Painted Turtle Carapace Measurements

Turtle Sex Length Width Height
1 female 98 81 38
2 female 103 84 38
3 female 103 86 42
4 female 105 86 42
5 female 109 88 44
6 female 123 92 50
7 female 123 95 46
8 female 133 99 51
9 female 133 102 51
10 female 133 102 51
11 female 134 100 48
12 female 136 102 49
13 female 138 98 51
14 female 138 99 51
15 female 141 105 53
16 female 147 108 57
17 female 149 107 55
18 female 153 107 56
19 female 155 115 63
20 female 155 117 60
21 female 158 115 62
22 female 159 118 63
23 female 162 124 61
24 female 177 132 67
25 male 93 74 37
26 male 94 78 35
27 male 96 80 35
28 male 101 84 39
29 male 102 85 38
30 male 103 81 37
31 male 104 83 39
32 male 106 83 39
33 male 107 82 38
34 male 112 89 40
35 male 113 88 40
36 male 114 86 40
37 male 116 90 43
38 male 117 90 41
39 male 117 91 41
40 male 119 93 41
41 male 120 89 40
42 male 120 93 44
43 male 121 95 42
44 male 125 93 45
45 male 127 96 45
46 male 128 95 45
47 male 131 95 46
48 male 135 106 47


Painted Turtle Carapace Measurements

The CORR Procedure

Sex=female

3 Variables: Length Height Width

Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
Length 24 136.04167 21.24900 3265 98.00000 177.00000
Height 24 52.04167 8.04595 1249 38.00000 67.00000
Width 24 102.58333 13.10465 2462 81.00000 132.00000

Pearson Correlation Coefficients, N = 24
Prob > |r| under H0: Rho=0
  Length Height Width
Length 1.00000
 0.97067
<.0001		 0.97312
<.0001
Height 0.97067
<.0001		 1.00000
 0.96590
<.0001
Width 0.97312
<.0001		 0.96590
<.0001		 1.00000

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ScatterPlot1.gif

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SymMatrixPlot3.gif


Painted Turtle Carapace Measurements

The CORR Procedure

Sex=male

3 Variables: Length Height Width

Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
Length 24 113.37500 11.77991 2721 93.00000 135.00000
Height 24 40.70833 3.35545 977.00000 35.00000 47.00000
Width 24 88.29167 7.07401 2119 74.00000 106.00000

Pearson Correlation Coefficients, N = 24
Prob > |r| under H0: Rho=0
  Length Height Width
Length 1.00000
 0.94556
<.0001		 0.94978
<.0001
Height 0.94556
<.0001		 1.00000
 0.91226
<.0001
Width 0.94978
<.0001		 0.91226
<.0001		 1.00000

ScatterPlot4.gif

ScatterPlot5.gif

ScatterPlot6.gif

SymMatrixPlot7.gif


Scatter Width * Length = Height


Painted Turtle Carapace Measurements
Scatter Plot

The PRINCOMP Procedure

Observations 48
Variables 3

Simple Statistics
  Length Height Width
Mean 124.7083333 46.37500000 95.43750000
StD 20.4948964 8.36564657 12.67583771

Correlation Matrix
  Length Height Width
Length 1.0000 0.9629 0.9779
Height 0.9629 1.0000 0.9599
Width 0.9779 0.9599 1.0000

Eigenvalues of the Correlation Matrix
  Eigenvalue Difference Proportion Cumulative
1 2.93380962 2.88959700 0.9779 0.9779
2 0.04421262 0.02223485 0.0147 0.9927
3 0.02197777   0.0073 1.0000

Eigenvectors
  Prin1 Prin2 Prin3
Length 0.578741 -.350410 -.736391
Height 0.575152 0.815543 0.063947
Width 0.578151 -.460545 0.673527


Eigenvalue Plot

Principal Components Scores Matrix Plot

Principal Component Pattern

Principal Components Scores Plot: 1st vs 2nd

Principal Components Scores Plot: 1st vs 3rd

Principal Components Scores Plot: 1st vs 2nd


Plot of Prin2 * Prin1 = Sex


Painted Turtle Carapace Measurements
MANOVA

The GLM Procedure

Class Level Information
Class Levels Values
Sex 2 female male

Number of Observations Read 48
Number of Observations Used 48


Painted Turtle Carapace Measurements
MANOVA

The GLM Procedure
 
Dependent Variable: Length

Source DF Sum of Squares Mean Square F Value Pr > F
Model 1 6165.33333 6165.33333 20.89 <.0001
Error 46 13576.58333 295.14312    
Corrected Total 47 19741.91667      

R-Square Coeff Var Root MSE Length Mean
0.312297 13.77593 17.17973 124.7083

Source DF Type I SS Mean Square F Value Pr > F
Sex 1 6165.333333 6165.333333 20.89 <.0001

Source DF Type III SS Mean Square F Value Pr > F
Sex 1 6165.333333 6165.333333 20.89 <.0001

Box Plot


Painted Turtle Carapace Measurements
MANOVA

The GLM Procedure
 
Dependent Variable: Width

Source DF Sum of Squares Mean Square F Value Pr > F
Model 1 2451.020833 2451.020833 22.10 <.0001
Error 46 5100.791667 110.886775    
Corrected Total 47 7551.812500      

R-Square Coeff Var Root MSE Width Mean
0.324561 11.03369 10.53028 95.43750

Source DF Type I SS Mean Square F Value Pr > F
Sex 1 2451.020833 2451.020833 22.10 <.0001

Source DF Type III SS Mean Square F Value Pr > F
Sex 1 2451.020833 2451.020833 22.10 <.0001

