Results: scab1.sas

Scab Disease Data based on Cochran and Cox (1958)

The FREQ Procedure

The FREQ Procedure

Table condition

One-Way Frequencies


condition	Frequency	Percent	Cumulative Frequency	Cumulative Percent
Control	8	25.00	8	25.00
Fall1200	4	12.50	12	37.50
Fall300	4	12.50	16	50.00
Fall600	4	12.50	20	62.50
Spring1200	4	12.50	24	75.00
Spring300	4	12.50	28	87.50
Spring600	4	12.50	32	100.00

Scab Disease Data based on Cochran and Cox (1958)

The MEANS Procedure

The MEANS Procedure

Summary statistics


Analysis Variable : infection Ave percent surface covered
condition	N Obs	N	Mean	Std Dev	Minimum	Maximum
Control	8	8	22.6250000	8.3637722	15.5600000	35.2600000
Spring300	4	4	16.7475000	10.7824900	5.1300000	30.1200000
Spring600	4	4	18.2500000	4.9273996	11.4000000	22.7500000
Spring1200	4	4	14.2525000	4.8578896	8.1100000	19.8400000
Fall300	4	4	9.4975000	4.9333854	5.0800000	14.8000000
Fall600	4	4	15.5025000	3.7887586	11.1000000	20.2300000
Fall1200	4	4	5.7500000	2.8700639	2.0100000	8.4800000

Scab Disease Data based on Cochran and Cox (1958)

Basic proc glm

The GLM Procedure

The GLM Procedure

Data

Class Levels


Class Level Information
Class	Levels	Values
condition	7	Control Spring300 Spring600 Spring1200 Fall300 Fall600 Fall1200

Number of Observations


Number of Observations Read	32
Number of Observations Used	32

Scab Disease Data based on Cochran and Cox (1958)

Basic proc glm

The GLM Procedure

Dependent Variable: infection Ave percent surface covered

Analysis of Variance

infection

Overall ANOVA


Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	6	972.413850	162.068975	3.61	0.0103
Error	25	1122.880900	44.915236
Corrected Total	31	2095.294750

Fit Statistics


R-Square	Coeff Var	Root MSE	infection Mean
0.464094	42.80644	6.701883	15.65625

Type I Model ANOVA


Source	DF	Type I SS	Mean Square	F Value	Pr > F
condition	6	972.4138500	162.0689750	3.61	0.0103

Type III Model ANOVA


Source	DF	Type III SS	Mean Square	F Value	Pr > F
condition	6	972.4138500	162.0689750	3.61	0.0103

Box Plot

Fit Plot for Ave percent surface covered by condition

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Dependent Variable: infection Ave percent surface covered

The REG Procedure

MODEL1

Fit

infection

Number of Observations


Number of Observations Read	32
Number of Observations Used	32

Analysis of Variance

Note:No intercept in model. R-Square is redefined.


Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	7	8816.19510	1259.45644	28.04	<.0001
Error	25	1122.88090	44.91524
Uncorrected Total	32	9939.07600

Fit Statistics


Root MSE	6.70188	R-Square	0.8870
Dependent Mean	15.65625	Adj R-Sq	0.8554
Coeff Var	42.80644

Parameter Estimates


Parameter Estimates
Variable	Label	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Control		1	22.62500	2.36947	9.55	<.0001
Fall300		1	9.49750	3.35094	2.83	0.0090
Fall600		1	15.50250	3.35094	4.63	<.0001
Fall1200		1	5.75000	3.35094	1.72	0.0985
Spring300		1	16.74750	3.35094	5.00	<.0001
Spring600		1	18.25000	3.35094	5.45	<.0001
Spring1200		1	14.25250	3.35094	4.25	0.0003

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test treatment

Results


Test treatment Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	6	162.06898	3.61	0.0103
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test Control_vs_Spring300

Results


Test Control_vs_Spring300 Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	92.12002	2.05	0.1645
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test Control_vs_Spring600

