Results: potato2018.sas

Rotten Potatoes: Factorial ANOVA several different ways

The FREQ Procedure

The Freq Procedure

Table 1 of temp * bact

Cross-Tabular Freq Table

Frequency
Table 1 of temp by bact
Controlling for oxygen=2%
temp(Storage Temperature) bact(Bacteria Type)
1 2 3 Total
10 Degrees
3
3
3
9
16 Degrees
3
3
3
9
Total
6
6
6
18

Table 2 of temp * bact

Cross-Tabular Freq Table

Frequency
Table 2 of temp by bact
Controlling for oxygen=6%
temp(Storage Temperature) bact(Bacteria Type)
1 2 3 Total
10 Degrees
3
3
3
9
16 Degrees
3
3
3
9
Total
6
6
6
18

Table 3 of temp * bact

Cross-Tabular Freq Table

Frequency
Table 3 of temp by bact
Controlling for oxygen=10%
temp(Storage Temperature) bact(Bacteria Type)
1 2 3 Total
10 Degrees
3
3
3
9
16 Degrees
3
3
3
9
Total
6
6
6
18

Rotten Potatoes: Factorial ANOVA several different ways

Three-way ANOVA with proc glm

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
bact 3 1 2 3
temp 2 10 Degrees 16 Degrees
oxygen 3 10% 2% 6%

Number of Observations

Number of Observations Read 54
Number of Observations Used 54

Rotten Potatoes: Factorial ANOVA several different ways

Three-way ANOVA with proc glm

The GLM Procedure

 

Dependent Variable: rot

Analysis of Variance

rot

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 17 1863.703704 109.629630 4.68 <.0001
Error 36 843.333333 23.425926    
Corrected Total 53 2707.037037      

Fit Statistics

R-Square Coeff Var Root MSE rot Mean
0.688466 51.44918 4.840034 9.407407

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
temp 1 848.0740741 848.0740741 36.20 <.0001
bact 2 651.8148148 325.9074074 13.91 <.0001
bact*temp 2 152.9259259 76.4629630 3.26 0.0498
oxygen 2 97.8148148 48.9074074 2.09 0.1387
temp*oxygen 2 1.5925926 0.7962963 0.03 0.9666
bact*oxygen 4 30.0740741 7.5185185 0.32 0.8621
bact*temp*oxygen 4 81.4074074 20.3518519 0.87 0.4921

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
temp 1 848.0740741 848.0740741 36.20 <.0001
bact 2 651.8148148 325.9074074 13.91 <.0001
bact*temp 2 152.9259259 76.4629630 3.26 0.0498
oxygen 2 97.8148148 48.9074074 2.09 0.1387
temp*oxygen 2 1.5925926 0.7962963 0.03 0.9666
bact*oxygen 4 30.0740741 7.5185185 0.32 0.8621
bact*temp*oxygen 4 81.4074074 20.3518519 0.87 0.4921

Rotten Potatoes: Factorial ANOVA several different ways

Three-way ANOVA with proc glm

The GLM Procedure

Means

temp

rot

Distribution of rot by temp

Distribution of rot by temp

Means

Level of
temp		 N rot
Mean Std Dev
10 Degrees 27 5.4444444 4.31752541
16 Degrees 27 13.3703704 7.27031979

bact

rot

Distribution of rot by bact

Distribution of rot by bact

Means

Level of
bact		 N rot
Mean Std Dev
1 18 5.2777778 4.19811660
2 18 9.1666667 6.61771242
3 18 13.7777778 7.71214135

bact*temp

rot

Distribution of rot by bact*temp

Distribution of rot by bact*temp

Means

Level of
bact		 Level of
temp		 N rot
Mean Std Dev
1 10 Degrees 9 3.5555556 4.27525178
1 16 Degrees 9 7.0000000 3.53553391
2 10 Degrees 9 4.7777778 3.11359028
2 16 Degrees 9 13.5555556 6.32675097
3 10 Degrees 9 8.0000000 4.55521679
3 16 Degrees 9 19.5555556 5.52519482

