Original Program from program editor.
********************************************************;
*** Steele & Torrie (1980) Table 7.1 ***;
*** Nitrogen content of red clover plants inoculated ***;
*** with combination cultures of Rhizobium strains ***;
********************************************************;
options ps=256 ls=99 nocenter nodate nonumber nolabel;
TITLE1 'Analysis of Variance (One-way ANOVA)';
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 print data=clover; var treatment percent;
TITLE3 'Raw data list (unsorted)'; run;
proc mixed data=clover order=data; class treatment;
TITLE3 'ANOVA with PROC MIXED';
model percent = treatment / htype=3 DDFM=Satterthwaite;
run; quit;
proc mixed data=clover order=data; class treatment;
TITLE3 'ANOVA with PROC MIXED - separate variances';
model percent = treatment / htype=3 DDFM=Satterthwaite outp=resids;
repeated / group = treatment;
lsmeans treatment / adjust=tukey pdiff;
** treatments in order=data ==========> 3DOk1 3DOk4 3DOk5 3DOk7 3DOk13;
contrast '3 low vrs 2 high' treatment -2 -2 -2 3 3;
contrast 'odd vrs even' treatment -1 4 -1 -1 -1;
contrast '1st vrs 2nd' treatment -1 1 0 0 0;
ods output diffs=ppp lsmeans=mmm;
ods listing exclude diffs ;* but not lsmeans;
run;
TITLE4 'Post hoc adjustment with macro by Arnold Saxton';
* SAS Macro by Arnold Saxton: Saxton, A.M. 1998. A macro for ;
* converting mean separation output to letter groupings in Proc Mixed. ;
* In Proc. 23rd SAS Users Group Intl., SAS Institute, Cary, NC, pp1243-1246.;
%include 'C:\Geaghan\EXST\EXST7005New\Fall2003\SaS\pdmix800.sas';
%pdmix800(ppp,mmm,alpha=0.05,sort=yes);
run;
proc univariate data=resids normal plot; var resid;
TITLE4 'Univariate analysis of residuals';
run;
proc sort data=clover; by treatment; run;
proc means noprint data=clover; by treatment; var percent;
output out=next1 mean=mean var=var; run;
options ps=45; proc plot data=next1; plot var*mean;
TITLE3 'Variance mean plot to examine homogeniety';
run;
options ps=61;
proc glm data=clover order=data; class treatment;
TITLE3 'ANOVA with SAS PROC GLM with post hoc and HOV tests';
model percent = treatment / SS3;
MEANS treatment / HOVTEST=BARTLETT HOVTEST=BF HOVTEST=LEVENE(TYPE=ABS)
HOVTEST=LEVENE(TYPE=SQUARE) HOVTEST=OBRIEN WELCH;
means treatment / lsd tukey bon scheffe duncan lines;
means treatment / lsd tukey bon scheffe duncan cldiff;
means treatment / dunnett('3DOk1');
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 options ps=256 ls=99 nocenter nodate nonumber nolabel;
7 TITLE1 'Analysis of Variance (One-way ANOVA)';
8
9 data clover; infile cards missover;
10 TITLE2 'Nitrogen content of red clover (S&T 1980)';
11 LABEL treatment = 'Rhizobium inoculum';
12 LABEL percent = 'Percent N content';
13 input treatment $ 1-6 percent;
14 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
14 ! run;
40 ;
41 proc print data=clover; var treatment percent;
42 TITLE3 'Raw data list (unsorted)'; run;
NOTE: There were 25 observations read from the data set WORK.CLOVER.
NOTE: The PROCEDURE PRINT printed page 1.
