Results: mathlogreg2.sas

Gender, Ethnicity and Math performance

Predict Passing the course (Y-N) with Logistic Regression

Course and HS variables

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.EXPLORE  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 373

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 No 141
2 Yes 232

Probability modeled is passed='Yes'.

Note:206 observations were deleted due to missing values for the response or explanatory variables.

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 496.661 391.374
SC 500.583 414.903
-2 Log L 494.661 379.374

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 115.2873 5 <.0001
Score 98.5590 5 <.0001
Wald 73.5896 5 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -14.7198 2.2707 42.0245 <.0001
c1 1 0.0861 0.5443 0.0250 0.8743
c3 1 0.3897 0.5027 0.6010 0.4382
hsgpa 1 0.1307 0.0359 13.2283 0.0003
hscalc 1 0.0695 0.0141 24.2776 <.0001
hsengl 1 -0.00386 0.0195 0.0392 0.8431

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
c1 1.090 0.375 3.168
c3 1.477 0.551 3.955
hsgpa 1.140 1.062 1.223
hscalc 1.072 1.043 1.102
hsengl 0.996 0.959 1.035

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 82.0 Somers' D 0.639
Percent Discordant 18.0 Gamma 0.639
Percent Tied 0.0 Tau-a 0.301
Pairs 32712 c 0.820

Test Statement Results

Linear Hypotheses Testing Results
Label Wald
Chi-Square		 DF Pr > ChiSq
course 0.6143 2 0.7355
HSvars 68.7257 3 <.0001

Gender, Ethnicity and Math performance

Predict Passing the course (Y-N) with Logistic Regression

Just HS variables

The LOGISTIC Procedure

The Logistic Procedure

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -15.9885 2.0503 60.8083 <.0001
hsgpa 1 0.1491 0.0331 20.3218 <.0001
hscalc 1 0.0582 0.0126 21.3526 <.0001
hsengl 1 0.00437 0.0164 0.0711 0.7898

Gender, Ethnicity and Math performance

Predict Passing the course (Y-N) with Logistic Regression

HS GPA, HS Calculus and Diagnostic Test

The LOGISTIC Procedure

The Logistic Procedure

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -14.6351 2.2803 41.1914 <.0001
hsgpa 1 0.1181 0.0311 14.4227 0.0001
hscalc 1 0.0592 0.0136 18.9109 <.0001
calc 1 0.0821 0.0650 1.5969 0.2063
precalc 1 0.2633 0.0890 8.7518 0.0031

Gender, Ethnicity and Math performance

Predict Passing the course (Y-N) with Logistic Regression

HS GPA, HS Calculus and Diagnostic Test

The LOGISTIC Procedure

The Logistic Procedure

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -14.6351 2.2803 41.1914 <.0001
hsgpa 1 0.1181 0.0311 14.4227 0.0001
hscalc 1 0.0592 0.0136 18.9109 <.0001
precalc 1 0.1812 0.1250 2.0999 0.1473
totscore 1 0.0821 0.0650 1.5969 0.2063

Test Statement Results

Linear Hypotheses Testing Results
Label Wald
Chi-Square		 DF Pr > ChiSq
precalc_n_totscore 13.8587 2 0.0010

Gender, Ethnicity and Math performance

Predict Passing the course (Y-N) with Logistic Regression

HS GPA, HS Calculus and Pre-calculus test

The LOGISTIC Procedure

The Logistic Procedure

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -14.7970 2.2683 42.5550 <.0001
hsgpa 1 0.1173 0.0310 14.3281 0.0002
hscalc 1 0.0638 0.0132 23.3346 <.0001
precalc 1 0.2989 0.0844 12.5464 0.0004

Gender, Ethnicity and Math performance

Predict Passing the course (Y-N) with Logistic Regression

Try gender, ethnic and mother tongue controlling for good stuff

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.EXPLORE  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 370

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 No 138
2 Yes 232

Probability modeled is passed='Yes'.

Note:209 observations were deleted due to missing values for the response or explanatory variables.

Class Level Information

Class Level Information
Class Value Design Variables
ethnic Asian 1 0 0 0 0
  East Indian 0 0 0 0 0
  Eastern European 0 1 0 0 0
  European not Eastern 0 0 1 0 0
  Middle-Eastern and Pakistani 0 0 0 1 0
  Other and DK 0 0 0 0 1

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 490.784 379.703
SC 494.698 422.752
-2 Log L 488.784 357.703

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 131.0808 10 <.0001
Score 110.8226 10 <.0001
Wald 80.9993 10 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
hsgpa 1 10.3205 0.0013
hscalc 1 24.3884 <.0001
precalc 1 13.5282 0.0002
ethnic 5 4.5364 0.4750
gender 1 0.8343 0.3610
mtongue 1 0.1917 0.6615

