Results: basicmath.sas

Gender, Ethnicity and Math performance

Are pre-calculus questions easier?

The MEANS Procedure

The Means Procedure

Summary statistics

Analysis Variable : diff Percentage correct: Precalc minus calc
N Mean Std Dev t Value Pr > |t| Lower 95%
CL for Mean		 Upper 95%
CL for Mean
480 18.7415825 21.2553367 19.32 <.0001 16.8352695 20.6478955

Gender, Ethnicity and Math performance

Correlations between quantitative variables

The CORR Procedure

The Corr Procedure

Variables Information

7 Variables: grade hsgpa hscalc hsengl precalc calc totscore

Pearson Correlations

Pearson Correlation Coefficients
Prob > |r| under H0: Rho=0
Number of Observations
  grade hsgpa hscalc hsengl precalc calc totscore
grade
Final mark
1.00000
 
393
0.58129
<.0001
337
0.53272
<.0001
332
0.16441
0.0022
345
0.37834
<.0001
346
0.36247
<.0001
346
0.42847
<.0001
346
hsgpa
High School GPA
0.58129
<.0001
337
1.00000
 
466
0.62249
<.0001
437
0.54327
<.0001
464
0.33965
<.0001
396
0.33876
<.0001
396
0.39002
<.0001
396
hscalc
HS Calculus
0.53272
<.0001
332
0.62249
<.0001
437
1.00000
 
448
0.08498
0.0749
440
0.36684
<.0001
384
0.43774
<.0001
384
0.47262
<.0001
384
hsengl
HS English
0.16441
0.0022
345
0.54327
<.0001
464
0.08498
0.0749
440
1.00000
 
480
0.06543
0.1893
404
0.04272
0.3917
404
0.05995
0.2293
404
precalc
Number precalculus correct
0.37834
<.0001
346
0.33965
<.0001
396
0.36684
<.0001
384
0.06543
0.1893
404
1.00000
 
480
0.50135
<.0001
480
0.81309
<.0001
480
calc
Number calculus correct
0.36247
<.0001
346
0.33876
<.0001
396
0.43774
<.0001
384
0.04272
0.3917
404
0.50135
<.0001
480
1.00000
 
480
0.91133
<.0001
480
totscore
Total # right on diagnostic test
0.42847
<.0001
346
0.39002
<.0001
396
0.47262
<.0001
384
0.05995
0.2293
404
0.81309
<.0001
480
0.91133
<.0001
480
1.00000
 
480

Gender, Ethnicity and Math performance

Give an equation for predicting calculus grade from HS GPA

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark

The Reg Procedure

MODEL1

Fit

grade

Number of Observations

Number of Observations Read 579
Number of Observations Used 337
Number of Observations with Missing Values 242

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 1 39116 39116 170.97 <.0001
Error 335 76644 228.78925    
Corrected Total 336 115760      

Fit Statistics

Root MSE 15.12578 R-Square 0.3379
Dependent Mean 59.28190 Adj R-Sq 0.3359
Coeff Var 25.51501    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -84.85069 11.05385 -7.68 <.0001
hsgpa High School GPA 1 1.78889 0.13681 13.08 <.0001

Gender, Ethnicity and Math performance

Do average marks differ significantly in the three courses?

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
class 3 Catch-up Elite Mainstream

Number of Observations

Number of Observations Read 579
Number of Observations Used 346

Gender, Ethnicity and Math performance

Do average marks differ significantly in the three courses?

The GLM Procedure

 

Dependent Variable: grade Final mark

Analysis of Variance

grade

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 612.6624 306.3312 0.84 0.4317
Error 343 124775.1873 363.7761    
Corrected Total 345 125387.8497      

Fit Statistics

R-Square Coeff Var Root MSE grade Mean
0.004886 32.03198 19.07291 59.54335

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
class 2 612.6623710 306.3311855 0.84 0.4317

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
class 2 612.6623710 306.3311855 0.84 0.4317

Box Plot

Fit Plot for Final mark by class

Gender, Ethnicity and Math performance

Do students in the three courses have different outcomes?