NOTE: PROCEDURE PRINT used (Total process time):
real time 0.01 seconds
cpu time 0.01 seconds
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
Raw data list (unsorted)
Obs treatment percent
1 3DOk1 19.4
2 3DOk1 32.6
3 3DOk1 27.0
4 3DOk1 32.1
5 3DOk1 33.0
6 3DOk4 17.0
7 3DOk4 19.4
8 3DOk4 9.1
9 3DOk4 11.9
10 3DOk4 15.8
11 3DOk5 17.7
12 3DOk5 24.8
13 3DOk5 27.9
14 3DOk5 25.2
15 3DOk5 24.3
16 3DOk7 20.7
17 3DOk7 21.0
18 3DOk7 20.5
19 3DOk7 18.8
20 3DOk7 18.6
21 3DOk13 14.3
22 3DOk13 14.4
23 3DOk13 11.8
24 3DOk13 11.6
25 3DOk13 14.2
43
44 proc mixed data=clover order=data; class treatment;
45 TITLE3 'ANOVA with PROC MIXED';
46 model percent = treatment / htype=3 DDFM=Satterthwaite;
47 run;
NOTE: The PROCEDURE MIXED printed page 2.
NOTE: PROCEDURE MIXED used (Total process time):
real time 0.06 seconds
cpu time 0.03 seconds
47 ! quit;
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
ANOVA with PROC MIXED
The Mixed Procedure
Model Information
Data Set WORK.CLOVER
Dependent Variable percent
Covariance Structure Diagonal
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Residual
Class Level Information
Class Levels Values
treatment 5 3DOk1 3DOk4 3DOk5 3DOk7 3DOk13
Dimensions
Covariance Parameters 1
Columns in X 6
Columns in Z 0
Subjects 1
Max Obs Per Subject 25
Observations Used 25
Observations Not Used 0
Total Observations 25
Covariance Parameter Estimates
Cov Parm Estimate
Residual 13.6334
Fit Statistics
-2 Res Log Likelihood 117.1
AIC (smaller is better) 119.1
AICC (smaller is better) 119.3
BIC (smaller is better) 120.1
Type 3 Tests of Fixed Effects
Num Den
Effect DF DF F Value Pr > F
treatment 4 20 15.38 <.0001
49 proc mixed data=clover order=data; class treatment;
50 TITLE3 'ANOVA with PROC MIXED - separate variances';
51 model percent = treatment / htype=3 DDFM=Satterthwaite outp=resids;
52 repeated / group = treatment;
53 lsmeans treatment / adjust=tukey pdiff;
54 ** treatments in order=data ==========> 3DOk1 3DOk4 3DOk5 3DOk7 3DOk13;
55 contrast '3 low vrs 2 high' treatment -2 -2 -2 3 3;
56 contrast 'odd vrs even' treatment -1 4 -1 -1 -1;
57 contrast '1st vrs 2nd' treatment -1 1 0 0 0;
58 ods output diffs=ppp lsmeans=mmm;
59 ods listing exclude diffs ;* but not lsmeans;
60 run;
NOTE:Convergence criteria met.
NOTE: The data set WORK.MMM has 5 observations and 7 variables.
NOTE: The data set WORK.PPP has 10 observations and 10 variables.
NOTE: The data set WORK.RESIDS has 25 observations and 9 variables.
NOTE: The PROCEDURE MIXED printed page 3.
NOTE: PROCEDURE MIXED used (Total process time):
real time 0.07 seconds
cpu time 0.07 seconds
61 TITLE4 'Post hoc adjustment with macro by Arnold Saxton';
62 * SAS Macro by Arnold Saxton: Saxton, A.M. 1998. A macro for ;
63 * converting mean separation output to letter groupings in Proc Mixed. ;
64 * In Proc. 23rd SAS Users Group Intl., SAS Institute, Cary, NC, pp1243-1246.;
65 %include 'C:\Geaghan\EXST\EXST7005New\Fall2003\SaS\pdmix800.sas';
693 %pdmix800(ppp,mmm,alpha=0.05,sort=yes);
PDMIX800 03.26.2002 processing
4.8945350075
Tukey-Kramer values for treatment are 7.72803 (avg) 2.81808 (min) 11.0084 (max).
