SAS example: ANOVA for a one way layout

The data consist of blood coagulation times for 24 animals
fed one of 4 different diets. I use * proc anova* to test the
hypothesis of no differences between mean coagulation times and
to get simulataneous confidence intervals for all
possible differences between mean times.

The data

A 62 A 60 A 63 A 59 B 63 B 67 B 71 B 64 B 65 B 66 C 68 C 66 C 71 C 67 C 68 C 68 D 56 D 62 D 60 D 61 D 63 D 64 D 63 D 59

I ran the following SAS code:

options pagesize=60 linesize=70; data coagul; infile 'coagul.dat'; input diet $ time ; label time='Coagulation Time'; proc sort data=coagul; by diet; proc anova data=coagul; class diet; model time = diet; means diet / bon regwq tukey cldiff; means diet / bon regwq tukey ; run;

The two lines labelled * means* request confidence
intervals for differences between the 4 population means.
The line ` class diet` is a required saying that the
variable * class* defines categories for the analysis of
variance. The model line declares that I am interested only in the
influence of diet on time; this line is also required.

The output from * proc anova* is

The SAS System 8 15:40 Thursday, October 26, 1995 Analysis of Variance Procedure Class Level Information Class Levels Values DIET 4 A B C D Number of observations in data set = 24 The SAS System 9 15:40 Thursday, October 26, 1995 Analysis of Variance Procedure Dependent Variable: TIME Coagulation Time Source DF Sum of Squares F Value Pr > F Model 3 228.00000000 13.57 0.0001 Error 20 112.00000000 Corrected Total 23 340.00000000 R-Square C.V. TIME Mean 0.670588 3.697550 64.0000000 Source DF Anova SS F Value Pr > F DIET 3 228.00000000 13.57 0.0001 The SAS System 10 15:40 Thursday, October 26, 1995 Analysis of Variance Procedure Tukey's Studentized Range (HSD) Test for variable: TIME NOTE: This test controls the type I experimentwise error rate. Alpha= 0.05 Confidence= 0.95 df= 20 MSE= 5.6 Critical Value of Studentized Range= 3.958 Comparisons significant at the 0.05 level are indicated by '***'. Simultaneous Simultaneous Lower Difference Upper DIET Confidence Between Confidence Comparison Limit Means Limit C - B -1.824 2.000 5.824 C - A 2.725 7.000 11.275 *** C - D 3.423 7.000 10.577 *** B - C -5.824 -2.000 1.824 B - A 0.725 5.000 9.275 *** B - D 1.423 5.000 8.577 *** A - C -11.275 -7.000 -2.725 *** A - B -9.275 -5.000 -0.725 *** A - D -4.056 0.000 4.056 D - C -10.577 -7.000 -3.423 *** D - B -8.577 -5.000 -1.423 *** D - A -4.056 0.000 4.056 The SAS System 11 15:40 Thursday, October 26, 1995 Analysis of Variance Procedure Bonferroni (Dunn) T tests for variable: TIME NOTE: This test controls the type I experimentwise error rate but generally has a higher type II error rate than Tukey's for all pairwise comparisons. Alpha= 0.05 Confidence= 0.95 df= 20 MSE= 5.6 Critical Value of T= 2.92712 Comparisons significant at the 0.05 level are indicated by '***'. Simultaneous Simultaneous Lower Difference Upper DIET Confidence Between Confidence Comparison Limit Means Limit C - B -1.999 2.000 5.999 C - A 2.529 7.000 11.471 *** C - D 3.259 7.000 10.741 *** B - C -5.999 -2.000 1.999 B - A 0.529 5.000 9.471 *** B - D 1.259 5.000 8.741 *** A - C -11.471 -7.000 -2.529 *** A - B -9.471 -5.000 -0.529 *** A - D -4.242 0.000 4.242 D - C -10.741 -7.000 -3.259 *** D - B -8.741 -5.000 -1.259 *** D - A -4.242 0.000 4.242 The SAS System 12 15:40 Thursday, October 26, 1995 Analysis of Variance Procedure Ryan-Einot-Gabriel-Welsch Multiple Range Test for variable: TIME NOTE: This test controls the type I experimentwise error rate. Alpha= 0.05 df= 20 MSE= 5.6 WARNING: Cell sizes are not equal. Harmonic Mean of cell sizes= 5.647059 Number of Means 2 3 4 Critical Range 3.4039958 3.5629957 3.9417679 Means with the same letter are not significantly different. REGWQ Grouping Mean N DIET A 68.000 6 C A A 66.000 6 B B 61.000 4 A B B 61.000 8 D The SAS System 13 15:40 Thursday, October 26, 1995 Analysis of Variance Procedure Tukey's Studentized Range (HSD) Test for variable: TIME NOTE: This test controls the type I experimentwise error rate, but generally has a higher type II error rate than REGWQ. Alpha= 0.05 df= 20 MSE= 5.6 Critical Value of Studentized Range= 3.958 Minimum Significant Difference= 3.9418 WARNING: Cell sizes are not equal. Harmonic Mean of cell sizes= 5.647059 Means with the same letter are not significantly different. Tukey Grouping Mean N DIET A 68.000 6 C A A 66.000 6 B B 61.000 4 A B B 61.000 8 D The SAS System 14 15:40 Thursday, October 26, 1995 Analysis of Variance Procedure Bonferroni (Dunn) T tests for variable: TIME NOTE: This test controls the type I experimentwise error rate, but generally has a higher type II error rate than REGWQ. Alpha= 0.05 df= 20 MSE= 5.6 Critical Value of T= 2.93 Minimum Significant Difference= 4.1223 WARNING: Cell sizes are not equal. Harmonic Mean of cell sizes= 5.647059 Means with the same letter are not significantly different. Bon Grouping Mean N DIET A 68.000 6 C A A 66.000 6 B B 61.000 4 A B B 61.000 8 D

The ANOVA table shows overwhelmingly significant evidence against the hypothesis of equal means. The multiple comparison procedures say that diets B and C are indistinguishable, as are A and D but that these two groups definitely differ from each other. The procedure called TUKEY is the only one under consideration in this course. The keyword CLDIFF on the first means line asked for actual confidence intervals while the second line produced the grouping just discussed.

Thu Sep 5 16:13:09 PDT 1996