Results: basicmath.sas

Prediction of Performance in First-year Calculus: Exploratory Sample

Frequency distributions of categorical variables

The FREQ Procedure

Table sex

One-Way Frequencies


sex	Frequency	Percent	Cumulative Frequency	Cumulative Percent
Frequency Missing = 28
Female	266	48.28	266	48.28
Male	285	51.72	551	100.00

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 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 tongue

One-Way Frequencies


Mother Tongue (Eng or Other)
tongue	Frequency	Percent	Cumulative Frequency	Cumulative Percent
Frequency Missing = 28
English	402	72.96	402	72.96
Other	149	27.04	551	100.00

Table course

One-Way Frequencies


course	Frequency	Percent	Cumulative Frequency	Cumulative Percent
Frequency Missing = 108
Catch-up	59	12.53	59	12.53
Mainstrm	373	79.19	432	91.72
Elite	39	8.28	471	100.00

Table passed

One-Way Frequencies


Passed the course
passed	Frequency	Percent	Cumulative Frequency	Cumulative Percent
No	274	47.32	274	47.32
Yes	305	52.68	579	100.00

Table gsplit

One-Way Frequencies


Median split on final grade
gsplit	Frequency	Percent	Cumulative Frequency	Cumulative Percent
Frequency Missing = 186
60orLess	211	53.69	211	53.69
Over60	182	46.31	393	100.00

Prediction of Performance in First-year Calculus: Exploratory Sample

Basic Descriptive Statistics on Quantitative Variables

The MEANS Procedure

Summary statistics


Variable	Label	N	Mean	Std Dev	Minimum	Maximum
hsgpa hscalc hsengl calc precalc totscore diff grade	High School GPA HS Calculus HS English Number calculus correct Number precalculus correct Total # right on diagnostic test Percentage correct: Precalc minus calc Final mark (if any)	466 448 480 480 480 480 480 393	79.2690987 75.4441964 75.8354167 3.3187500 4.4020833 7.7208333 18.7415825 58.7379135	6.0384921 12.1918487 8.7180371 2.4918369 1.7621620 3.7036888 21.2553367 19.1831935	65.0000000 50.0000000 50.0000000 0 0 0 -41.4141414 1.0000000	97.3000000 100.0000000 96.0000000 11.0000000 9.0000000 20.0000000 70.7070707 99.0000000

Prediction of Performance in First-year Calculus: Exploratory Sample

Basic Descriptive Statistics on Quantitative Variables

The UNIVARIATE Procedure

Variable: grade (Final mark (if any))

The UNIVARIATE Procedure

grade

Moments


Moments
N	393	Sum Weights	393
Mean	58.7379135	Sum Observations	23084
Std Deviation	19.1831935	Variance	367.994911
Skewness	-0.5121423	Kurtosis	0.35144502
Uncorrected SS	1500160	Corrected SS	144254.005
Coeff Variation	32.658963	Std Error Mean	0.9676641

Basic Measures of Location and Variability


Basic Statistical Measures
Location		Variability
Mean	58.73791	Std Deviation	19.18319
Median	60.00000	Variance	367.99491
Mode	50.00000	Range	98.00000
		Interquartile Range	22.00000

Tests For Location


Tests for Location: Mu0=0
Test	Statistic		p Value
Student's t	t	60.70073	Pr > \|t\|	<.0001
Sign	M	196.5	Pr >= \|M\|	<.0001
Signed Rank	S	38710.5	Pr >= \|S\|	<.0001

Tests For Normality


Tests for Normality
Test	Statistic		p Value
Shapiro-Wilk	W	0.977228	Pr < W	<0.0001
Kolmogorov-Smirnov	D	0.100457	Pr > D	<0.0100
Cramer-von Mises	W-Sq	0.318394	Pr > W-Sq	<0.0050
Anderson-Darling	A-Sq	2.08731	Pr > A-Sq	<0.0050