694 run;
695
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
ANOVA with PROC MIXED - separate variances
The Mixed Procedure
Model Information
Data Set WORK.CLOVER
Dependent Variable percent
Covariance Structure Variance Components
Group Effect treatment
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite
Class Level Information
Class Levels Values
treatment 5 3DOk1 3DOk4 3DOk5 3DOk7 3DOk13
Dimensions
Covariance Parameters 5
Columns in X 6
Columns in Z 0
Subjects 25
Max Obs Per Subject 1
Observations Used 25
Observations Not Used 0
Total Observations 25
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 117.05518418
1 1 104.64497787 0.00000000
Convergence criteria met.
Covariance Parameter Estimates
Cov Parm Group Estimate
Residual treatment 3DOk1 33.6420
Residual treatment 3DOk4 16.9430
Residual treatment 3DOk5 14.2670
Residual treatment 3DOk7 1.2770
Residual treatment 3DOk13 2.0380
Fit Statistics
-2 Res Log Likelihood 104.6
AIC (smaller is better) 114.6
AICC (smaller is better) 118.9
BIC (smaller is better) 120.7
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 12.41 0.0145
Type 3 Tests of Fixed Effects
Num Den
Effect DF DF F Value Pr > F
treatment 4 7.08 25.64 0.0003
Contrasts
Num Den
Label DF DF F Value Pr > F
3 low vrs 2 high 1 12.7 21.59 0.0005
odd vrs even 1 5.55 11.66 0.0161
1st vrs 2nd 1 7.21 19.87 0.0027
Least Squares Means
Standard
Effect treatment Estimate Error DF t Value Pr > |t|
treatment 3DOk1 28.8200 2.5939 4 11.11 0.0004
treatment 3DOk4 14.6400 1.8408 4 7.95 0.0014
treatment 3DOk5 23.9800 1.6892 4 14.20 0.0001
treatment 3DOk7 19.9200 0.5054 4 39.42 <.0001
treatment 3DOk13 13.2600 0.6384 4 20.77 <.0001
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
ANOVA with PROC MIXED - separate variances
Post hoc adjustment with macro by Arnold Saxton
Effect=treatment ADJUSTMENT=Tukey-Kramer(P<0.05) BYGROUP=1
Obs treatment Estimate StdErr MSGROUP
1 3DOk1 28.8200 2.5939 A
2 3DOk5 23.9800 1.6892 A
3 3DOk7 19.9200 0.5054 AB
4 3DOk4 14.6400 1.8408 BC
5 3DOk13 13.2600 0.6384 C
696 proc univariate data=resids normal plot; var resid;
697 TITLE4 'Univariate analysis of residuals';
698 run;
NOTE: The PROCEDURE UNIVARIATE printed page 5.
NOTE: PROCEDURE UNIVARIATE used (Total process time):
real time 0.01 seconds
cpu time 0.01 seconds
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
ANOVA with PROC MIXED - separate variances
Univariate analysis of residuals
The UNIVARIATE Procedure
Variable: Resid
Moments
N 25 Sum Weights 25
Mean 0 Sum Observations 0
Std Deviation 3.37063298 Variance 11.3611667
Skewness -1.1101822 Kurtosis 1.50767295
Uncorrected SS 272.668 Corrected SS 272.668
Coeff Variation . Std Error Mean 0.6741266
Basic Statistical Measures
Location Variability
Mean 0.000000 Std Deviation 3.37063
Median 0.820000 Variance 11.36117
Mode . Range 14.18000
Interquartile Range 2.68000
Tests for Location: Mu0=0n
Test -Statistic- -----p Value------
Student's t t 0 Pr > |t| 1.0000
Sign M 3.5 Pr >= |M| 0.2295
Signed Rank S 11.5 Pr >= |S| 0.7639
Tests for Normality
Test --Statistic--- -----p Value------
Shapiro-Wilk W 0.908103 Pr < W 0.0277
Kolmogorov-Smirnov D 0.177818 Pr > D 0.0406
Cramer-von Mises W-Sq 0.143275 Pr > W-Sq 0.0271
Anderson-Darling A-Sq 0.822014 Pr > A-Sq 0.0298
Quantiles (Definition 5)
Quantile Estimate
100% Max 4.76
99% 4.76
95% 4.18
90% 3.92
75% Q3 1.22
50% Median 0.82
25% Q1 -1.46
10% -5.54
5% -6.28
1% -9.42
0% Min -9.42
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
-9.42 1 3.28 4
-6.28 11 3.78 2
-5.54 8 3.92 13
-2.74 9 4.18 5
-1.82 3 4.76 7
Stem Leaf Boxplot
4 28 2 |
2 4389 4 |
0 3688901122 10 +--+--+
-0 87531 5 +-----+
-2 7 1 |
-4 5 1 0
-6 3 1 0
-8 4 1 0
----+----+----+----+
Normal Probability Plot
5+ +++*++ *
| ++**+* *
| **********
| ** ***+++
| *+++++
| ++++*+
| ++++++ *
-9+++ *
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
699
700 proc sort data=clover; by treatment; run;
NOTE: There were 25 observations read from the data set WORK.CLOVER.