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter   DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept   1 -14.2314 2.4312 34.2655 <.0001
hsgpa   1 0.1043 0.0325 10.3205 0.0013
hscalc   1 0.0687 0.0139 24.3884 <.0001
precalc   1 0.3205 0.0871 13.5282 0.0002
ethnic Asian 1 -0.3522 0.4642 0.5758 0.4480
ethnic Eastern European 1 -0.0314 0.5126 0.0038 0.9512
ethnic European not Eastern 1 0.2889 0.4266 0.4587 0.4982
ethnic Middle-Eastern and Pakistani 1 -0.4521 0.5419 0.6963 0.4040
ethnic Other and DK 1 0.6539 0.8954 0.5334 0.4652
gender   1 0.2465 0.2698 0.8343 0.3610
mtongue   1 -0.1485 0.3391 0.1917 0.6615

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
hsgpa 1.110 1.042 1.183
hscalc 1.071 1.042 1.101
precalc 1.378 1.161 1.634
ethnic Asian vs East Indian 0.703 0.283 1.746
ethnic Eastern European vs East Indian 0.969 0.355 2.647
ethnic European not Eastern vs East Indian 1.335 0.579 3.081
ethnic Middle-Eastern and Pakistani vs East Indian 0.636 0.220 1.840
ethnic Other and DK vs East Indian 1.923 0.333 11.120
gender 1.279 0.754 2.171
mtongue 0.862 0.443 1.676

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 83.7 Somers' D 0.674
Percent Discordant 16.3 Gamma 0.674
Percent Tied 0.0 Tau-a 0.316
Pairs 32016 c 0.837

Coefficients for Contrasts

Coefficients of Contrast Demographics
Parameter Row1 Row2 Row3 Row4 Row5 Row6 Row7
Intercept 0 0 0 0 0 0 0
hsgpa 0 0 0 0 0 0 0
hscalc 0 0 0 0 0 0 0
precalc 0 0 0 0 0 0 0
ethnicAsian 1 0 0 0 0 0 0
ethnicEastern European 0 1 0 0 0 0 0
ethnicEuropean not Eastern 0 0 1 0 0 0 0
ethnicMiddle-Eastern and Pakist 0 0 0 1 0 0 0
ethnicOther and DK 0 0 0 0 1 0 0
gender 0 0 0 0 0 1 0
mtongue 0 0 0 0 0 0 1

Wald Test for Contrasts

Contrast Test Results
Contrast DF Wald
Chi-Square		 Pr > ChiSq
Demographics 7 6.0125 0.5383

Gender, Ethnicity and Math performance

Predict Passing the course (Y-N) with Logistic Regression

HS GPA, HS Calculus, Pre-calculus test, Gender and Mother tongue

The LOGISTIC Procedure

The Logistic Procedure

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -14.8254 2.3097 41.2002 <.0001
hsgpa 1 0.1142 0.0315 13.1794 0.0003
hscalc 1 0.0633 0.0134 22.4045 <.0001
precalc 1 0.3187 0.0860 13.7156 0.0002
gender 1 0.3206 0.2631 1.4855 0.2229
mtongue 1 0.0781 0.3154 0.0613 0.8044

Gender, Ethnicity and Math performance

Predict Passing the course (Y-N) with Logistic Regression

Try automatic (stepwise) selection

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.EXPLORE  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 368

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 No 138
2 Yes 230

Probability modeled is passed='Yes'.

Note:211 observations were deleted due to missing values for the response or explanatory variables.

Stepwise Selection Procedure

Step 0

Step 0. Intercept entered:

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

-2 Log L = 486.911

Residual Chi-Square

Residual Chi-Square Test
Chi-Square DF Pr > ChiSq
111.4077 14 <.0001

Step 1

Step 1. Effect hscalc entered:

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 488.911 398.544
SC 492.819 406.360
-2 Log L 486.911 394.544

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 92.3666 1 <.0001
Score 85.5385 1 <.0001
Wald 68.7679 1 <.0001

Residual Chi-Square

Residual Chi-Square Test
Chi-Square DF Pr > ChiSq
38.7030 13 0.0002

Note:No effects for the model in Step 1 are removed.

Step 2

Step 2. Effect hsgpa entered:

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 488.911 382.659
SC 492.819 394.384
-2 Log L 486.911 376.659

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 110.2512 2 <.0001
Score 94.7678 2 <.0001
Wald 71.1676 2 <.0001

Residual Chi-Square

Residual Chi-Square Test
Chi-Square DF Pr > ChiSq
22.0384 12 0.0371

Note:No effects for the model in Step 2 are removed.

Step 3

Step 3. Effect precalc entered:

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 488.911 370.567
SC 492.819 386.199
-2 Log L 486.911 362.567

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 124.3437 3 <.0001
Score 104.2190 3 <.0001
Wald 77.6336 3 <.0001

Residual Chi-Square

Residual Chi-Square Test
Chi-Square DF Pr > ChiSq
8.7229 11 0.6475

Note:No effects for the model in Step 3 are removed.