The FREQ Procedure

The Freq Procedure

Table class * passed

Cross-Tabular Freq Table

Frequency
Row Pct
Table of class by passed
class passed(Passed the course)
No Yes Total
Catch-up
44
74.58
15
25.42
59
 
Mainstream
149
39.95
224
60.05
373
 
Elite
8
20.51
31
79.49
39
 
Total
201
270
471
Frequency Missing = 108

Statistics for Table of class by passed

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 2 33.5096 <.0001
Likelihood Ratio Chi-Square 2 34.4171 <.0001
Mantel-Haenszel Chi-Square 1 31.6717 <.0001
Phi Coefficient   0.2667  
Contingency Coefficient   0.2577  
Cramer's V   0.2667  

Sample Size = 471
Frequency Missing = 108

WARNING: 19% of the data are missing.

Table class * outcome

Cross-Tabular Freq Table

Frequency
Row Pct
Table of class by outcome
class outcome(Passed, Failed or Disappeared)
Disappeared Failed Passed Total
Catch-up
35
59.32
9
15.25
15
25.42
59
 
Mainstream
88
23.59
61
16.35
224
60.05
373
 
Elite
2
5.13
6
15.38
31
79.49
39
 
Total
125
76
270
471
Frequency Missing = 108

Statistics for Table of class by outcome

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 4 46.2026 <.0001
Likelihood Ratio Chi-Square 4 45.7760 <.0001
Mantel-Haenszel Chi-Square 1 42.0087 <.0001
Phi Coefficient   0.3132  
Contingency Coefficient   0.2989  
Cramer's V   0.2215  

Sample Size = 471
Frequency Missing = 108

WARNING: 19% of the data are missing.

Gender, Ethnicity and Math performance

Do students in the three courses have different outcomes?

Do the three courses attract different kinds of student?

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
class 3 Catch-up Elite Mainstream

Number of Observations for hsgpa

Data for Analysis of hsgpa
Number of Observations Read 579
Number of Observations Used 396

Number of Observations for hscalc

Data for Analysis of hscalc
Number of Observations Read 579
Number of Observations Used 384

Number of Observations for hsengl

Data for Analysis of hsengl
Number of Observations Read 579
Number of Observations Used 404

Number of Observations for precalc calc totscore

Data for Analysis of precalc calc totscore
Number of Observations Read 579
Number of Observations Used 471

Note:Variables in each group are consistent with respect to the presence or absence of missing values.

Gender, Ethnicity and Math performance

Do students in the three courses have different outcomes?

Do the three courses attract different kinds of student?

The GLM Procedure

 

Dependent Variable: hsgpa High School GPA

Missing Value Pattern 1

Analysis of Variance

hsgpa

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 521.50863 260.75432 7.36 0.0007
Error 393 13928.38013 35.44117    
Corrected Total 395 14449.88876      

Fit Statistics

R-Square Coeff Var Root MSE hsgpa Mean
0.036091 7.464203 5.953249 79.75732

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
class 2 521.5086329 260.7543164 7.36 0.0007

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
class 2 521.5086329 260.7543164 7.36 0.0007

Gender, Ethnicity and Math performance

Do students in the three courses have different outcomes?

Do the three courses attract different kinds of student?

The GLM Procedure

Means

class

Means

Level of
class		 N hsgpa
Mean Std Dev
Catch-up 35 76.0771429 5.01808996
Elite 31 80.3258065 7.09877772
Mainstream 330 80.0942424 5.92774094

Gender, Ethnicity and Math performance

Do students in the three courses have different outcomes?

Do the three courses attract different kinds of student?

The GLM Procedure

 

Dependent Variable: hscalc HS Calculus

Missing Value Pattern 2

Analysis of Variance

hscalc

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 5692.82480 2846.41240 20.43 <.0001
Error 381 53079.73509 139.31689    
Corrected Total 383 58772.55990      

Fit Statistics

R-Square Coeff Var Root MSE hscalc Mean
0.096862 15.52369 11.80326 76.03385

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
class 2 5692.824804 2846.412402 20.43 <.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
class 2 5692.824804 2846.412402 20.43 <.0001

Gender, Ethnicity and Math performance

Do students in the three courses have different outcomes?

Do the three courses attract different kinds of student?

The GLM Procedure

Means

class

Means

Level of
class		 N hscalc
Mean Std Dev
Catch-up 21 61.1904762 9.5478744
Elite 30 81.8333333 8.9792225
Mainstream 333 76.4474474 12.1385489

Gender, Ethnicity and Math performance

Do students in the three courses have different outcomes?