Quantiles


Quantiles (Definition 5)
Level	Quantile
100% Max	99
99%	95
95%	88
90%	82
75% Q3	72
50% Median	60
25% Q1	50
10%	32
5%	22
1%	4
0% Min	1

Extreme Observations


Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
1	176	95	268
2	319	95	340
2	9	96	452
4	498	97	486
4	70	99	286

Missing Values


Missing Values
Missing Value	Count	Percent Of
Missing Value	Count	All Obs	Missing Obs
.	186	32.12	100.00

Plots for grade

Prediction of Performance in First-year Calculus: Exploratory Sample

Calculus vs. Pre-calculus scale

The MEANS Procedure

Summary statistics


Analysis Variable : diff Percentage correct: Precalc minus calc
N	Mean	Std Dev	t Value	Pr > \|t\|
480	18.7415825	21.2553367	19.32	<.0001

Prediction of Performance in First-year Calculus: Exploratory Sample

Some Relationships between categorical variables

The FREQ Procedure

Table tongue * sex

Cross-Tabular Freq Table

Frequency Percent Row Pct Col Pct

Table of tongue by sex
tongue(Mother Tongue (Eng or Other))	sex
tongue(Mother Tongue (Eng or Other))	Female	Male	Total
English	198 35.93 49.25 74.44	204 37.02 50.75 71.58	402 72.96
Other	68 12.34 45.64 25.56	81 14.70 54.36 28.42	149 27.04
Total	266 48.28	285 51.72	551 100.00
Frequency Missing = 28

Statistics for Table of tongue by sex

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	1	0.5693	0.4505
Likelihood Ratio Chi-Square	1	0.5699	0.4503
Continuity Adj. Chi-Square	1	0.4337	0.5102
Mantel-Haenszel Chi-Square	1	0.5683	0.4510
Phi Coefficient		0.0321
Contingency Coefficient		0.0321
Cramer's V		0.0321

Fisher's Exact Test


Fisher's Exact Test
Cell (1,1) Frequency (F)	198
Left-sided Pr <= F	0.8024
Right-sided Pr >= F	0.2552

Table Probability (P)	0.0576
Two-sided Pr <= P	0.5018

Effective Sample Size = 551
Frequency Missing = 28

Table ethnic * sex

Cross-Tabular Freq Table

Frequency Row Pct

Table of ethnic by sex
ethnic(Judged Nationality of name)	sex
ethnic(Judged Nationality of name)	Female	Male	Total
Asian	48 36.64	83 63.36	131
Eastern European	37 58.73	26 41.27	63
European not Eastern	107 55.15	87 44.85	194
Middle-Eastern and Pakistani	30 41.67	42 58.33	72
East Indian	35 45.45	42 54.55	77
Other and DK	9 64.29	5 35.71	14
Total	266	285	551
Frequency Missing = 28

Statistics for Table of ethnic by sex

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	5	16.4773	0.0056
Likelihood Ratio Chi-Square	5	16.6120	0.0053
Mantel-Haenszel Chi-Square	1	1.7025	0.1920
Phi Coefficient		0.1729
Contingency Coefficient		0.1704
Cramer's V		0.1729

Effective Sample Size = 551
Frequency Missing = 28

Table sex * course

Cross-Tabular Freq Table

Frequency Row Pct

Table of sex by course
sex	course
sex	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 course

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.