Rotten Potatoes: Factorial ANOVA several different ways

Three-way ANOVA with proc reg and effect coding

The REG Procedure

Model: MODEL1

Dependent Variable: rot

The Reg Procedure

MODEL1

Fit

rot

Number of Observations

Number of Observations Read 54
Number of Observations Used 54

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 17 1863.70370 109.62963 4.68 <.0001
Error 36 843.33333 23.42593    
Corrected Total 53 2707.03704      

Fit Statistics

Root MSE 4.84003 R-Square 0.6885
Dependent Mean 9.40741 Adj R-Sq 0.5414
Coeff Var 51.44918    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept 1 9.40741 0.65865 14.28 <.0001
b1 1 -4.12963 0.93146 -4.43 <.0001
b2 1 -0.24074 0.93146 -0.26 0.7975
t 1 -3.96296 0.65865 -6.02 <.0001
ox1 1 1.87037 0.93146 2.01 0.0522
ox2 1 -1.24074 0.93146 -1.33 0.1912
tb1 1 2.24074 0.93146 2.41 0.0214
tb2 1 -0.42593 0.93146 -0.46 0.6502
tox1 1 -0.09259 0.93146 -0.10 0.9214
tox2 1 0.24074 0.93146 0.26 0.7975
b1ox1 1 1.01852 1.31729 0.77 0.4445
b1ox2 1 -0.87037 1.31729 -0.66 0.5130
b2ox1 1 -1.37037 1.31729 -1.04 0.3051
b2ox2 1 0.74074 1.31729 0.56 0.5774
tb1ox1 1 1.31481 1.31729 1.00 0.3249
tb1ox2 1 -1.68519 1.31729 -1.28 0.2090
tb2ox1 1 -0.18519 1.31729 -0.14 0.8890
tb2ox2 1 1.81481 1.31729 1.38 0.1768

Rotten Potatoes: Factorial ANOVA several different ways

Three-way ANOVA with proc reg and effect coding

The REG Procedure

Model: MODEL1

Test Temperature

Results

Test Temperature Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 848.07407 36.20 <.0001
Denominator 36 23.42593    

Rotten Potatoes: Factorial ANOVA several different ways

Three-way ANOVA with proc reg and effect coding

The REG Procedure

Model: MODEL1

Test Bacteria

Results

Test Bacteria Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 2 325.90741 13.91 <.0001
Denominator 36 23.42593    

Rotten Potatoes: Factorial ANOVA several different ways

Three-way ANOVA with proc reg and effect coding

The REG Procedure

Model: MODEL1

Test Bact_by_Temp

Results

Test Bact_by_Temp Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 2 76.46296 3.26 0.0498
Denominator 36 23.42593    

Rotten Potatoes: Factorial ANOVA several different ways

Three-way ANOVA with proc reg and effect coding

The REG Procedure

Model: MODEL1

Test Oxygen

Results

Test Oxygen Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 2 48.90741 2.09 0.1387
Denominator 36 23.42593    

Rotten Potatoes: Factorial ANOVA several different ways

Three-way ANOVA with proc reg and effect coding

The REG Procedure

Model: MODEL1

Test Temp_by_Oxygen

Results

Test Temp_by_Oxygen Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 2 0.79630 0.03 0.9666
Denominator 36 23.42593    

Rotten Potatoes: Factorial ANOVA several different ways

Three-way ANOVA with proc reg and effect coding

The REG Procedure

Model: MODEL1

Test Bact_by_Oxygen

Results

Test Bact_by_Oxygen Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 4 7.51852 0.32 0.8621
Denominator 36 23.42593    

Rotten Potatoes: Factorial ANOVA several different ways

Three-way ANOVA with proc reg and effect coding

The REG Procedure

Model: MODEL1

Test Bact_by_Temp_by_Oxygen

Results

Test Bact_by_Temp_by_Oxygen Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 4 20.35185 0.87 0.4921
Denominator 36 23.42593    

