 28.8 (28.5)– 31.0 (29.5)– 25.0 (25.2)

• F(2,10) = 3.94, p = .05 sig outcome unlike before

• To perform a bootstrapped F:– rmanovab(stressdata, tr=.2, alpha = .05, nboot = 1000)

Multiple comparisons

• Again, the omnibus F in RM is most likely uninteresting, so perhaps we want to test to see what the specifics of the situation are

• Function rmmcp can be used– rmmcp(x, con=0,tr=.2, alpha=.05, dif=F)– dif=T uses difference scores, dif=F the marginal means– To test a specific contrast, one can add the con function with appropriate weights

or specify a matrix of weights• The procedure for testing pairwise comparisons uses Rom’s

correction (a modified Bonferonni) for multiple comparisons– Order p-values in descending order– Test largest at .05, if less than .05 reject and all subsequent– If not test next at corrected critical. If less than .05 reject and all subsequent. If

not continue until rejection or all hypes have been tested• But as mentioned previously, one could use an FDR method also

that may be more powerful

R output

• rmmcp(stressdata, tr=.1, con=c(0,1,-1),alpha=.05, dif=F)

– Compares ‘during’ and ‘after’ times

• Results from the contrast– t= 2.7, p = .03

• Once again, do not be afraid to implement robust procedures when necessary