Note:No (additional) effects met the 0.05 significance level for entry into the model.

Model Building Summary

Summary of Stepwise Selection
Step Effect DF Number
In		 Score
Chi-Square		 Wald
Chi-Square		 Pr > ChiSq Variable
Label
Entered Removed
1 hscalc   1 1 85.5385   <.0001 HS Calculus
2 hsgpa   1 2 17.3610   <.0001 High School GPA
3 precalc   1 3 13.8105   0.0002 Number precalculus correct

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -14.4886 2.2714 40.6869 <.0001
hsgpa 1 0.1147 0.0312 13.5684 0.0002
hscalc 1 0.0616 0.0132 21.6572 <.0001
precalc 1 0.3098 0.0851 13.2413 0.0003

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
hsgpa 1.122 1.055 1.192
hscalc 1.064 1.036 1.092
precalc 1.363 1.154 1.611

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 82.9 Somers' D 0.658
Percent Discordant 17.1 Gamma 0.658
Percent Tied 0.0 Tau-a 0.309
Pairs 31740 c 0.829

Gender, Ethnicity and Math performance

Explore missingness on omitted variables

The FREQ Procedure

The Freq Procedure

Table gender

One-Way Frequencies

gender Frequency Percent Cumulative
Frequency		 Cumulative
Percent
Frequency Missing = 28
0 285 51.72 285 51.72
1 266 48.28 551 100.00

Table mtongue

One-Way Frequencies

English vs. Other
mtongue Frequency Percent Cumulative
Frequency		 Cumulative
Percent
Frequency Missing = 28
0 149 27.04 149 27.04
1 402 72.96 551 100.00

Table ethnic

One-Way Frequencies

Judged Nationality of name
ethnic Frequency Percent Cumulative
Frequency		 Cumulative
Percent
Asian 131 22.63 131 22.63
Eastern European 63 10.88 194 33.51
European not Eastern 195 33.68 389 67.18
Middle-Eastern and Pakistani 72 12.44 461 79.62
East Indian 78 13.47 539 93.09
Other and DK 40 6.91 579 100.00

Table gender * mtongue

Cross-Tabular Freq Table

Frequency
Table of gender by mtongue
gender mtongue(English vs. Other)
. 0 1 Total
.
28
0
0
28
0
0
81
204
285
1
0
68
198
266
Total
28
149
402
579

Table gender * course2

Cross-Tabular Freq Table

Frequency
Table of gender by course2
gender course2
. Catch-up Mainstream Elite Total
.
21
3
2
2
28
0
55
28
173
29
285
1
32
28
198
8
266
Total
108
59
373
39
579

Gender, Ethnicity and Math performance

Explore missingness on omitted variables

Try adding missingness on gender/mtongue and course

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.EXPLORE2  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 375

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 No 141
2 Yes 234

Probability modeled is passed='Yes'.

Note:204 observations were deleted due to missing values for the response or explanatory variables.

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 498.554 377.537
SC 502.481 397.171
-2 Log L 496.554 367.537

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 129.0174 4 <.0001
Score 107.9122 4 <.0001
Wald 79.6873 4 <.0001

Note:The following parameters have been set to 0, since the variables are a linear combination of other variables as shown.

Linear

coursemiss = Intercept

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -14.7262 2.2805 41.6978 <.0001
hsgpa 1 0.1163 0.0312 13.8834 0.0002
hscalc 1 0.0640 0.0132 23.4083 <.0001
precalc 1 0.2991 0.0844 12.5617 0.0004
sexmiss 1 -0.2970 1.0429 0.0811 0.7758
coursemiss 0 0 . . .

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
hsgpa 1.123 1.057 1.194
hscalc 1.066 1.039 1.094
precalc 1.349 1.143 1.591
sexmiss 0.743 0.096 5.738

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 83.2 Somers' D 0.664
Percent Discordant 16.8 Gamma 0.664
Percent Tied 0.0 Tau-a 0.312
Pairs 32994 c 0.832

Gender, Ethnicity and Math performance

Explore missingness on omitted variables

Try adding missingness on gender/mtongue and course

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.EXPLORE2  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 375

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 No 141
2 Yes 234

Probability modeled is passed='Yes'.

Note:204 observations were deleted due to missing values for the response or explanatory variables.