NOTE: The data set WORK.CLOVER has 25 observations and 2 variables.
NOTE: PROCEDURE SORT used (Total process time):
real time 0.01 seconds
cpu time 0.01 seconds
701 proc means noprint data=clover; by treatment; var percent;
702 output out=next1 mean=mean var=var; run;
NOTE: There were 25 observations read from the data set WORK.CLOVER.
NOTE: The data set WORK.NEXT1 has 5 observations and 5 variables.
NOTE: PROCEDURE MEANS used (Total process time):
real time 0.01 seconds
cpu time 0.01 seconds
703 options ps=45;
703 ! proc plot data=next1; plot var*mean;
704 TITLE3 'Variance mean plot to examine homogeniety';
705 run;
706 options ps=61;
707
NOTE: There were 5 observations read from the data set WORK.NEXT1.
NOTE: The PROCEDURE PLOT printed page 6.
NOTE: PROCEDURE PLOT used (Total process time):
real time 0.01 seconds
cpu time 0.01 seconds
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
Variance mean plot to examine homogeniety
Plot of var*mean. Legend: A = 1 obs, B = 2 obs, etc.
var |
|
40 +
|
|
|
| A
|
30 +
|
|
|
|
|
20 +
|
| A
| A
|
|
10 +
|
|
|
|
| A A
0 +
|
--+---------+---------+---------+---------+---------+---------+---------+---------+---------+--
12 14 16 18 20 22 24 26 28 30
mean
708 proc glm data=clover order=data; class treatment;
709 TITLE3 'ANOVA with SAS PROC GLM with post hoc and HOV tests';
710 model percent = treatment / SS3;
711 MEANS treatment / HOVTEST=BARTLETT HOVTEST=BF HOVTEST=LEVENE(TYPE=ABS)
712 HOVTEST=LEVENE(TYPE=SQUARE) HOVTEST=OBRIEN WELCH;
713 means treatment / lsd tukey bon scheffe duncan lines;
714 means treatment / lsd tukey bon scheffe duncan cldiff;
715 means treatment / dunnett('3DOk1');
716 run;
717 quit;
NOTE: The PROCEDURE GLM printed pages 7-20.