Rotten Potatoes: Factorial ANOVA several different ways

Three-way ANOVA with proc reg and effect coding

The REG Procedure

Model: MODEL1

Test Conditional_Indep

Results

Test Conditional_Indep Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 12 17.57407 0.75 0.6945
Denominator 36 23.42593    

Rotten Potatoes: Factorial ANOVA several different ways

Two-way table of means from proc tabulate

The Tabulate Procedure

Cross-tabular summary report

Table 1

  Bacteria Type All
1 2 3
Mean Mean Mean Mean
rot rot rot rot
Storage Temperature 3.56 4.78 8.00 5.44
10 Degrees
16 Degrees 7.00 13.56 19.56 13.37
All 5.28 9.17 13.78 9.41

Rotten Potatoes: Factorial ANOVA several different ways

Two-way ANOVA, ignoring oxygen level

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
bact 3 1 2 3
temp 2 10 Degrees 16 Degrees

Number of Observations

Number of Observations Read 54
Number of Observations Used 54

Rotten Potatoes: Factorial ANOVA several different ways

Two-way ANOVA, ignoring oxygen level

The GLM Procedure

 

Dependent Variable: rot

Analysis of Variance

rot

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 5 1652.814815 330.562963 15.05 <.0001
Error 48 1054.222222 21.962963    
Corrected Total 53 2707.037037      

Fit Statistics

R-Square Coeff Var Root MSE rot Mean
0.610562 49.81676 4.686466 9.407407

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
temp 1 848.0740741 848.0740741 38.61 <.0001
bact 2 651.8148148 325.9074074 14.84 <.0001
bact*temp 2 152.9259259 76.4629630 3.48 0.0387

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
temp 1 848.0740741 848.0740741 38.61 <.0001
bact 2 651.8148148 325.9074074 14.84 <.0001
bact*temp 2 152.9259259 76.4629630 3.48 0.0387

Interaction Plot

Interaction Plot for rot by Bacteria Type

Rotten Potatoes: Factorial ANOVA several different ways

Two-way ANOVA, ignoring oxygen level

The GLM Procedure

Least Squares Means

Adjustment for Multiple Comparisons: Tukey

Least Squares Means

bact

rot

LSMeans

bact rot LSMEAN LSMEAN Number
1 5.2777778 1
2 9.1666667 2
3 13.7777778 3

Difference Matrix

Least Squares Means for Effect bact
t for H0: LSMean(i)=LSMean(j) / Pr > |t|

Dependent Variable: rot
i/j 1 2 3
1
 
 
-2.48944
0.0424
-5.4412
<.0001
2
2.489438
0.0424
 
 
-2.95176
0.0133
3
5.4412
<.0001
2.951762
0.0133
 
 

Rotten Potatoes: Factorial ANOVA several different ways

Two-way ANOVA, ignoring oxygen level

The GLM Procedure

Least Squares Means

Adjustment for Multiple Comparisons: Bonferroni

Least Squares Means

bact

rot

LSMeans

bact rot LSMEAN LSMEAN Number
1 5.2777778 1
2 9.1666667 2
3 13.7777778 3

Difference Matrix

Least Squares Means for Effect bact
t for H0: LSMean(i)=LSMean(j) / Pr > |t|

Dependent Variable: rot
i/j 1 2 3
1
 
 
-2.48944
0.0489
-5.4412
<.0001
2
2.489438
0.0489
 
 
-2.95176
0.0146
3
5.4412
<.0001
2.951762
0.0146
 
 

Rotten Potatoes: Factorial ANOVA several different ways

Look at the ODS output tables

The Print Procedure

Data Set WORK.OVERALL

Obs Dependent Source DF SS MS FValue ProbF
1 rot Model 5 1652.814815 330.562963 15.05 <.0001
2 rot Error 48 1054.222222 21.962963 _ _
3 rot Corrected Total 53 2707.037037 _ _ _