Table ethnic * tongue

Cross-Tabular Freq Table

Frequency Row Pct

Table of ethnic by tongue
ethnic(Judged Nationality of name)	tongue(Mother Tongue (Eng or Other))
ethnic(Judged Nationality of name)	English	Other	Total
Asian	62 47.33	69 52.67	131
Eastern European	40 63.49	23 36.51	63
European not Eastern	179 92.27	15 7.73	194
Middle-Eastern and Pakistani	50 69.44	22 30.56	72
East Indian	59 76.62	18 23.38	77
Other and DK	12 85.71	2 14.29	14
Total	402	149	551
Frequency Missing = 28

Statistics for Table of ethnic by tongue

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	5	85.2730	<.0001
Likelihood Ratio Chi-Square	5	89.8245	<.0001
Mantel-Haenszel Chi-Square	1	30.9788	<.0001
Phi Coefficient		0.3934
Contingency Coefficient		0.3661
Cramer's V		0.3934

Effective Sample Size = 551
Frequency Missing = 28

Prediction of Performance in First-year Calculus: Exploratory Sample

Ethnic by Tongue: Asians vs. Eastern Europeans

The FREQ Procedure

Table ethnic * tongue

Cross-Tabular Freq Table

Frequency Row Pct

Table of ethnic by tongue
ethnic(Judged Nationality of name)	tongue(Mother Tongue (Eng or Other))
ethnic(Judged Nationality of name)	English	Other	Total
Asian	62 47.33	69 52.67	131
Eastern European	40 63.49	23 36.51	63
Total	102	92	194

Statistics for Table of ethnic by tongue

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	1	4.4577	0.0347
Likelihood Ratio Chi-Square	1	4.5032	0.0338
Continuity Adj. Chi-Square	1	3.8330	0.0503
Mantel-Haenszel Chi-Square	1	4.4347	0.0352
Phi Coefficient		-0.1516
Contingency Coefficient		0.1499
Cramer's V		-0.1516

Fisher's Exact Test


Fisher's Exact Test
Cell (1,1) Frequency (F)	62
Left-sided Pr <= F	0.0247
Right-sided Pr >= F	0.9886

Table Probability (P)	0.0133
Two-sided Pr <= P	0.0457

Sample Size = 194

Prediction of Performance in First-year Calculus: Exploratory Sample

Ethnic by Tongue: Asians vs. Other Europeans

The FREQ Procedure

Table ethnic * tongue

Cross-Tabular Freq Table

Frequency Row Pct

Table of ethnic by tongue
ethnic(Judged Nationality of name)	tongue(Mother Tongue (Eng or Other))
ethnic(Judged Nationality of name)	English	Other	Total
Asian	62 47.33	69 52.67	131
European not Eastern	179 92.27	15 7.73	194
Total	241	84	325
Frequency Missing = 1

Statistics for Table of ethnic by tongue

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	1	82.3991	<.0001
Likelihood Ratio Chi-Square	1	84.6033	<.0001
Continuity Adj. Chi-Square	1	80.0710	<.0001
Mantel-Haenszel Chi-Square	1	82.1455	<.0001
Phi Coefficient		-0.5035
Contingency Coefficient		0.4497
Cramer's V		-0.5035

Fisher's Exact Test


Fisher's Exact Test
Cell (1,1) Frequency (F)	62
Left-sided Pr <= F	<.0001
Right-sided Pr >= F	1.0000

Table Probability (P)	<.0001
Two-sided Pr <= P	<.0001

Effective Sample Size = 325
Frequency Missing = 1

Prediction of Performance in First-year Calculus: Exploratory Sample

Ethnic by Tongue: Asians vs. Middle East

The FREQ Procedure

Table ethnic * tongue

Cross-Tabular Freq Table

Frequency Row Pct

Table of ethnic by tongue
ethnic(Judged Nationality of name)	tongue(Mother Tongue (Eng or Other))
ethnic(Judged Nationality of name)	English	Other	Total
Asian	62 47.33	69 52.67	131
Middle-Eastern and Pakistani	50 69.44	22 30.56	72
Total	112	91	203

Statistics for Table of ethnic by tongue

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	1	9.1889	0.0024
Likelihood Ratio Chi-Square	1	9.3794	0.0022
Continuity Adj. Chi-Square	1	8.3164	0.0039
Mantel-Haenszel Chi-Square	1	9.1436	0.0025
Phi Coefficient		-0.2128
Contingency Coefficient		0.2081
Cramer's V		-0.2128