NOTE: PROCEDURE GLM used (Total process time):
real time 0.12 seconds
cpu time 0.09 seconds
NOTE: SAS Institute Inc., SAS Campus Drive, Cary, NC USA 27513-2414
NOTE: The SAS System used:
real time 2.00 seconds
cpu time 0.90 seconds
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
ANOVA with SAS PROC GLM with post hoc and HOV tests
The GLM Procedure
Class Level Information
Class Levels Values
treatment 5 3DOk1 3DOk13 3DOk4 3DOk5 3DOk7
Number of observations 25
Dependent Variable: percent
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 4 838.597600 209.649400 15.38 <.0001
Error 20 272.668000 13.633400
Corrected Total 24 1111.265600
R-Square Coeff Var Root MSE percent Mean
0.754633 18.34796 3.692343 20.12400
Source DF Type III SS Mean Square F Value Pr > F
treatment 4 838.5976000 209.6494000 15.38 <.0001
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
ANOVA with SAS PROC GLM with post hoc and HOV tests
The GLM Procedure
Levene's Test for Homogeneity of percent Variance
ANOVA of Squared Deviations from Group Means
Sum of Mean
Source DF Squares Square F Value Pr > F
treatment 4 2236.3 559.1 1.68 0.1943
Error 20 6661.1 333.1
O'Brien's Test for Homogeneity of percent Variance
ANOVA of O'Brien's Spread Variable, W = 0.5
Sum of Mean
Source DF Squares Square F Value Pr > F
treatment 4 3494.2 873.5 1.23 0.3285
Error 20 14166.4 708.3
Brown and Forsythe's Test for Homogeneity of percent Variance
ANOVA of Absolute Deviations from Group Medians
Sum of Mean
Source DF Squares Square F Value Pr > F
treatment 4 32.7944 8.1986 0.87 0.4966
Error 20 187.5 9.3766
Bartlett's Test for Homogeneity of percent Variance
Source DF Chi-Square Pr > ChiSq
treatment 4 11.2820 0.0236
Welch's ANOVA for percent
Source DF F Value Pr > F
treatment 4.0000 21.12 0.0001
Error 9.3550
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
ANOVA with SAS PROC GLM with post hoc and HOV tests
The GLM Procedure
Level of -----------percent-----------
treatment N Mean Std Dev
3DOk1 5 28.8200000 5.80017241
3DOk13 5 13.2600000 1.42758537
3DOk4 5 14.6400000 4.11618756
3DOk5 5 23.9800000 3.77716825
3DOk7 5 19.9200000 1.13004425
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
ANOVA with SAS PROC GLM with post hoc and HOV tests
The GLM Procedure
t Tests (LSD) for percent
NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 13.6334
Critical Value of t 2.08596
Least Significant Difference 4.8712
Means with the same letter are not significantly different.
t Grouping Mean N treatment
A 28.820 5 3DOk1
A
B A 23.980 5 3DOk5
B
B 19.920 5 3DOk7
C 14.640 5 3DOk4
C
C 13.260 5 3DOk13
Duncan's Multiple Range Test for percent
NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 13.6334
Number of Means 2 3 4 5
Critical Range 4.871 5.113 5.267 5.374
Means with the same letter are not significantly different.
Duncan Grouping Mean N treatment
A 28.820 5 3DOk1
A
B A 23.980 5 3DOk5
B
B 19.920 5 3DOk7
C 14.640 5 3DOk4
C
C 13.260 5 3DOk13
Tukey's Studentized Range (HSD) Test for percent
NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type
II error rate than REGWQ.
Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 13.6334
Critical Value of Studentized Range 4.23186
Minimum Significant Difference 6.9879
Means with the same letter are not significantly different.
Tukey Grouping Mean N treatment
A 28.820 5 3DOk1
A
B A 23.980 5 3DOk5
B
B C 19.920 5 3DOk7
C
C 14.640 5 3DOk4
C
C 13.260 5 3DOk13
Bonferroni (Dunn) t Tests for percent
NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type
II error rate than REGWQ.
Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 13.6334
Critical Value of t 3.15340
Minimum Significant Difference 7.364
Means with the same letter are not significantly different.
Bon Grouping Mean N treatment
A 28.820 5 3DOk1
A
B A 23.980 5 3DOk5
B
B C 19.920 5 3DOk7
C
C 14.640 5 3DOk4
C
C 13.260 5 3DOk13
Scheffe's Test for percent
NOTE: This test controls the Type I experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 13.6334
Critical Value of F 2.86608
Minimum Significant Difference 7.9069
Means with the same letter are not significantly different.
Scheffe Grouping Mean N treatment
A 28.820 5 3DOk1
A
B A 23.980 5 3DOk5
B
B C 19.920 5 3DOk7
C
C 14.640 5 3DOk4
C
C 13.260 5 3DOk13
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
ANOVA with SAS PROC GLM with post hoc and HOV tests
The GLM Procedure
t Tests (LSD) for percent
NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 13.6334
Critical Value of t 2.08596
Least Significant Difference 4.8712
Comparisons significant at the 0.05 level are indicated by ***.