Rotten Potatoes: Factorial ANOVA several different ways

Look at the ODS output tables

The Print Procedure

Data Set WORK.TWOWAY

Obs Dependent HypothesisType Source DF SS MS FValue ProbF
1 rot 1 temp 1 848.0740741 848.0740741 38.61 <.0001
2 rot 1 bact 2 651.8148148 325.9074074 14.84 <.0001
3 rot 1 bact*temp 2 152.9259259 76.4629630 3.48 0.0387
4 rot 3 temp 1 848.0740741 848.0740741 38.61 <.0001
5 rot 3 bact 2 651.8148148 325.9074074 14.84 <.0001
6 rot 3 bact*temp 2 152.9259259 76.4629630 3.48 0.0387

Rotten Potatoes: Factorial ANOVA several different ways

Proportions of remaining variation

The IML Procedure

_LIT1001

Take a look at the matrices

anova1

anova1
5 1652.8148 330.56296 15.050927 7.0035E-9
48 1054.2222 21.962963 _ _
53 2707.037 _ _ _

anova2

anova2
1 1 848.07407 848.07407 38.613828 1.1802E-7
1 2 651.81481 325.90741 14.838954 9.6084E-6
1 2 152.92593 76.462963 3.4814503 0.0387363
3 1 848.07407 848.07407 38.613828 1.1802E-7
3 2 651.81481 325.90741 14.838954 9.6084E-6
3 2 152.92593 76.462963 3.4814503 0.0387363

_LIT1002

Proportion of remaining variation

Temperature_Bacteria_Temp_by_Ba_

Temperature Bacteria Temp_by_Bact
0.445816 0.3820637 0.1266836

Rotten Potatoes: Factorial ANOVA several different ways

Using the proc reg test statement and cell means coding

The REG Procedure

Model: MODEL1

Dependent Variable: rot

The Reg Procedure

MODEL1

Fit

rot

Number of Observations

Number of Observations Read 54
Number of Observations Used 54

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 6 6431.77778 1071.96296 48.81 <.0001
Error 48 1054.22222 21.96296    
Uncorrected Total 54 7486.00000      

Fit Statistics

Root MSE 4.68647 R-Square 0.8592
Dependent Mean 9.40741 Adj R-Sq 0.8416
Coeff Var 49.81676    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
mu11 1 3.55556 1.56216 2.28 0.0273
mu12 1 4.77778 1.56216 3.06 0.0036
mu13 1 8.00000 1.56216 5.12 <.0001
mu21 1 7.00000 1.56216 4.48 <.0001
mu22 1 13.55556 1.56216 8.68 <.0001
mu23 1 19.55556 1.56216 12.52 <.0001

Rotten Potatoes: Factorial ANOVA several different ways

Using the proc reg test statement and cell means coding

The REG Procedure

Model: MODEL1

Test Overall

Results

Test Overall Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 5 330.56296 15.05 <.0001
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Using the proc reg test statement and cell means coding

The REG Procedure

Model: MODEL1

Test Temperature

Results

Test Temperature Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 848.07407 38.61 <.0001
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Using the proc reg test statement and cell means coding

The REG Procedure

Model: MODEL1

Test Bacteria

Results

Test Bacteria Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 2 325.90741 14.84 <.0001
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Using the proc reg test statement and cell means coding

The REG Procedure

Model: MODEL1

Test Bact_by_Temp1

Results

Test Bact_by_Temp1 Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 2 76.46296 3.48 0.0387
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Using the proc reg test statement and cell means coding

The REG Procedure

Model: MODEL1

Test Bact_by_Temp2

Results

Test Bact_by_Temp2 Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 2 76.46296 3.48 0.0387
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
combo 6 11 12 13 21 22 23

Number of Observations

Number of Observations Read 54
Number of Observations Used 54

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

The GLM Procedure

 