Do the three courses attract different kinds of student?

The GLM Procedure

 

Dependent Variable: hsengl HS English

Missing Value Pattern 3

Analysis of Variance

hsengl

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 904.15262 452.07631 6.63 0.0015
Error 401 27344.67907 68.19122    
Corrected Total 403 28248.83168      

Fit Statistics

R-Square Coeff Var Root MSE hsengl Mean
0.032007 10.83447 8.257798 76.21782

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
class 2 904.1526157 452.0763079 6.63 0.0015

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
class 2 904.1526157 452.0763079 6.63 0.0015

Gender, Ethnicity and Math performance

Do students in the three courses have different outcomes?

Do the three courses attract different kinds of student?

The GLM Procedure

Means

class

Means

Level of
class		 N hsengl
Mean Std Dev
Catch-up 36 73.5277778 7.6587433
Elite 32 72.2812500 11.3058203
Mainstream 336 76.8809524 7.9793087

Gender, Ethnicity and Math performance

Do students in the three courses have different outcomes?

Do the three courses attract different kinds of student?

The GLM Procedure

 

Dependent Variable: precalc Number precalculus correct

Missing Value Pattern 4

Analysis of Variance

precalc

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 127.329928 63.664964 23.13 <.0001
Error 468 1288.215719 2.752598    
Corrected Total 470 1415.545648      

Fit Statistics

R-Square Coeff Var Root MSE precalc Mean
0.089951 37.65947 1.659095 4.405520

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
class 2 127.3299283 63.6649642 23.13 <.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
class 2 127.3299283 63.6649642 23.13 <.0001

Gender, Ethnicity and Math performance

Do students in the three courses have different outcomes?

Do the three courses attract different kinds of student?

The GLM Procedure

 

Dependent Variable: calc Number calculus correct

calc

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 315.176692 157.588346 28.66 <.0001
Error 468 2573.154518 5.498193    
Corrected Total 470 2888.331210      

Fit Statistics

R-Square Coeff Var Root MSE calc Mean
0.109121 70.38951 2.344823 3.331210

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
class 2 315.1766918 157.5883459 28.66 <.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
class 2 315.1766918 157.5883459 28.66 <.0001

Gender, Ethnicity and Math performance

Do students in the three courses have different outcomes?

Do the three courses attract different kinds of student?

The GLM Procedure

 

Dependent Variable: totscore Total # right on diagnostic test

totscore

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 841.321053 420.660527 36.12 <.0001
Error 468 5450.033511 11.645371    
Corrected Total 470 6291.354565      

Fit Statistics

R-Square Coeff Var Root MSE totscore Mean
0.133727 44.10819 3.412531 7.736730

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
class 2 841.3210533 420.6605266 36.12 <.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
class 2 841.3210533 420.6605266 36.12 <.0001

Gender, Ethnicity and Math performance

Do students in the three courses have different outcomes?

Do the three courses attract different kinds of student?

The GLM Procedure

Means

class

Means

Level of
class		 N precalc calc totscore
Mean Std Dev Mean Std Dev Mean Std Dev
Catch-up 59 3.16949153 1.60980340 1.30508475 1.47688205 4.47457627 2.47996060
Elite 39 5.33333333 1.76714658 4.56410256 2.82651796 9.89743590 3.98546617
Mainstream 373 4.50402145 1.65526528 3.52278820 2.40018833 8.02680965 3.47407136

Gender, Ethnicity and Math performance

Is there a sex dfference in average marks?

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
sex 2 Female Male

Number of Observations

Number of Observations Read 579
Number of Observations Used 383

Gender, Ethnicity and Math performance

Is there a sex dfference in average marks?

The GLM Procedure

 

Dependent Variable: grade Final mark

Analysis of Variance

grade

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 1 110.7945 110.7945 0.30 0.5870
Error 381 142806.7564 374.8209    
Corrected Total 382 142917.5509      

Fit Statistics

R-Square Coeff Var Root MSE grade Mean
0.000775 33.00246 19.36029 58.66319

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
sex 1 110.7945190 110.7945190 0.30 0.5870

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
sex 1 110.7945190 110.7945190 0.30 0.5870

Box Plot

Fit Plot for Final mark by sex

Gender, Ethnicity and Math performance

Is there a sex dfference in average marks?