Results


Test Control_vs_Spring600 Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	51.04167	1.14	0.2966
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test Control_vs_Spring1200

Results


Test Control_vs_Spring1200 Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	186.93002	4.16	0.0520
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test Control_vs_Fall300

Results


Test Control_vs_Fall300 Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	459.55002	10.23	0.0037
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test Control_vs_Fall600

Results


Test Control_vs_Fall600 Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	135.28002	3.01	0.0950
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test Control_vs_Fall1200

Results


Test Control_vs_Fall1200 Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	759.37500	16.91	0.0004
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test Control_vs_Fall

Results


Test Control_vs_Fall Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	735.07500	16.37	0.0004
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test Control_vs_Spring

Results


Test Control_vs_Spring Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	185.00833	4.12	0.0532
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test Spring_vs_Fall

Results


Test Spring_vs_Fall Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	228.16667	5.08	0.0332
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test SpringSulphur

Results


Test SpringSulphur Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	2	16.30836	0.36	0.6991
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test FallSulphur

Results


Test FallSulphur Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	2	96.81003	2.16	0.1369
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test Fall300_vs_Spring300

Results


Test Fall300_vs_Spring300 Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	105.12500	2.34	0.1386
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test Fall600_vs_Spring600

Results


Test Fall600_vs_Spring600 Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	15.09751	0.34	0.5673
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Custom tests with proc reg

The REG Procedure

Model: MODEL1

Test Fall1200_vs_Spring1200

Results


Test Fall1200_vs_Spring1200 Results for Dependent Variable infection
Source	DF	Mean Square	F Value	Pr > F
Numerator	1	144.58501	3.22	0.0849
Denominator	25	44.91524

Scab Disease Data based on Cochran and Cox (1958)

Using proc glm -- NOT basic

The GLM Procedure

The GLM Procedure

Data

Class Levels


Class Level Information
Class	Levels	Values
condition	7	Control Spring300 Spring600 Spring1200 Fall300 Fall600 Fall1200

Number of Observations


Number of Observations Read	32
Number of Observations Used	32

Scab Disease Data based on Cochran and Cox (1958)

Using proc glm -- NOT basic

The GLM Procedure

Dependent Variable: infection Ave percent surface covered

Analysis of Variance

infection

Overall ANOVA


Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	6	972.413850	162.068975	3.61	0.0103
Error	25	1122.880900	44.915236
Corrected Total	31	2095.294750

Fit Statistics


R-Square	Coeff Var	Root MSE	infection Mean
0.464094	42.80644	6.701883	15.65625

Type I Model ANOVA


Source	DF	Type I SS	Mean Square	F Value	Pr > F
condition	6	972.4138500	162.0689750	3.61	0.0103

Type III Model ANOVA


Source	DF	Type III SS	Mean Square	F Value	Pr > F
condition	6	972.4138500	162.0689750	3.61	0.0103

Box Plot

Fit Plot for Ave percent surface covered by condition

Scab Disease Data based on Cochran and Cox (1958)

Using proc glm -- NOT basic

The GLM Procedure

Least Squares Means

Least Squares Means

condition

infection

LSMeans


condition	infection LSMEAN	LSMEAN Number
Control	22.6250000	1
Spring300	16.7475000	2
Spring600	18.2500000	3
Spring1200	14.2525000	4
Fall300	9.4975000	5
Fall600	15.5025000	6
Fall1200	5.7500000	7

