1 / 13

Multiple comparisons

Multiple comparisons. What do we do with a significant F ratio?. A priori (planned) comparisons. A priori comparisons are planned before the data are collected.

eilis
Download Presentation

Multiple comparisons

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. Multiple comparisons What do we do with a significant F ratio?

  2. A priori (planned) comparisons • A priori comparisons are planned before the data are collected. • One strategy is to allow the Type I error rate for the study to rise, in order to maximize power and minimize Type II error rates. • For that strategy to be effective, make very few two-group comparisons -- the ones specified in your research hypotheses.

  3. Planned comparisons • Another strategy for planned comparisons sets the a level lower than .05, in order to keep the experimentwise error rate at a. • For example, with three comparisons, set a at .0167, so that the total Type I error rate will be .0167 + .0167 + .0167 = .05 • That approach sacrifices power, and increases Type II error. Sound familiar?

  4. Orthogonality in planned comparisons • Some scholars insist that planned comparisons must be orthogonal or independent. Only k - 1 comparisons can be orthogonal. • Orthogonal comparisons have coefficients which when multiplied together sum to 0: Contrast A: 1 -1 0 S = 0 Contrast B: .5 .5 -1 S = 0 Product (A x B): .5 -.5 0 S = 0

  5. Using t for planned comparisons • Using either orthogonal contrast coefficients or a minimum number of contrasts (textbook approach), you could compare two groups using the independent samples t or ANOVA. t = M1 - M2 M1 - M2 SM1 -M2 SS1 + SS211 n1 + n2 - 2 n1 n2 But, since you already know MSW, use it: +

  6. t with MSW t = M1 - M2 = M1 - M2 MSW 1 + 1 sW2 1 + 1 n1 n2 n1 n2 Obviously, if n1 = n2, the denominator simplifies to 2sW2/n

  7. A posteriori tests • Several post hoc tests have been developed to find the differences between means if the ANOVA F ratio is significant. • Tukey’s HSD keeps the total Type I error rate (the experimentwise error rate) at a. • Newman-Keuls keeps the Type I error rate at a for each comparison.

  8. Tukey’s HSD • Both Tukey and Newman-Keuls use the studentized range distribution, q, rather than t or F. qobt = Mi - Mj MSW/n where i refers to the larger mean and n is the sample size, with all samples being the same size..

  9. Evaluating Tukey • Use table B-5 to find the critical value of q. • If qobt > qcrit, reject H0. If not, retain H0. • Analogous to the confidence interval approach, you can simplify multiple Tukey HSD tests by determining the size of the mean difference (Mi – Mj ) that is significant: • HSD = qMSW/n Any mean differences that equal or exceed HSD are significant.

  10. Newman-Keuls test • Calculation of qobt is the same as for Tukey’s HSD. • The value of qcrit differs for each comparison, depending on r, the number of means encompassed by the two means being compared. • Compare qobt to the appropriate qcrit starting from the largest and moving down as far as necessary: Logic.

  11. The case of unequal sample sizes • If sample sizes are not equal, but are not greatly different, either, you may use Tukey’s HSD or Newman-Keuls. • However, what value of n should you use in the equation? • Use the harmonic mean: • n = k . (1/n1) + (1/n2) + … + (1/nk) ~

  12. The Scheffe test • This is a very conservative test, with relatively low power. • F is still equal to MSB/ MSW , but MSB is re-computed using only the two groups being compared. MSB = F is compared to the same critical value as for the ANOVA.

  13. Type I Error and Power • Which of the three approaches has the highest risk of Type I error? • Which has the most power?

More Related