Results: potato.sas

Rotten Potatoes: Factorial ANOVA several different ways

First, illustrate a 2-factor ANOVA

The FREQ Procedure

The FREQ Procedure

Table 1 of bact * oxygen

Cross-Tabular Freq Table

Frequency
Table 1 of bact by oxygen
Controlling for temp=10 Degrees
bact(Bacteria Type) oxygen(Oxygen level)
2 percent 6 percent 10% Total
1
3
3
3
9
2
3
3
3
9
3
3
3
3
9
Total
9
9
9
27

Table 2 of bact * oxygen

Cross-Tabular Freq Table

Frequency
Table 2 of bact by oxygen
Controlling for temp=16 Degrees
bact(Bacteria Type) oxygen(Oxygen level)
2 percent 6 percent 10% Total
1
3
3
3
9
2
3
3
3
9
3
3
3
3
9
Total
9
9
9
27

Rotten Potatoes: Factorial ANOVA several different ways

First, illustrate a 2-factor ANOVA

The MEANS Procedure

The MEANS Procedure

Summary statistics

Analysis Variable : rot
Bacteria Type Storage Temperature N Obs N Mean Std Dev Minimum Maximum
1 10 Degrees 9 9 3.5555556 4.2752518 0 9.0000000
  16 Degrees 9 9 7.0000000 3.5355339 0 10.0000000
2 10 Degrees 9 9 4.7777778 3.1135903 0 10.0000000
  16 Degrees 9 9 13.5555556 6.3267510 3.0000000 23.0000000
3 10 Degrees 9 9 8.0000000 4.5552168 2.0000000 15.0000000
  16 Degrees 9 9 19.5555556 5.5251948 8.0000000 26.0000000

Rotten Potatoes: Factorial ANOVA several different ways

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

Standard 2-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

Number of Observations

Number of Observations Read 54
Number of Observations Used 54

Rotten Potatoes: Factorial ANOVA several different ways

First, illustrate a 2-factor ANOVA

Standard 2-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 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

First, illustrate a 2-factor ANOVA

Standard 2-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

First, illustrate a 2-factor ANOVA

Proportion of remaining variation

The IML Procedure

Temperature_Bacteria_Temp_by_Ba_

Temperature Bacteria Temp_by_Bact
0.4214605 0.3589744 0.1265656

Rotten Potatoes: Factorial ANOVA several different ways

First, illustrate a 2-factor ANOVA

Standard 2-way ANOVA with proc glm AGAIN

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

First, illustrate a 2-factor ANOVA

Standard 2-way ANOVA with proc glm AGAIN

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

First, illustrate a 2-factor ANOVA

Standard 2-way ANOVA with proc glm AGAIN

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

First, illustrate a 2-factor ANOVA

Look at an ODS output table

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

First, illustrate a 2-factor ANOVA

Automated proportion 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
0.4214847 0.3589581 0.1161201

Rotten Potatoes: Factorial ANOVA several different ways

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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 5 1652.81481 330.56296 15.05 <.0001
Error 48 1054.22222 21.96296    
Corrected Total 53 2707.03704      

Fit Statistics

Root MSE 4.68647 R-Square 0.6106
Dependent Mean 9.40741 Adj R-Sq 0.5700
Coeff Var 49.81676    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept 1 9.40741 0.63775 14.75 <.0001
b1 1 -4.12963 0.90191 -4.58 <.0001
b2 1 -0.24074 0.90191 -0.27 0.7907
t 1 -3.96296 0.63775 -6.21 <.0001
tb1 1 2.24074 0.90191 2.48 0.0165
tb2 1 -0.42593 0.90191 -0.47 0.6389

Rotten Potatoes: Factorial ANOVA several different ways

First, illustrate a 2-factor ANOVA

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 38.61 <.0001
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

First, illustrate a 2-factor ANOVA

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 14.84 <.0001
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

First, illustrate a 2-factor ANOVA

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 3.48 0.0387
Denominator 48 21.96296    