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 498.554 377.537
SC 502.481 397.171
-2 Log L 496.554 367.537

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 129.0174 4 <.0001
Score 107.9122 4 <.0001
Wald 79.6873 4 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -14.7262 2.2805 41.6978 <.0001
hsgpa 1 0.1163 0.0312 13.8834 0.0002
hscalc 1 0.0640 0.0132 23.4083 <.0001
precalc 1 0.2991 0.0844 12.5617 0.0004
sexmiss 1 -0.2970 1.0429 0.0811 0.7758

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
hsgpa 1.123 1.057 1.194
hscalc 1.066 1.039 1.094
precalc 1.349 1.143 1.591
sexmiss 0.743 0.096 5.738

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 83.2 Somers' D 0.664
Percent Discordant 16.8 Gamma 0.664
Percent Tied 0.0 Tau-a 0.312
Pairs 32994 c 0.832

Gender, Ethnicity and Math performance

Explore missingness on omitted variables

HS GPA, HS Calculus and Pre-calculus test

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.EXPLORE  
Response Variable passed Passed the course
Number of Response Levels 2  
Model binary logit  
Optimization Technique Fisher's scoring  

Observations Summary

Number of Observations Read 579
Number of Observations Used 375

Response Profile

Response Profile
Ordered
Value		 passed Total
Frequency
1 No 141
2 Yes 234

Probability modeled is passed='Yes'.

Note:204 observations were deleted due to missing values for the response or explanatory variables.

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 498.554 375.618
SC 502.481 391.326
-2 Log L 496.554 367.618

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 128.9358 3 <.0001
Score 107.7971 3 <.0001
Wald 79.6583 3 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -14.7970 2.2683 42.5550 <.0001
hsgpa 1 0.1173 0.0310 14.3281 0.0002
hscalc 1 0.0638 0.0132 23.3346 <.0001
precalc 1 0.2989 0.0844 12.5464 0.0004

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
hsgpa 1.124 1.058 1.195
hscalc 1.066 1.039 1.094
precalc 1.348 1.143 1.591

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 83.2 Somers' D 0.664
Percent Discordant 16.8 Gamma 0.664
Percent Tied 0.0 Tau-a 0.312
Pairs 32994 c 0.832

Gender, Ethnicity and Math performance

Explore missingness on omitted variables

HS GPA, HS Calculus and Pre-calculus test

The Print Procedure

Data Set WORK.EXPLORE3

Obs hsgpa hscalc precalc pihat passed
1 78.0 65 2 0.28847 No
2 66.0 54 6 0.13985 Yes
3 80.2 77 4 0.67222 Yes
4 81.7 80 5 0.79970 Yes
5 86.8 87 4 0.89381 Yes
6 76.7 53 3 0.17923 Yes
7 85.8 86 3 0.83892 Yes
8 73.0 75 4 0.43682 No
9 72.3 63 6 0.37672 No
10 90.3 87 8 0.97672 Yes
11 . . 8 . Yes
12 . . 6 . Yes
13 87.2 84 . . Yes

Gender, Ethnicity and Math performance

Explore the distribution of estimated probabilities

The UNIVARIATE Procedure

Variable: pihat (Estimated Probability)

The Univariate Procedure

pihat

Moments

Moments
N 375 Sum Weights 375
Mean 0.62399888 Sum Observations 233.999579
Std Deviation 0.26929182 Variance 0.07251808
Skewness -0.3676074 Kurtosis -1.140799
Uncorrected SS 173.137237 Corrected SS 27.121763
Coeff Variation 43.1558177 Std Error Mean 0.01390617

Basic Measures of Location and Variability

Basic Statistical Measures
Location Variability
Mean 0.623999 Std Deviation 0.26929
Median 0.670185 Variance 0.07252
Mode 0.326099 Range 0.95826
    Interquartile Range 0.47953

Note: The mode displayed is the smallest of 3 modes with a count of 2.

Tests For Location

Tests for Location: Mu0=0
Test Statistic p Value
Student's t t 44.87209 Pr > |t| <.0001
Sign M 187.5 Pr >= |M| <.0001
Signed Rank S 35250 Pr >= |S| <.0001

Tests For Normality

Tests for Normality
Test Statistic p Value
Shapiro-Wilk W 0.931786 Pr < W <0.0001
Kolmogorov-Smirnov D 0.104768 Pr > D <0.0100
Cramer-von Mises W-Sq 1.224091 Pr > W-Sq <0.0050
Anderson-Darling A-Sq 7.843335 Pr > A-Sq <0.0050

Quantiles

Quantiles (Definition 5)
Level Quantile
100% Max 0.9949748
99% 0.9914191
95% 0.9771104
90% 0.9537774
75% Q3 0.8536269
50% Median 0.6701851
25% Q1 0.3740967
10% 0.2337966
5% 0.1693272
1% 0.0955652
0% Min 0.0367136

Extreme Observations

Extreme Observations
Lowest Highest
Value Obs Value Obs
0.0367136 380 0.990771 418
0.0511361 47 0.991419 50
0.0784379 409 0.993027 452
0.0955652 193 0.993405 414
0.0983791 120 0.994975 286

Plots for pihat

Plots for pihat