Difference Matrix


Least Squares Means for Effect condition t for H0: LSMean(i)=LSMean(j) / Pr > \|t\| Dependent Variable: infection
i/j	1	2	3	4	5	6	7
1		1.432122 0.1645	1.066021 0.2966	2.040059 0.0520	3.198671 0.0037	1.735481 0.0950	4.111794 0.0004
2	-1.43212 0.1645		-0.31705 0.7538	0.526488 0.6032	1.529876 0.1386	0.262717 0.7949	2.320663 0.0288
3	-1.06602 0.2966	0.317054 0.7538		0.843542 0.4069	1.846929 0.0766	0.57977 0.5673	2.637717 0.0142
4	-2.04006 0.0520	-0.52649 0.6032	-0.84354 0.4069		1.003387 0.3253	-0.26377 0.7941	1.794175 0.0849
5	-3.19867 0.0037	-1.52988 0.1386	-1.84693 0.0766	-1.00339 0.3253		-1.26716 0.2168	0.790788 0.4365
6	-1.73548 0.0950	-0.26272 0.7949	-0.57977 0.5673	0.263772 0.7941	1.267159 0.2168		2.057947 0.0502
7	-4.11179 0.0004	-2.32066 0.0288	-2.63772 0.0142	-1.79417 0.0849	-0.79079 0.4365	-2.05795 0.0502

condition Mean Plot

Plot of infection least-squares means for condition.

condition Diffogram

Plot of all pairwise infection least-squares means differences for condition at significance level 0.05.

Note:To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used.

Scab Disease Data based on Cochran and Cox (1958)

Using proc glm -- NOT basic

The GLM Procedure

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

Least Squares Means

condition

infection

LSMeans


condition	infection LSMEAN	LSMEAN Number
Control	22.6250000	1
Spring300	16.7475000	2
Spring600	18.2500000	3
Spring1200	14.2525000	4
Fall300	9.4975000	5
Fall600	15.5025000	6
Fall1200	5.7500000	7

Difference Matrix


Least Squares Means for Effect condition t for H0: LSMean(i)=LSMean(j) / Pr > \|t\| Dependent Variable: infection
i/j	1	2	3	4	5	6	7
1		1.432122 0.7798	1.066021 0.9322	2.040059 0.4162	3.198671 0.0502	1.735481 0.6002	4.111794 0.0060
2	-1.43212 0.7798		-0.31705 0.9999	0.526488 0.9982	1.529876 0.7250	0.262717 1.0000	2.320663 0.2735
3	-1.06602 0.9322	0.317054 0.9999		0.843542 0.9776	1.846929 0.5311	0.57977 0.9969	2.637717 0.1571
4	-2.04006 0.4162	-0.52649 0.9982	-0.84354 0.9776		1.003387 0.9485	-0.26377 1.0000	1.794175 0.5637
5	-3.19867 0.0502	-1.52988 0.7250	-1.84693 0.5311	-1.00339 0.9485		-1.26716 0.8601	0.790788 0.9838
6	-1.73548 0.6002	-0.26272 1.0000	-0.57977 0.9969	0.263772 1.0000	1.267159 0.8601		2.057947 0.4061
7	-4.11179 0.0060	-2.32066 0.2735	-2.63772 0.1571	-1.79417 0.5637	-0.79079 0.9838	-2.05795 0.4061

condition Mean Plot

Plot of infection least-squares means for condition.

condition Diffogram

Plot of all pairwise infection least-squares means differences for condition with Tukey-Kramer adjustment at significance level 0.05.

Scab Disease Data based on Cochran and Cox (1958)

Using proc glm -- NOT basic

The GLM Procedure

Least Squares Means

Adjustment for Multiple Comparisons: Bonferroni

Least Squares Means

condition

infection

LSMeans


condition	infection LSMEAN	LSMEAN Number
Control	22.6250000	1
Spring300	16.7475000	2
Spring600	18.2500000	3
Spring1200	14.2525000	4
Fall300	9.4975000	5
Fall600	15.5025000	6
Fall1200	5.7500000	7

