Table A.1 Random numbers (section 1)

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1 A Tables Table Contents Page A.1 Random numbers 696 A.2 Orthogonal polynomial trend contrast coefficients 702 A.3 Standard normal distribution 703 A.4 Student s t-distribution 704 A.5 Chi-squared distribution 705 A.6 F-distribution 706 A.7 Power of the F-test 712 A.8 Studentized range distribution 718 (Tukey s method) A.9 Multivariate t-distribution maximum 720 (Dunnett s one-sided method; Hsu s method) A.10 Multivariate t-distribution absolute maximum 722 (Dunnett s two-sided method) A.11 Critical coefficients for the Voss Wang method

2 696 Appendix A Tables Table A.1 Random numbers (section 1) Random numbers were generated using the SAS statements retain seed ; and rn=floor(10*ranuni(seed));.

3 Appendix A Tables 697 Table A.1 Random numbers (section 2)

4 698 Appendix A Tables Table A.1 Random numbers (section 3)

5 Appendix A Tables 699 Table A.1 Random numbers (section 4)

6 700 Appendix A Tables Table A.1 Random numbers (section 5)

7 Appendix A Tables 701 Table A.1 Random numbers (section 6)

8 702 Appendix A Tables Table A.2 Coefficients c i for orthogonal polynomial trend contrasts v 3 Trend c 1 c 2 c 3 Linear Quadratic v 4 Trend c 1 c 2 c 3 c 4 Linear Quadratic Cubic v 5 Trend c 1 c 2 c 3 c 4 c 5 Linear Quadratic Cubic Quartic v 6 Trend c 1 c 2 c 3 c 4 c 5 c 6 Linear Quadratic Cubic Quartic Quintic v 7 Trend c 1 c 2 c 3 c 4 c 5 c 6 c 7 Linear Quadratic Cubic Quartic Quintic Sextic

9 Appendix A Tables 703 Table A.3 Standard normal distribution: Upper α critical coefficients, z α, and upper-tail probabilities, α P(Z >z α ) α z α z α Values were generated using the SAS statements z alpha = probit(1-alpha); and alpha = 1-probnorm(z alpha);.

10 704 Appendix A Tables Table A.4 Student s t-distribution: Upper α critical coefficients, t df,α, where α P(t df >t df,α ) α df Values t df,α were generated using the SAS statements t = tinv(1-alpha,df); for df < and t = probit(1-alpha) for df.

11 Appendix A Tables 705 Table A.5 Chi-squared distribution: Upper α critical coefficients, χ 2 df,α, where α P(χ 2 df >χ 2 df,α ) α df Values were generated using the SAS statement chi2 = cinv(1-alpha,df);.

12 706 Appendix A Tables Table A.6 F-distribution: Upper α critical coefficients, F ν1,ν 2,α, where α P(F ν1,ν 2 >F ν1,ν 2,α) ν 1 ν 2 α Values F ν1,ν 2,α were generated using the SAS statement f = round(finv(1-alpha,df1,df2),0.01);.

13 Appendix A Tables 707 Table A.6 (continued) F-distribution: Upper α critical coefficients, F ν1,ν 2,α ν 1 ν 2 α

14 708 Appendix A Tables Table A.6 (continued) F-distribution: Upper α critical coefficients, F ν1,ν 2,α ν 1 ν 2 α

15 Appendix A Tables 709 Table A.6 (continued) F-distribution: Upper α critical coefficients, F ν1,ν 2,α ν 1 ν 2 α

16 710 Appendix A Tables Table A.6 (continued) F-distribution: Upper α critical coefficients, F ν1,ν 2,α ν 1 ν 2 α

17 Appendix A Tables 711 Table A.6 (continued) F-distribution: Upper α critical coefficients, F ν1,ν 2,α ν 1 ν 2 α

18 712 Appendix A Tables Table A.7 Power of the F-test: π(φ) P(F ν1,ν 2,φ >F ν1,ν 2,α) ν 1 1, α 0.05 φ ν ν 1 1, α 0.01 φ ν Power was computed using the SAS statements nc=v*phi**2;, Falpha=finv(1-alpha,nu1,nu2);, power =1-probf(Falpha,nu1,nu2,nc);, and power = round(power,.01); for values of the parameters v, phi, alpha, nu1=v-1 and nu2. Falpha is the upper-α critical value of the F -distribution with nu1 and nu2 degrees of freedom, and nc is the noncentrality parameter for the corresponding noncentral F -distribution.

19 Appendix A Tables 713 Table A.7 (continued) Power of the F-test: π(φ) P(F ν1,ν 2,φ >F ν1,ν 2,α) ν 1 2, α 0.05 φ ν ν 1 2, α 0.01 φ ν

20 714 Appendix A Tables Table A.7 (continued) Power of the F-test: π(φ) P(F ν1,ν 2,φ >F ν1,ν 2,α) ν 1 3, α 0.05 φ ν ν 1 3, α 0.01 φ ν

21 Appendix A Tables 715 Table A.7 (continued) Power of the F-test: π(φ) P(F ν1,ν 2,φ >F ν1,ν 2,α) ν 1 4, α 0.05 φ ν ν 1 4, α 0.01 φ ν

22 716 Appendix A Tables Table A.7 (continued) Power of the F-test: π(φ) P(F ν1,ν 2,φ >F ν1,ν 2,α) ν 1 5, α 0.05 φ ν ν 1 5, α 0.01 φ ν

23 Appendix A Tables 717 Table A.7 (continued) Power of the F-test: π(φ) P(F ν1,ν 2,φ >F ν1,ν 2,α) ν 1 6, α 0.05 φ ν ν 1 6, α 0.01 φ ν

24 718 Appendix A Tables Table A.8 Tukey s method: Upper α critical values, q v,df,α, of the Studentized range distribution v df α Values q v,df,α were generated using the SAS statement qt = probmc( range,.,prob,df,v);, where prob 1 α, and df=. for df.

25 Appendix A Tables 719 Table A.8 (continued) Tukey s method: Upper α critical coefficients, q v,df,α of the Studentized range distribution v df α

26 720 Appendix A Tables Table A.9 Dunnett s one-sided method; Hsu s method: Upper α critical coefficients w D1 t (0.5) v 1,df,α v 1 df α Values w D1 t (0.5) v 1,df,α were generated using the SAS statement wd1 = probmc( dunnett1,.,prob,df,vm1);, where prob 1 α, vm1 v 1, t (0.5) v 1,df,α is the upper α critical value for the maximum of a (v 1)-variate t-distribution with common correlation ρ 0.5 and degrees of freedom df, and df=. for df.

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794 Appendix A:Tables

794 Appendix A:Tables Appendix A Tables A Table Contents Page A.1 Random numbers 794 A.2 Orthogonal polynomial trend contrast coefficients 800 A.3 Standard normal distribution 801 A.4 Student s t-distribution 802 A.5 Chi-squared