Results: scab1.sas

Scab Disease Data

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

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
Fall1200	4	4	5.7500000	2.8700639	2.0100000	8.4800000
Fall300	4	4	9.4975000	4.9333854	5.0800000	14.8000000
Fall600	4	4	15.5025000	3.7887586	11.1000000	20.2300000
Spring1200	4	4	14.2525000	4.8578896	8.1100000	19.8400000
Spring300	4	4	16.7475000	10.7824900	5.1300000	30.1200000
Spring600	4	4	18.2500000	4.9273996	11.4000000	22.7500000

Scab Disease Data

The GLM Procedure

Data

Class Levels


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

Number of Observations


Number of Observations Read	32
Number of Observations Used	32

Scab Disease Data

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

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
Fall1200	5.7500000	2
Fall300	9.4975000	3
Fall600	15.5025000	4
Spring1200	14.2525000	5
Spring300	16.7475000	6
Spring600	18.2500000	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		4.111794 0.0060	3.198671 0.0502	1.735481 0.6002	2.040059 0.4162	1.432122 0.7798	1.066021 0.9322
2	-4.11179 0.0060		-0.79079 0.9838	-2.05795 0.4061	-1.79417 0.5637	-2.32066 0.2735	-2.63772 0.1571
3	-3.19867 0.0502	0.790788 0.9838		-1.26716 0.8601	-1.00339 0.9485	-1.52988 0.7250	-1.84693 0.5311
4	-1.73548 0.6002	2.057947 0.4061	1.267159 0.8601		0.263772 1.0000	-0.26272 1.0000	-0.57977 0.9969
5	-2.04006 0.4162	1.794175 0.5637	1.003387 0.9485	-0.26377 1.0000		-0.52649 0.9982	-0.84354 0.9776
6	-1.43212 0.7798	2.320663 0.2735	1.529876 0.7250	0.262717 1.0000	0.526488 0.9982		-0.31705 0.9999
7	-1.06602 0.9322	2.637717 0.1571	1.846929 0.5311	0.57977 0.9969	0.843542 0.9776	0.317054 0.9999

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

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
Fall1200	5.7500000	2
Fall300	9.4975000	3
Fall600	15.5025000	4
Spring1200	14.2525000	5
Spring300	16.7475000	6
Spring600	18.2500000	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		4.111794 0.0078	3.198671 0.0783	1.735481 1.0000	2.040059 1.0000	1.432122 1.0000	1.066021 1.0000
2	-4.11179 0.0078		-0.79079 1.0000	-2.05795 1.0000	-1.79417 1.0000	-2.32066 0.6038	-2.63772 0.2972
3	-3.19867 0.0783	0.790788 1.0000		-1.26716 1.0000	-1.00339 1.0000	-1.52988 1.0000	-1.84693 1.0000
4	-1.73548 1.0000	2.057947 1.0000	1.267159 1.0000		0.263772 1.0000	-0.26272 1.0000	-0.57977 1.0000
5	-2.04006 1.0000	1.794175 1.0000	1.003387 1.0000	-0.26377 1.0000		-0.52649 1.0000	-0.84354 1.0000
6	-1.43212 1.0000	2.320663 0.6038	1.529876 1.0000	0.262717 1.0000	0.526488 1.0000		-0.31705 1.0000
7	-1.06602 1.0000	2.637717 0.2972	1.846929 1.0000	0.57977 1.0000	0.843542 1.0000	0.317054 1.0000

condition Mean Plot

condition Diffogram

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

Scab Disease Data

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
Fall1200	5.7500000	2
Fall300	9.4975000	3
Fall600	15.5025000	4
Spring1200	14.2525000	5
Spring300	16.7475000	6
Spring600	18.2500000	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		4.111794 0.0310	3.198671 0.1613	1.735481 0.8008	2.040059 0.6569	1.432122 0.9080	1.066021 0.9770
2	-4.11179 0.0310		-0.79079 0.9952	-2.05795 0.6478	-1.79417 0.7753	-2.32066 0.5120	-2.63772 0.3587
3	-3.19867 0.1613	0.790788 0.9952		-1.26716 0.9469	-1.00339 0.9831	-1.52988 0.8783	-1.84693 0.7514
4	-1.73548 0.8008	2.057947 0.6478	1.267159 0.9469		0.263772 1.0000	-0.26272 1.0000	-0.57977 0.9992
5	-2.04006 0.6569	1.794175 0.7753	1.003387 0.9831	-0.26377 1.0000		-0.52649 0.9995	-0.84354 0.9932
6	-1.43212 0.9080	2.320663 0.5120	1.529876 0.8783	0.262717 1.0000	0.526488 0.9995		-0.31705 1.0000
7	-1.06602 0.9770	2.637717 0.3587	1.846929 0.7514	0.57977 0.9992	0.843542 0.9932	0.317054 1.0000

condition Mean Plot

condition Diffogram

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

Scab Disease Data

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
Overall test for comparison	6	972.4138500	162.0689750	3.61	0.0103
Av. of Fall vs. Control	1	735.0750000	735.0750000	16.37	0.0004
Av. of Spring vs. Control	1	185.0083333	185.0083333	4.12	0.0532
Fall vs. Spring	1	228.1666667	228.1666667	5.08	0.0332
Spring Amount	2	32.6167167	16.3083583	0.36	0.6991
Fall Amount	2	193.6200500	96.8100250	2.16	0.1369
Spr vs. Fall for 300 lbs.	1	105.1250000	105.1250000	2.34	0.1386
Spr vs. Fall for 600 lbs.	1	15.0975125	15.0975125	0.34	0.5673
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

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

The IML Procedure

critval


critval
2.49041

ScheffeCritval


ScheffeCritval
14.94246

Scab Disease Data

Table of Scheffe critical values for COLLECTIONS of contrasts

The IML Procedure

numdf_dendf_alpha

Initial test has

and

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

Test differences among treatments excluding control

Using contrasts of all means (traditional)

The GLM Procedure

Data

Class Levels


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

Number of Observations


Number of Observations Read	32
Number of Observations Used	32

Scab Disease Data

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

Scab Disease Data

Test differences among treatments excluding control

Subset the data by excluding control

The GLM Procedure

Data

Class Levels


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

Number of Observations


Number of Observations Read	24
Number of Observations Used	24

Scab Disease Data

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