Original Program from program editor.
********************************************************;
*** Steele & Torrie (1980) Table 7.1 ***;
*** Nitrogen content of red clover plants inoculated ***;
*** with combination cultures of Rhizobium strains ***;
********************************************************;
*** This example was used to demonstrate one-way ***;
*** ANOVA and is used again here to compare and ***;
*** demonstrate some non-parametric alternatives ***;
********************************************************;
options ps=256 ls=99 nocenter nodate nonumber;
TITLE1 'Examples of some nonparametric analyses';
data clover; infile cards missover;
TITLE2 'Nitrogen content of red clover (S&T 1980)';
LABEL treatment = 'Rhizobium inoculum';
LABEL percent = 'Percent N content';
input treatment $ 1-6 percent;
cards; run;
3DOk1 19.4
3DOk1 32.6
3DOk1 27.0
3DOk1 32.1
3DOk1 33.0
3DOk4 17.0
3DOk4 19.4
3DOk4 9.1
3DOk4 11.9
3DOk4 15.8
3DOk5 17.7
3DOk5 24.8
3DOk5 27.9
3DOk5 25.2
3DOk5 24.3
3DOk7 20.7
3DOk7 21.0
3DOk7 20.5
3DOk7 18.8
3DOk7 18.6
3DOk13 14.3
3DOk13 14.4
3DOk13 11.8
3DOk13 11.6
3DOk13 14.2
;
proc npar1way data=clover;
TITLE3 'Demonstration of SAS NPAR1WAY';
class treatment; var percent;
run;
quit;
Below is output from the SAS log (bold) and output from the SAS Output window.
1 ********************************************************;
2 *** Steele & Torrie (1980) Table 7.1 ***;
3 *** Nitrogen content of red clover plants inoculated ***;
4 *** with combination cultures of Rhizobium strains ***;
5 ********************************************************;
6 *** This example was used to demonstrate one-way ***;
7 *** ANOVA and is used again here to compare and ***;
8 *** demonstrate some non-parametric alternatives ***;
9 ********************************************************;
10
11 options ps=256 ls=99 nocenter nodate nonumber;
12 TITLE1 'Examples of some nonparametric analyses';
13
14 data clover; infile cards missover;
15 TITLE2 'Nitrogen content of red clover (S&T 1980)';
16 LABEL treatment = 'Rhizobium inoculum';
17 LABEL percent = 'Percent N content';
18 input treatment $ 1-6 percent;
19 cards;
NOTE: The data set WORK.CLOVER has 25 observations and 2 variables.
NOTE: DATA statement used (Total process time):
real time 0.01 seconds
cpu time 0.01 seconds
19 ! run;
45 ;
46
47 proc npar1way data=clover;
48 TITLE3 'Demonstration of SAS NPAR1WAY';
49 class treatment; var percent;
50 run;
NOTE: There were 25 observations read from the data set WORK.CLOVER.
NOTE: The PROCEDURE NPAR1WAY printed pages 1-6.
NOTE: PROCEDURE NPAR1WAY used (Total process time):
real time 0.03 seconds
cpu time 0.03 seconds
51 quit;
52
NOTE: SAS Institute Inc., SAS Campus Drive, Cary, NC USA 27513-2414
NOTE: The SAS System used:
real time 0.32 seconds
cpu time 0.21 seconds
Examples of some nonparametric analyses
Nitrogen content of red clover (S&T 1980)
Demonstration of SAS NPAR1WAY
The NPAR1WAY Procedure
Analysis of Variance for Variable percent
Classified by Variable treatment
treatment N Mean
-----------------------------------------
3DOk1 5 28.820
3DOk4 5 14.640
3DOk5 5 23.980
3DOk7 5 19.920
3DOk13 5 13.260
Source DF Sum of Squares Mean Square F Value Pr > F
-------------------------------------------------------------------
Among 4 838.59760 209.64940 15.3776 <.0001
Within 20 272.66800 13.63340
Average scores were used for ties.
Wilcoxon Scores (Rank Sums) for Variable percent
Classified by Variable treatment
Sum of Expected Std Dev Mean
treatment N Scores Under H0 Under H0 Score
-------------------------------------------------------------------------
3DOk1 5 106.50 65.0 14.716770 21.30
3DOk4 5 35.50 65.0 14.716770 7.10
3DOk5 5 89.00 65.0 14.716770 17.80
3DOk7 5 71.00 65.0 14.716770 14.20
3DOk13 5 23.00 65.0 14.716770 4.60
Average scores were used for ties.
Kruskal-Wallis Test
Chi-Square 18.3523
DF 4
Pr > Chi-Square 0.0011
Median Scores (Number of Points Above Median) for Variable percent
Classified by Variable treatment
Sum of Expected Std Dev Mean
treatment N Scores Under H0 Under H0 Score
-------------------------------------------------------------------------
3DOk1 5 4.50 2.40 0.978093 0.90
3DOk4 5 0.50 2.40 0.978093 0.10
3DOk5 5 4.00 2.40 0.978093 0.80
3DOk7 5 3.00 2.40 0.978093 0.60
3DOk13 5 0.00 2.40 0.978093 0.00
Average scores were used for ties.
Median One-Way Analysis
Chi-Square 13.9652
DF 4
Pr > Chi-Square 0.0074
Van der Waerden Scores (Normal) for Variable percent
Classified by Variable treatment
Sum of Expected Std Dev Mean
treatment N Scores Under H0 Under H0 Score
-------------------------------------------------------------------------
3DOk1 5 5.310985 0.0 1.812483 1.062197
3DOk4 5 -3.638749 0.0 1.812483 -0.727750
3DOk5 5 2.580554 0.0 1.812483 0.516111
3DOk7 5 0.592548 0.0 1.812483 0.118510
3DOk13 5 -4.845337 0.0 1.812483 -0.969067
Average scores were used for ties.
Van der Waerden One-Way Analysis
Chi-Square 17.5178
DF 4
Pr > Chi-Square 0.0015
Savage Scores (Exponential) for Variable percent
Classified by Variable treatment
Sum of Expected Std Dev Mean
treatment N Scores Under H0 Under H0 Score
-------------------------------------------------------------------------
3DOk1 5 6.434914 0.0 1.878855 1.286983
3DOk4 5 -3.223352 0.0 1.878855 -0.644670
3DOk5 5 1.602038 0.0 1.878855 0.320408
3DOk7 5 -0.827699 0.0 1.878855 -0.165540
3DOk13 5 -3.985901 0.0 1.878855 -0.797180
Average scores were used for ties.
Savage One-Way Analysis
Chi-Square 16.0760
DF 4
Pr > Chi-Square 0.0029
Kolmogorov-Smirnov Test for Variable percent
Classified by Variable treatment
EDF at Deviation from Mean
treatment N Maximum at Maximum
------------------------------------------------------
3DOk1 5 0.000 -0.804984
3DOk4 5 0.800 0.983870
3DOk5 5 0.000 -0.804984
3DOk7 5 0.000 -0.804984
3DOk13 5 1.000 1.431084
Total 25 0.360
Maximum Deviation Occurred at Observation 6
Value of percent at Maximum = 17.0
Kolmogorov-Smirnov Statistics (Asymptotic)
KS 0.445421 KSa 2.227106
Cramer-von Mises Test for Variable percent
Classified by Variable treatment
Summed Deviation
treatment N from Mean
-------------------------------------------
3DOk1 5 0.675840
3DOk4 5 0.370240
3DOk5 5 0.325440
3DOk7 5 0.216640
3DOk13 5 0.792640
Cramer-von Mises Statistics (Asymptotic)
CM 0.095232 CMa 2.380800