Difference
treatment Between 95% Confidence
Comparison Means Limits
3DOk1 - 3DOk5 4.840 -0.031 9.711
3DOk1 - 3DOk7 8.900 4.029 13.771 ***
3DOk1 - 3DOk4 14.180 9.309 19.051 ***
3DOk1 - 3DOk13 15.560 10.689 20.431 ***
3DOk5 - 3DOk1 -4.840 -9.711 0.031
3DOk5 - 3DOk7 4.060 -0.811 8.931
3DOk5 - 3DOk4 9.340 4.469 14.211 ***
3DOk5 - 3DOk13 10.720 5.849 15.591 ***
3DOk7 - 3DOk1 -8.900 -13.771 -4.029 ***
3DOk7 - 3DOk5 -4.060 -8.931 0.811
3DOk7 - 3DOk4 5.280 0.409 10.151 ***
3DOk7 - 3DOk13 6.660 1.789 11.531 ***
3DOk4 - 3DOk1 -14.180 -19.051 -9.309 ***
3DOk4 - 3DOk5 -9.340 -14.211 -4.469 ***
3DOk4 - 3DOk7 -5.280 -10.151 -0.409 ***
3DOk4 - 3DOk13 1.380 -3.491 6.251
3DOk13 - 3DOk1 -15.560 -20.431 -10.689 ***
3DOk13 - 3DOk5 -10.720 -15.591 -5.849 ***
3DOk13 - 3DOk7 -6.660 -11.531 -1.789 ***
3DOk13 - 3DOk4 -1.380 -6.251 3.491
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
ANOVA with SAS PROC GLM with post hoc and HOV tests
The GLM Procedure
Tukey's Studentized Range (HSD) Test for percent
NOTE: This test controls the Type I experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 13.6334
Critical Value of Studentized Range 4.23186
Minimum Significant Difference 6.9879
Comparisons significant at the 0.05 level are indicated by ***.
Difference
treatment Between Simultaneous 95%
Comparison Means Confidence Limits
3DOk1 - 3DOk5 4.840 -2.148 11.828
3DOk1 - 3DOk7 8.900 1.912 15.888 ***
3DOk1 - 3DOk4 14.180 7.192 21.168 ***
3DOk1 - 3DOk13 15.560 8.572 22.548 ***
3DOk5 - 3DOk1 -4.840 -11.828 2.148
3DOk5 - 3DOk7 4.060 -2.928 11.048
3DOk5 - 3DOk4 9.340 2.352 16.328 ***
3DOk5 - 3DOk13 10.720 3.732 17.708 ***
3DOk7 - 3DOk1 -8.900 -15.888 -1.912 ***
3DOk7 - 3DOk5 -4.060 -11.048 2.928
3DOk7 - 3DOk4 5.280 -1.708 12.268
3DOk7 - 3DOk13 6.660 -0.328 13.648
3DOk4 - 3DOk1 -14.180 -21.168 -7.192 ***
3DOk4 - 3DOk5 -9.340 -16.328 -2.352 ***
3DOk4 - 3DOk7 -5.280 -12.268 1.708
3DOk4 - 3DOk13 1.380 -5.608 8.368
3DOk13 - 3DOk1 -15.560 -22.548 -8.572 ***
3DOk13 - 3DOk5 -10.720 -17.708 -3.732 ***
3DOk13 - 3DOk7 -6.660 -13.648 0.328
3DOk13 - 3DOk4 -1.380 -8.368 5.608
Bonferroni (Dunn) t Tests for percent
NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type
II error rate than Tukey's for all pairwise comparisons.
Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 13.6334
Critical Value of t 3.15340
Minimum Significant Difference 7.364
Comparisons significant at the 0.05 level are indicated by ***.