Box Plot


Painted Turtle Carapace Measurements
MANOVA

The GLM Procedure
 
Dependent Variable: Height

Source DF Sum of Squares Mean Square F Value Pr > F
Model 1 1541.333333 1541.333333 40.56 <.0001
Error 46 1747.916667 37.998188    
Corrected Total 47 3289.250000      

R-Square Coeff Var Root MSE Height Mean
0.468597 13.29222 6.164267 46.37500

Source DF Type I SS Mean Square F Value Pr > F
Sex 1 1541.333333 1541.333333 40.56 <.0001

Source DF Type III SS Mean Square F Value Pr > F
Sex 1 1541.333333 1541.333333 40.56 <.0001

Box Plot


Painted Turtle Carapace Measurements
MANOVA

The GLM Procedure
Multivariate Analysis of Variance

E = Error SSCP Matrix
  Length Width Height
Length 13576.583333 8052.7916667 4676.5833333
Width 8052.7916667 5100.7916667 2840.4583333
Height 4676.5833333 2840.4583333 1747.9166667

Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r|
DF = 46 Length Width Height
Length 1.000000
 0.967681
<.0001		 0.960004
<.0001
Width 0.967681
<.0001		 1.000000
 0.951282
<.0001
Height 0.960004
<.0001		 0.951282
<.0001		 1.000000


Painted Turtle Carapace Measurements
MANOVA

The GLM Procedure
Multivariate Analysis of Variance

H = Type III SSCP Matrix for Sex
  Length Width Height
Length 6165.3333333 3887.3333333 3082.6666667
Width 3887.3333333 2451.0208333 1943.6666667
Height 3082.6666667 1943.6666667 1541.3333333

Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SSCP Matrix for Sex
E = Error SSCP Matrix
Characteristic Root Percent Characteristic Vector V'EV=1
Length Width Height
1.57351354 100.00 -0.01637687 -0.00819332 0.07503693
0.00000000 0.00 -0.03215493 0.05631978 -0.00671104
0.00000000 0.00 -0.01606589 -0.01362218 0.04930974

MANOVA Test Criteria and Exact F Statistics
for the Hypothesis of No Overall Sex Effect
H = Type III SSCP Matrix for Sex
E = Error SSCP Matrix

S=1 M=0.5 N=21
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.38857382 23.08 3 44 <.0001
Pillai's Trace 0.61142618 23.08 3 44 <.0001
Hotelling-Lawley Trace 1.57351354 23.08 3 44 <.0001
Roy's Greatest Root 1.57351354 23.08 3 44 <.0001


Painted Turtle Carapace Measurements
Discriminant Functions

Obs Hypothesis CharRoot Percent Length Width Height
1 Sex 1.57351354 100.00 -0.01637687 -0.00819332 0.07503693
2 Sex 0.00000000 0.00 -0.03215493 0.05631978 -0.00671104
3 Sex 0.00000000 0.00 -0.01606589 -0.01362218 0.04930974


Painted Turtle Carapace Measurements
Study Discriminant Function
Observations Ordered Along Discriminant Function

Turtle Score Sex Length Width Height
41 0.30705 male 120 89 40
40 0.36569 male 119 93 41
43 0.39159 male 121 95 42
27 0.39865 male 96 80 35
39 0.41483 male 117 91 41
38 0.42302 male 117 90 41
30 0.42589 male 103 81 37
33 0.42723 male 107 82 38
35 0.42988 male 113 88 40
36 0.42989 male 114 86 40
34 0.43806 male 112 89 40
48 0.44737 male 135 106 47
26 0.44779 male 94 78 35
2 0.47635 female 103 84 38
29 0.48453 male 102 85 38
46 0.50206 male 128 95 45
45 0.51024 male 127 96 45
32 0.51045 male 106 83 39
47 0.52796 male 131 95 46
31 0.54320 male 104 83 39
44 0.56758 male 125 93 45
42 0.57442 male 120 93 44
1 0.58281 female 98 81 38
28 0.58414 male 101 84 39
11 0.58794 female 134 100 48
37 0.58947 male 116 90 43
12 0.61384 female 136 102 49
25 0.64701 male 93 74 37
7 0.65898 female 123 95 46
4 0.72735 female 105 86 42
14 0.75574 female 138 99 51
3 0.76011 female 103 86 42
13 0.76393 female 138 98 51
5 0.79553 female 109 88 44
15 0.80752 female 141 105 53
17 0.81019 female 149 107 55
9 0.81304 female 133 102 51
10 0.81304 female 133 102 51
18 0.81972 female 153 107 56
8 0.83762 female 133 99 51
23 0.90823 female 162 124 61
6 0.98371 female 123 92 50
16 0.98483 female 147 108 57
20 1.00518 female 155 117 60
24 1.04725 female 177 132 67
21 1.12251 female 158 115 62
22 1.15659 female 159 118 63
19 1.24668 female 155 115 63


Painted Turtle Carapace Measurements
Study Discriminant Function
Correlations of Orignal Variables with Discriminant Function

The CORR Procedure

1 With Variables: Score
3 Variables: Length Width Height

Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
Score 48 0.65556 0.23400 31.46670 0.30705 1.24668
Length 48 124.70833 20.49490 5986 93.00000 177.00000
Width 48 95.43750 12.67584 4581 74.00000 132.00000
Height 48 46.37500 8.36565 2226 35.00000 67.00000

Pearson Correlation Coefficients, N = 48
Prob > |r| under H0: Rho=0
  Length Width Height
Score 0.71468
<.0001		 0.72858
<.0001		 0.87544
<.0001


Plot of Score * Turtle = Sex


VBAR chart of Score