Difference Matrix


Least Squares Means for Effect condition t for H0: LSMean(i)=LSMean(j) / Pr > \|t\| Dependent Variable: infection
i/j	1	2	3	4	5	6	7
1		1.432122 1.0000	1.066021 1.0000	2.040059 1.0000	3.198671 0.0783	1.735481 1.0000	4.111794 0.0078
2	-1.43212 1.0000		-0.31705 1.0000	0.526488 1.0000	1.529876 1.0000	0.262717 1.0000	2.320663 0.6038
3	-1.06602 1.0000	0.317054 1.0000		0.843542 1.0000	1.846929 1.0000	0.57977 1.0000	2.637717 0.2972
4	-2.04006 1.0000	-0.52649 1.0000	-0.84354 1.0000		1.003387 1.0000	-0.26377 1.0000	1.794175 1.0000
5	-3.19867 0.0783	-1.52988 1.0000	-1.84693 1.0000	-1.00339 1.0000		-1.26716 1.0000	0.790788 1.0000
6	-1.73548 1.0000	-0.26272 1.0000	-0.57977 1.0000	0.263772 1.0000	1.267159 1.0000		2.057947 1.0000
7	-4.11179 0.0078	-2.32066 0.6038	-2.63772 0.2972	-1.79417 1.0000	-0.79079 1.0000	-2.05795 1.0000

condition Mean Plot

Plot of infection least-squares means for condition.

condition Diffogram

Plot of all pairwise infection least-squares means differences for condition with Bonferroni adjustment at significance level 0.05.

Scab Disease Data based on Cochran and Cox (1958)

Using proc glm -- NOT basic

The GLM Procedure

Least Squares Means

Adjustment for Multiple Comparisons: Scheffe

Least Squares Means

condition

infection

LSMeans


condition	infection LSMEAN	LSMEAN Number
Control	22.6250000	1
Spring300	16.7475000	2
Spring600	18.2500000	3
Spring1200	14.2525000	4
Fall300	9.4975000	5
Fall600	15.5025000	6
Fall1200	5.7500000	7

Difference Matrix


Least Squares Means for Effect condition t for H0: LSMean(i)=LSMean(j) / Pr > \|t\| Dependent Variable: infection
i/j	1	2	3	4	5	6	7
1		1.432122 0.9080	1.066021 0.9770	2.040059 0.6569	3.198671 0.1613	1.735481 0.8008	4.111794 0.0310
2	-1.43212 0.9080		-0.31705 1.0000	0.526488 0.9995	1.529876 0.8783	0.262717 1.0000	2.320663 0.5120
3	-1.06602 0.9770	0.317054 1.0000		0.843542 0.9932	1.846929 0.7514	0.57977 0.9992	2.637717 0.3587
4	-2.04006 0.6569	-0.52649 0.9995	-0.84354 0.9932		1.003387 0.9831	-0.26377 1.0000	1.794175 0.7753
5	-3.19867 0.1613	-1.52988 0.8783	-1.84693 0.7514	-1.00339 0.9831		-1.26716 0.9469	0.790788 0.9952
6	-1.73548 0.8008	-0.26272 1.0000	-0.57977 0.9992	0.263772 1.0000	1.267159 0.9469		2.057947 0.6478
7	-4.11179 0.0310	-2.32066 0.5120	-2.63772 0.3587	-1.79417 0.7753	-0.79079 0.9952	-2.05795 0.6478

condition Mean Plot

Plot of infection least-squares means for condition.

condition Diffogram

Plot of all pairwise infection least-squares means differences for condition with Scheffe adjustment at significance level 0.05.

Scab Disease Data based on Cochran and Cox (1958)

Using proc glm -- NOT basic

The GLM Procedure

Dependent Variable: infection Ave percent surface covered

Analysis of Variance

infection

Contrasts


Contrast	DF	Contrast SS	Mean Square	F Value	Pr > F
1. Overall test	6	972.4138500	162.0689750	3.61	0.0103
4. Av. of Fall vs. Control	1	735.0750000	735.0750000	16.37	0.0004
5. Av. of Spring vs. Control	1	185.0083333	185.0083333	4.12	0.0532
6. Fall vs. Spring	1	228.1666667	228.1666667	5.08	0.0332
7. Spring Amount	2	32.6167167	16.3083583	0.36	0.6991
8. Fall Amount	2	193.6200500	96.8100250	2.16	0.1369
9a. Spr vs. Fall for 300 lbs.	1	105.1250000	105.1250000	2.34	0.1386
9b. Spr vs. Fall for 600 lbs.	1	15.0975125	15.0975125	0.34	0.5673
9c. Spr vs. Fall, 1200 lbs	1	144.5850125	144.5850125	3.22	0.0849