The GLM Procedure

Means

sex

grade

Distribution of grade by sex

Distribution of grade by sex

Means

Level of
sex		 N grade
Mean Std Dev
Female 193 58.1295337 18.4319923
Male 190 59.2052632 20.2598196

The Ttest Procedure

Final mark

Gender, Ethnicity and Math performance

Could we conclude NO sex difference?

The TTEST Procedure

 

Variable: grade (Final mark)

Statistics

sex Method N Mean Std Dev Std Err Minimum Maximum
Female   193 58.1295 18.4320 1.3268 4.0000 97.0000
Male   190 59.2053 20.2598 1.4698 1.0000 99.0000
Diff (1-2) Pooled   -1.0757 19.3603 1.9786    
Diff (1-2) Satterthwaite   -1.0757   1.9801    

Confidence Limits

sex Method Mean 95% CL Mean Std Dev 95% CL Std Dev
Female   58.1295 55.5126 60.7464 18.4320 16.7583 20.4800
Male   59.2053 56.3059 62.1046 20.2598 18.4070 22.5306
Diff (1-2) Pooled -1.0757 -4.9661 2.8146 19.3603 18.0779 20.8400
Diff (1-2) Satterthwaite -1.0757 -4.9691 2.8176      

T-Tests

Method Variances DF t Value Pr > |t|
Pooled Equal 381 -0.54 0.5870
Satterthwaite Unequal 376.45 -0.54 0.5873

Equality of Variances

Equality of Variances
Method Num DF Den DF F Value Pr > F
Folded F 189 192 1.21 0.1926

Summary Panel

Summary Panel for grade

Q-Q Plots

Q-Q Plots for grade

Gender, Ethnicity and Math performance

Do average marks depend on mother tongue?

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
tongue 2 English Other

Number of Observations

Number of Observations Read 579
Number of Observations Used 383

Gender, Ethnicity and Math performance

Do average marks depend on mother tongue?

The GLM Procedure

 

Dependent Variable: grade Final mark

Analysis of Variance

grade

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 1 2064.4317 2064.4317 5.58 0.0186
Error 381 140853.1192 369.6932    
Corrected Total 382 142917.5509      

Fit Statistics

R-Square Coeff Var Root MSE grade Mean
0.014445 32.77594 19.22741 58.66319

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
tongue 1 2064.431684 2064.431684 5.58 0.0186

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
tongue 1 2064.431684 2064.431684 5.58 0.0186

Box Plot

Fit Plot for Final mark by Mother Tongue (Eng or Other)

Gender, Ethnicity and Math performance

Do average marks depend on mother tongue?

The GLM Procedure

Means

tongue

grade

Distribution of grade by tongue

Distribution of grade by tongue

Means

Level of
tongue		 N grade
Mean Std Dev
English 289 57.3391003 19.2338287
Other 94 62.7340426 19.2075117

Gender, Ethnicity and Math performance

Do average marks depend on ethnic background?

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
ethnic 6 Asian East Indian Eastern European European not Eastern Middle-Eastern and Pakistani Other and DK

Number of Observations

Number of Observations Read 579
Number of Observations Used 393

Gender, Ethnicity and Math performance

Do average marks depend on ethnic background?

The GLM Procedure

 

Dependent Variable: grade Final mark

Analysis of Variance

grade

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 5 3640.9573 728.1915 2.00 0.0772
Error 387 140613.0478 363.3412    
Corrected Total 392 144254.0051      

Fit Statistics

R-Square Coeff Var Root MSE grade Mean
0.025240 32.45180 19.06151 58.73791

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
ethnic 5 3640.957278 728.191456 2.00 0.0772

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
ethnic 5 3640.957278 728.191456 2.00 0.0772

Box Plot

Fit Plot for Final mark by Judged Nationality of name

Gender, Ethnicity and Math performance

Do average marks depend on ethnic background?