Difference
treatment Between Simultaneous 95%
Comparison Means Confidence Limits
3DOk1 - 3DOk5 4.840 -2.524 12.204
3DOk1 - 3DOk7 8.900 1.536 16.264 ***
3DOk1 - 3DOk4 14.180 6.816 21.544 ***
3DOk1 - 3DOk13 15.560 8.196 22.924 ***
3DOk5 - 3DOk1 -4.840 -12.204 2.524
3DOk5 - 3DOk7 4.060 -3.304 11.424
3DOk5 - 3DOk4 9.340 1.976 16.704 ***
3DOk5 - 3DOk13 10.720 3.356 18.084 ***
3DOk7 - 3DOk1 -8.900 -16.264 -1.536 ***
3DOk7 - 3DOk5 -4.060 -11.424 3.304
3DOk7 - 3DOk4 5.280 -2.084 12.644
3DOk7 - 3DOk13 6.660 -0.704 14.024
3DOk4 - 3DOk1 -14.180 -21.544 -6.816 ***
3DOk4 - 3DOk5 -9.340 -16.704 -1.976 ***
3DOk4 - 3DOk7 -5.280 -12.644 2.084
3DOk4 - 3DOk13 1.380 -5.984 8.744
3DOk13 - 3DOk1 -15.560 -22.924 -8.196 ***
3DOk13 - 3DOk5 -10.720 -18.084 -3.356 ***
3DOk13 - 3DOk7 -6.660 -14.024 0.704
3DOk13 - 3DOk4 -1.380 -8.744 5.984
Analysis of Variance (One-way ANOVA)
Nitrogen content of red clover (S&T 1980)
ANOVA with SAS PROC GLM with post hoc and HOV tests
The GLM Procedure
Scheffe's Test for percent
NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type
II error rate than Tukey's for all pairwise comparisons.
Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 13.6334
Critical Value of F 2.86608
Minimum Significant Difference 7.9069
Comparisons significant at the 0.05 level are indicated by ***.
Difference
treatment Between Simultaneous 95%
Comparison Means Confidence Limits
3DOk1 - 3DOk5 4.840 -3.067 12.747
3DOk1 - 3DOk7 8.900 0.993 16.807 ***
3DOk1 - 3DOk4 14.180 6.273 22.087 ***
3DOk1 - 3DOk13 15.560 7.653 23.467 ***
3DOk5 - 3DOk1 -4.840 -12.747 3.067
3DOk5 - 3DOk7 4.060 -3.847 11.967
3DOk5 - 3DOk4 9.340 1.433 17.247 ***
3DOk5 - 3DOk13 10.720 2.813 18.627 ***
3DOk7 - 3DOk1 -8.900 -16.807 -0.993 ***
3DOk7 - 3DOk5 -4.060 -11.967 3.847
3DOk7 - 3DOk4 5.280 -2.627 13.187
3DOk7 - 3DOk13 6.660 -1.247 14.567
3DOk4 - 3DOk1 -14.180 -22.087 -6.273 ***
3DOk4 - 3DOk5 -9.340 -17.247 -1.433 ***
3DOk4 - 3DOk7 -5.280 -13.187 2.627
3DOk4 - 3DOk13 1.380 -6.527 9.287
3DOk13 - 3DOk1 -15.560 -23.467 -7.653 ***
3DOk13 - 3DOk5 -10.720 -18.627 -2.813 ***
3DOk13 - 3DOk7 -6.660 -14.567 1.247
3DOk13 - 3DOk4 -1.380 -9.287 6.527
Dunnett's t Tests for percent
NOTE: This test controls the Type I experimentwise error for comparisons of all treatments against a control.
Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 13.6334
Critical Value of Dunnett's t 2.65112
Minimum Significant Difference 6.191
Comparisons significant at the 0.05 level are indicated by ***.
Difference
treatment Between Simultaneous 95%
Comparison Means Confidence Limits
3DOk5 - 3DOk1 -4.840 -11.031 1.351
3DOk7 - 3DOk1 -8.900 -15.091 -2.709 ***
3DOk4 - 3DOk1 -14.180 -20.371 -7.989 ***
3DOk13 - 3DOk1 -15.560 -21.751 -9.369 ***