Estimates


Parameter	Estimate	Standard Error	t Value	Pr > \|t\|	95% Confidence Limits
Control vs. Fall 1200	16.8750000	4.10404843	4.11	0.0004	8.4225540	25.3274460
Control vs. Mean of Fall	12.3750000	3.05897709	4.05	0.0004	6.0749188	18.6750812

Scab Disease Data based on Cochran and Cox (1958)

Critical value for all possible 1-df Scheffe F-tests

The IML Procedure

critval


critval
2.49041

ScheffeCritval


ScheffeCritval
14.94246

Scab Disease Data based on Cochran and Cox (1958)

Table of Scheffe critical values for COLLECTIONS of contrasts

The IML Procedure

numdf_dendf_alpha

Initial test has

6

and

25

degrees of freedom.

Using significance level alpha =

0.05

S_table

Number of Contrasts in followup F-test	Scheffe Critical Value
1	14.94246
2	7.4712301
3	4.98082
4	3.735615
5	2.988492
6	2.49041

Scab Disease Data based on Cochran and Cox (1958)

Test differences among treatments excluding control

Using contrasts of all means (traditional)

The GLM Procedure

The GLM Procedure

Data

Class Levels


Class Level Information
Class	Levels	Values
condition	7	Control Spring300 Spring600 Spring1200 Fall300 Fall600 Fall1200

Number of Observations


Number of Observations Read	32
Number of Observations Used	32

Scab Disease Data based on Cochran and Cox (1958)

Test differences among treatments excluding control

Using contrasts of all means (traditional)

The GLM Procedure

Dependent Variable: infection Ave percent surface covered

Analysis of Variance

infection

Overall ANOVA


Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	6	972.413850	162.068975	3.61	0.0103
Error	25	1122.880900	44.915236
Corrected Total	31	2095.294750

Fit Statistics


R-Square	Coeff Var	Root MSE	infection Mean
0.464094	42.80644	6.701883	15.65625

Type I Model ANOVA


Source	DF	Type I SS	Mean Square	F Value	Pr > F
condition	6	972.4138500	162.0689750	3.61	0.0103

Type III Model ANOVA


Source	DF	Type III SS	Mean Square	F Value	Pr > F
condition	6	972.4138500	162.0689750	3.61	0.0103

Contrasts


Contrast	DF	Contrast SS	Mean Square	F Value	Pr > F
Differences excluding control	5	454.4034333	90.8806867	2.02	0.1099

Box Plot

Fit Plot for Ave percent surface covered by condition

Scab Disease Data based on Cochran and Cox (1958)

Test differences among treatments excluding control

Subset the data by excluding control

The GLM Procedure

The GLM Procedure

Data

Class Levels


Class Level Information
Class	Levels	Values
condition	6	Spring300 Spring600 Spring1200 Fall300 Fall600 Fall1200

Number of Observations


Number of Observations Read	24
Number of Observations Used	24

Scab Disease Data based on Cochran and Cox (1958)

Test differences among treatments excluding control

Subset the data by excluding control

The GLM Procedure

Dependent Variable: infection Ave percent surface covered

Analysis of Variance

infection

Overall ANOVA


Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	5	454.403433	90.880687	2.58	0.0625
Error	18	633.212100	35.178450
Corrected Total	23	1087.615533

Fit Statistics


R-Square	Coeff Var	Root MSE	infection Mean
0.417798	44.48357	5.931142	13.33333

Type I Model ANOVA


Source	DF	Type I SS	Mean Square	F Value	Pr > F
condition	5	454.4034333	90.8806867	2.58	0.0625

Type III Model ANOVA


Source	DF	Type III SS	Mean Square	F Value	Pr > F
condition	5	454.4034333	90.8806867	2.58	0.0625

Box Plot

Fit Plot for Ave percent surface covered by condition