The GLM Procedure

Means

ethnic

grade

Distribution of grade by ethnic

Distribution of grade by ethnic

Means

Level of
ethnic		 N grade
Mean Std Dev
Asian 87 60.0574713 20.9314253
East Indian 53 65.1886792 18.5317364
Eastern European 46 55.7608696 20.2771736
European not Eastern 142 56.2816901 17.8581353
Middle-Eastern and Pakistani 50 59.3600000 19.9691190
Other and DK 15 58.6000000 12.1526011

Gender, Ethnicity and Math performance

Do average marks depend on ethnic background?

The GLM Procedure

Means

ethnic

grade

Distribution of grade by ethnic

Distribution of grade by ethnic

Pairwise Multiple Comparisons

Tukey

Gender, Ethnicity and Math performance

Do average marks depend on ethnic background?

The GLM Procedure

 

Tukey's Studentized Range (HSD) Test for grade

Note:This test controls the Type I experimentwise error rate.

Information

Alpha 0.05
Error Degrees of Freedom 387
Error Mean Square 363.3412
Critical Value of Studentized Range 4.05039

Pairs

Comparisons significant at the 0.05 level are indicated by ***.
ethnic
Comparison		 Difference
Between
Means		 Simultaneous 95% Confidence Limits  
East Indian - Asian 5.131 -4.382 14.644  
East Indian - Middle-Eastern and Pakistani 5.829 -4.934 16.592  
East Indian - Other and DK 6.589 -9.378 22.555  
East Indian - European not Eastern 8.907 0.119 17.695 ***
East Indian - Eastern European 9.428 -1.573 20.429  
Asian - East Indian -5.131 -14.644 4.382  
Asian - Middle-Eastern and Pakistani 0.697 -8.991 10.386  
Asian - Other and DK 1.457 -13.805 16.720  
Asian - European not Eastern 3.776 -3.657 11.209  
Asian - Eastern European 4.297 -5.656 14.249  
Middle-Eastern and Pakistani - East Indian -5.829 -16.592 4.934  
Middle-Eastern and Pakistani - Asian -0.697 -10.386 8.991  
Middle-Eastern and Pakistani - Other and DK 0.760 -15.312 16.832  
Middle-Eastern and Pakistani - European not Eastern 3.078 -5.899 12.056  
Middle-Eastern and Pakistani - Eastern European 3.599 -7.554 14.753  
Other and DK - East Indian -6.589 -22.555 9.378  
Other and DK - Asian -1.457 -16.720 13.805  
Other and DK - Middle-Eastern and Pakistani -0.760 -16.832 15.312  
Other and DK - European not Eastern 2.318 -12.503 17.140  
Other and DK - Eastern European 2.839 -13.393 19.071  
European not Eastern - East Indian -8.907 -17.695 -0.119 ***
European not Eastern - Asian -3.776 -11.209 3.657  
European not Eastern - Middle-Eastern and Pakistani -3.078 -12.056 5.899  
European not Eastern - Other and DK -2.318 -17.140 12.503  
European not Eastern - Eastern European 0.521 -8.741 9.783  
Eastern European - East Indian -9.428 -20.429 1.573  
Eastern European - Asian -4.297 -14.249 5.656  
Eastern European - Middle-Eastern and Pakistani -3.599 -14.753 7.554  
Eastern European - Other and DK -2.839 -19.071 13.393  
Eastern European - European not Eastern -0.521 -9.783 8.741  

Bonferroni

Gender, Ethnicity and Math performance

Do average marks depend on ethnic background?

The GLM Procedure

 

Bonferroni (Dunn) t Tests for grade

Note:This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than Tukey's for all pairwise comparisons.

Information

Alpha 0.05
Error Degrees of Freedom 387
Error Mean Square 363.3412
Critical Value of t 2.95354