Dependent Variable: rot

Analysis of Variance

rot

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 5 1652.814815 330.562963 15.05 <.0001
Error 48 1054.222222 21.962963    
Corrected Total 53 2707.037037      

Fit Statistics

R-Square Coeff Var Root MSE rot Mean
0.610562 49.81676 4.686466 9.407407

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
combo 5 1652.814815 330.562963 15.05 <.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
combo 5 1652.814815 330.562963 15.05 <.0001

Contrasts

Contrast DF Contrast SS Mean Square F Value Pr > F
Main Effect for Temperature 1 848.0740741 848.0740741 38.61 <.0001
Main Effect for Bacteria 2 651.8148148 325.9074074 14.84 <.0001
Temperature by Bacteria Interaction 2 152.9259259 76.4629630 3.48 0.0387

Box Plot

Fit Plot for rot by combo

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Dependent Variable: rot

The Reg Procedure

MODEL1

Fit

rot

Number of Observations

Number of Observations Read 54
Number of Observations Used 54

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 6 6431.77778 1071.96296 48.81 <.0001
Error 48 1054.22222 21.96296    
Uncorrected Total 54 7486.00000      

Fit Statistics

Root MSE 4.68647 R-Square 0.8592
Dependent Mean 9.40741 Adj R-Sq 0.8416
Coeff Var 49.81676    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
mu11 1 3.55556 1.56216 2.28 0.0273
mu12 1 4.77778 1.56216 3.06 0.0036
mu13 1 8.00000 1.56216 5.12 <.0001
mu21 1 7.00000 1.56216 4.48 <.0001
mu22 1 13.55556 1.56216 8.68 <.0001
mu23 1 19.55556 1.56216 12.52 <.0001

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test Bact1vs2

Results

Test Bact1vs2 Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 136.11111 6.20 0.0163
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test Bact1vs3

Results

Test Bact1vs3 Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 650.25000 29.61 <.0001
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test Bact2vs3

Results

Test Bact2vs3 Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 191.36111 8.71 0.0049
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test Temp_for_Bac1

Results

Test Temp_for_Bac1 Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 53.38889 2.43 0.1255
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test Temp_for_Bac2

Results

Test Temp_for_Bac2 Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 346.72222 15.79 0.0002
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test Temp_for_Bac3

Results

Test Temp_for_Bac3 Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 600.88889 27.36 <.0001
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test Bact_for_CoolTemp

Results

Test Bact_for_CoolTemp Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 2 47.44444 2.16 0.1264
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test Bact_for_WarmTemp

Results

Test Bact_for_WarmTemp Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 2 354.92593 16.16 <.0001
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test Bact1vs2_for_WarmTemp

Results

Test Bact1vs2_for_WarmTemp Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 193.38889 8.81 0.0047
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test Bact1vs3_for_WarmTemp

Results

Test Bact1vs3_for_WarmTemp Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 709.38889 32.30 <.0001
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test Bact2vs3_for_WarmTemp

Results

Test Bact2vs3_for_WarmTemp Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 162.00000 7.38 0.0092
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test TempEffectBact1_vs_2

Results

Test TempEffectBact1_vs_2 Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 64.00000 2.91 0.0943
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test TempEffectBact1_vs_3

Results

Test TempEffectBact1_vs_3 Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 148.02778 6.74 0.0125
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Further exploration using cell means coding

The REG Procedure

Model: MODEL1

Test TempEffectBact2_vs_3

Results

Test TempEffectBact2_vs_3 Results for Dependent Variable rot
Source DF Mean
Square		 F Value Pr > F
Numerator 1 17.36111 0.79 0.3784
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

Proc glm: Using contrasts on the combination variable

Table of critical values for all possible Scheffe tests

The IML Procedure

numdf_dendf_alpha

Initial test has 5 and 48 degrees of freedom. Using significance level alpha = 0.05

S_table

Number of Contrasts in followup test Scheffe Critical Value
1 12.042571
2 6.0212853
3 4.0141902
4 3.0106426
5 2.4085141