STA 402S 1998: SAS Lesson 3
Multiple comparisons
options linesize=79 pagesize=35;
title 'STA 402S98 SAS Lesson 3: Multiple Comparisons';
proc format; /* Used to label values of the categorical variables */
value carfmt 1 = 'US'
2 = 'Japanese'
3 = 'Other' ;
data auto;
infile 'cars.dat';
input country mpg weight length;
label country = 'Country of Origin'
mpg = 'Miles per Gallon';
format country carfmt.;
proc sort; by country;
proc univariate plot; var mpg; by country; /* side-by-side boxplots */
proc glm;
class country;
model mpg = country ;
means country;
means country / alpha=.05 bon tukey scheffe; /* alpha=.05 is default */;
estimate 'JAPvsUSO' country 1 -.5 -.5;
Part of the list file looks like this.
Variable=MPG Miles per Gallon
|
40 + 0
|
| 0 |
| |
30 + | +-----+
| | | |
| | *--+--* +-----+
| +-----+ | | *--+--*
20 + *--+--* +-----+ | |
| +-----+ | +-----+
| | |
| |
10 +
------------+-----------+-----------+-----------
COUNTRY US Japanese Other
General Linear Models Procedure
Class Level Information
Class Levels Values
COUNTRY 3 Japanese Other US
Number of observations in data set = 75
NOTE: Due to missing values, only 74 observations can be used in this
analysis.
STA 402S98 SAS Lesson 3: Multiple Comparisons
General Linear Models Procedure
Dependent Variable: MPG Miles per Gallon
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 421.83533359 210.91766679 7.41 0.0012
Error 71 2021.62412587 28.47357924
Corrected Total 73 2443.45945946
R-Square C.V. Root MSE MPG Mean
0.172639 25.05512 5.3360640 21.297297
General Linear Models Procedure
Level of -------------MPG-------------
COUNTRY N Mean SD
Japanese 11 26.1818182 6.11258017
Other 11 23.3636364 7.07492371
US 52 19.8269231 4.74329725
Tukey's Studentized Range (HSD) Test for variable: MPG
NOTE: This test controls the type I experimentwise error rate.
Alpha= 0.05 Confidence= 0.95 df= 71 MSE= 28.47358
Critical Value of Studentized Range= 3.385
Comparisons significant at the 0.05 level are indicated by '***'.
Simultaneous Simultaneous
Lower Difference Upper
COUNTRY Confidence Between Confidence
Comparison Limit Means Limit
Japanese - Other -2.629 2.818 8.265
Japanese - US 2.116 6.355 10.594 ***
Other - Japanese -8.265 -2.818 2.629
Other - US -0.703 3.537 7.776
US - Japanese -10.594 -6.355 -2.116 ***
US - Other -7.776 -3.537 0.703
General Linear Models Procedure
Bonferroni (Dunn) T tests for variable: MPG
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= 71 MSE= 28.47358
Critical Value of T= 2.45202
Comparisons significant at the 0.05 level are indicated by '***'.
Simultaneous Simultaneous
Lower Difference Upper
COUNTRY Confidence Between Confidence
Comparison Limit Means Limit
Japanese - Other -2.761 2.818 8.397
Japanese - US 2.013 6.355 10.697 ***
Other - Japanese -8.397 -2.818 2.761
Other - US -0.806 3.537 7.879
US - Japanese -10.697 -6.355 -2.013 ***
US - Other -7.879 -3.537 0.806
General Linear Models Procedure
Scheffe's test for variable: MPG
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= 71 MSE= 28.47358
Critical Value of F= 3.12576
Comparisons significant at the 0.05 level are indicated by '***'.
Simultaneous Simultaneous
Lower Difference Upper
COUNTRY Confidence Between Confidence
Comparison Limit Means Limit
Japanese - Other -2.871 2.818 8.507
Japanese - US 1.927 6.355 10.783 ***
Other - Japanese -8.507 -2.818 2.871
Other - US -0.891 3.537 7.964
US - Japanese -10.783 -6.355 -1.927 ***
US - Other -7.964 -3.537 0.891
General Linear Models Procedure
Dependent Variable: MPG Miles per Gallon
T for H0: Pr > |T| Std Error of
Parameter Estimate Parameter=0 Estimate
JAPvsUSO -4.94580420 -3.64 0.0005 1.35713759