Pairs

Comparisons significant at the 0.05 level are indicated by ***.
ethnic
Comparison		 Difference
Between
Means		 Simultaneous 95% Confidence Limits  
East Indian - Asian 5.131 -4.679 14.941  
East Indian - Middle-Eastern and Pakistani 5.829 -5.271 16.928  
East Indian - Other and DK 6.589 -9.877 23.054  
East Indian - European not Eastern 8.907 -0.155 17.969  
East Indian - Eastern European 9.428 -1.917 20.773  
Asian - East Indian -5.131 -14.941 4.679  
Asian - Middle-Eastern and Pakistani 0.697 -9.294 10.689  
Asian - Other and DK 1.457 -14.282 17.197  
Asian - European not Eastern 3.776 -3.889 11.441  
Asian - Eastern European 4.297 -5.967 14.560  
Middle-Eastern and Pakistani - East Indian -5.829 -16.928 5.271  
Middle-Eastern and Pakistani - Asian -0.697 -10.689 9.294  
Middle-Eastern and Pakistani - Other and DK 0.760 -15.814 17.334  
Middle-Eastern and Pakistani - European not Eastern 3.078 -6.180 12.336  
Middle-Eastern and Pakistani - Eastern European 3.599 -7.903 15.101  
Other and DK - East Indian -6.589 -23.054 9.877  
Other and DK - Asian -1.457 -17.197 14.282  
Other and DK - Middle-Eastern and Pakistani -0.760 -17.334 15.814  
Other and DK - European not Eastern 2.318 -12.966 17.603  
Other and DK - Eastern European 2.839 -13.900 19.579  
European not Eastern - East Indian -8.907 -17.969 0.155  
European not Eastern - Asian -3.776 -11.441 3.889  
European not Eastern - Middle-Eastern and Pakistani -3.078 -12.336 6.180  
European not Eastern - Other and DK -2.318 -17.603 12.966  
European not Eastern - Eastern European 0.521 -9.030 10.072  
Eastern European - East Indian -9.428 -20.773 1.917  
Eastern European - Asian -4.297 -14.560 5.967  
Eastern European - Middle-Eastern and Pakistani -3.599 -15.101 7.903  
Eastern European - Other and DK -2.839 -19.579 13.900  
Eastern European - European not Eastern -0.521 -10.072 9.030  

Scheffe

Gender, Ethnicity and Math performance

Do average marks depend on ethnic background?

The GLM Procedure

 

Scheffe's Test for grade

Note:This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than Tukey's for all pairwise comparisons.

Information

Alpha 0.05
Error Degrees of Freedom 387
Error Mean Square 363.3412
Critical Value of F 2.23731

Pairs

Comparisons significant at the 0.05 level are indicated by ***.
ethnic
Comparison		 Difference
Between
Means		 Simultaneous 95% Confidence Limits  
East Indian - Asian 5.131 -5.978 16.240  
East Indian - Middle-Eastern and Pakistani 5.829 -6.740 18.398  
East Indian - Other and DK 6.589 -12.057 25.234  
East Indian - European not Eastern 8.907 -1.355 19.169  
East Indian - Eastern European 9.428 -3.419 22.275  
Asian - East Indian -5.131 -16.240 5.978  
Asian - Middle-Eastern and Pakistani 0.697 -10.617 12.012  
Asian - Other and DK 1.457 -16.366 19.281  
Asian - European not Eastern 3.776 -4.904 12.456  
Asian - Eastern European 4.297 -7.326 15.919  
Middle-Eastern and Pakistani - East Indian -5.829 -18.398 6.740  
Middle-Eastern and Pakistani - Asian -0.697 -12.012 10.617  
Middle-Eastern and Pakistani - Other and DK 0.760 -18.009 19.529  
Middle-Eastern and Pakistani - European not Eastern 3.078 -7.406 13.562  
Middle-Eastern and Pakistani - Eastern European 3.599 -9.426 16.624  
Other and DK - East Indian -6.589 -25.234 12.057  
Other and DK - Asian -1.457 -19.281 16.366  
Other and DK - Middle-Eastern and Pakistani -0.760 -19.529 18.009  
Other and DK - European not Eastern 2.318 -14.990 19.627  
Other and DK - Eastern European 2.839 -16.117 21.795  
European not Eastern - East Indian -8.907 -19.169 1.355  
European not Eastern - Asian -3.776 -12.456 4.904  
European not Eastern - Middle-Eastern and Pakistani -3.078 -13.562 7.406  
European not Eastern - Other and DK -2.318 -19.627 14.990  
European not Eastern - Eastern European 0.521 -10.295 11.337  
Eastern European - East Indian -9.428 -22.275 3.419  
Eastern European - Asian -4.297 -15.919 7.326  
Eastern European - Middle-Eastern and Pakistani -3.599 -16.624 9.426  
Eastern European - Other and DK -2.839 -21.795 16.117  
Eastern European - European not Eastern -0.521 -11.337 10.295