Rotten Potatoes: Factorial ANOVA several different ways

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

First, illustrate a 2-factor ANOVA

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

Prediction of Performance in First-year Calculus

An unbalanced example: The math data

The FREQ Procedure

The FREQ Procedure

Table sex * course2

Cross-Tabular Freq Table

Frequency
Row Pct
Table of sex by course2
sex course2
Catch-up Mainstrm Elite Total
Female
28
11.97
198
84.62
8
3.42
234
 
Male
28
12.17
173
75.22
29
12.61
230
 
Total
56
371
37
464
Frequency Missing = 115

Statistics for Table of sex by course2

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 2 13.5701 0.0011
Likelihood Ratio Chi-Square 2 14.3106 0.0008
Mantel-Haenszel Chi-Square 1 4.6978 0.0302
Phi Coefficient   0.1710  
Contingency Coefficient   0.1686  
Cramer's V   0.1710  

Effective Sample Size = 464
Frequency Missing = 115

WARNING: 20% of the data are missing.

Prediction of Performance in First-year Calculus

An unbalanced example: The math data

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
course2 3 Catch-up Elite Mainstrm
sex 2 Female Male

Number of Observations

Number of Observations Read 579
Number of Observations Used 379

Prediction of Performance in First-year Calculus

An unbalanced example: The math data

The GLM Procedure

Dependent Variable: hscalc HS Calculus

Analysis of Variance

hscalc

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 5 5697.29718 1139.45944 8.12 <.0001
Error 373 52354.82947 140.36147    
Corrected Total 378 58052.12665      

Fit Statistics

R-Square Coeff Var Root MSE hscalc Mean
0.098141 15.57088 11.84742 76.08707

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
sex 1 243.298636 243.298636 1.73 0.1888
course2 2 5162.094033 2581.047017 18.39 <.0001
course2*sex 2 291.904508 145.952254 1.04 0.3545

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
sex 1 12.769025 12.769025 0.09 0.7631
course2 2 4323.240672 2161.620336 15.40 <.0001
course2*sex 2 291.904508 145.952254 1.04 0.3545

Interaction Plot

Interaction Plot for HS Calculus by course2

Prediction of Performance in First-year Calculus

Oxygen by temperature by bactieria type

The TABULATE Procedure

Cross-tabular summary report

Table 1

Oxygen level 2 percent

Oxygen level 2 percent
  Bacteria Type All
1 2 3
Mean Mean Mean Mean
rot rot rot rot
Storage Temperature 7.67 5.00 9.00 7.22
10 Degrees
16 Degrees 8.67 14.33 23.00 15.33
All 8.17 9.67 16.00 11.28

Prediction of Performance in First-year Calculus

Oxygen by temperature by bactieria type

Oxygen level 6 percent

Oxygen level 6 percent
  Bacteria Type All
1 2 3
Mean Mean Mean Mean
rot rot rot rot
Storage Temperature 0.00 6.33 7.00 4.44
10 Degrees
16 Degrees 6.33 11.00 18.33 11.89
All 3.17 8.67 12.67 8.17

Prediction of Performance in First-year Calculus

Oxygen by temperature by bactieria type

Oxygen level 10%

Oxygen level 10%
  Bacteria Type All
1 2 3
Mean Mean Mean Mean
rot rot rot rot
Storage Temperature 3.00 3.00 8.00 4.67
10 Degrees
16 Degrees 6.00 15.33 17.33 12.89
All 4.50 9.17 12.67 8.78

Prediction of Performance in First-year Calculus

Oxygen by temperature by bactieria type

All

All
  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

Prediction of Performance in First-year Calculus

Three-way ANOVA with proc glm

The GLM Procedure

The GLM Procedure

Data

Class Levels

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

Number of Observations

Number of Observations Read 54
Number of Observations Used 54

Prediction of Performance in First-year Calculus

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
oxygen*temp 2 1.5925926 0.7962963 0.03 0.9666
oxygen*bact 4 30.0740741 7.5185185 0.32 0.8621
oxygen*bact*temp 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
oxygen*temp 2 1.5925926 0.7962963 0.03 0.9666
oxygen*bact 4 30.0740741 7.5185185 0.32 0.8621
oxygen*bact*temp 4 81.4074074 20.3518519 0.87 0.4921

Prediction of Performance in First-year Calculus

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