Fisher's Exact Test


Fisher's Exact Test
Cell (1,1) Frequency (F)	62
Left-sided Pr <= F	0.0018
Right-sided Pr >= F	0.9993

Table Probability (P)	0.0012
Two-sided Pr <= P	0.0031

Sample Size = 203

Prediction of Performance in First-year Calculus: Exploratory Sample

Ethnic by Tongue: Asians vs. East Indian

The FREQ Procedure

Table ethnic * tongue

Cross-Tabular Freq Table

Frequency Row Pct

Table of ethnic by tongue
ethnic(Judged Nationality of name)	tongue(Mother Tongue (Eng or Other))
ethnic(Judged Nationality of name)	English	Other	Total
Asian	62 47.33	69 52.67	131
East Indian	59 76.62	18 23.38	77
Total	121	87	208
Frequency Missing = 1

Statistics for Table of ethnic by tongue

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	1	17.1046	<.0001
Likelihood Ratio Chi-Square	1	17.7929	<.0001
Continuity Adj. Chi-Square	1	15.9218	<.0001
Mantel-Haenszel Chi-Square	1	17.0223	<.0001
Phi Coefficient		-0.2868
Contingency Coefficient		0.2757
Cramer's V		-0.2868

Fisher's Exact Test


Fisher's Exact Test
Cell (1,1) Frequency (F)	62
Left-sided Pr <= F	<.0001
Right-sided Pr >= F	1.0000

Table Probability (P)	<.0001
Two-sided Pr <= P	<.0001

Effective Sample Size = 208
Frequency Missing = 1

Prediction of Performance in First-year Calculus: Exploratory Sample

Ethnic by Tongue: Asians vs. Other / DK

The FREQ Procedure

Table ethnic * tongue

Cross-Tabular Freq Table

Frequency Row Pct

Table of ethnic by tongue
ethnic(Judged Nationality of name)	tongue(Mother Tongue (Eng or Other))
ethnic(Judged Nationality of name)	English	Other	Total
Asian	62 47.33	69 52.67	131
Other and DK	12 85.71	2 14.29	14
Total	74	71	145
Frequency Missing = 26

Statistics for Table of ethnic by tongue

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	1	7.4580	0.0063
Likelihood Ratio Chi-Square	1	8.2370	0.0041
Continuity Adj. Chi-Square	1	6.0010	0.0143
Mantel-Haenszel Chi-Square	1	7.4066	0.0065
Phi Coefficient		-0.2268
Contingency Coefficient		0.2212
Cramer's V		-0.2268

Fisher's Exact Test


Fisher's Exact Test
Cell (1,1) Frequency (F)	62
Left-sided Pr <= F	0.0057
Right-sided Pr >= F	0.9993

Table Probability (P)	0.0050
Two-sided Pr <= P	0.0093

Effective Sample Size = 145
Frequency Missing = 26

WARNING: 15% of the data are missing.

Prediction of Performance in First-year Calculus: Exploratory Sample

Eastern European vs. Other European

The FREQ Procedure

Table ethnic * tongue

Cross-Tabular Freq Table

Frequency Row Pct

Table of ethnic by tongue
ethnic(Judged Nationality of name)	tongue(Mother Tongue (Eng or Other))
ethnic(Judged Nationality of name)	English	Other	Total
Eastern European	40 63.49	23 36.51	63
European not Eastern	179 92.27	15 7.73	194
Total	219	38	257
Frequency Missing = 1

Statistics for Table of ethnic by tongue

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	1	31.2542	<.0001
Likelihood Ratio Chi-Square	1	27.0599	<.0001
Continuity Adj. Chi-Square	1	29.0120	<.0001
Mantel-Haenszel Chi-Square	1	31.1326	<.0001
Phi Coefficient		-0.3487
Contingency Coefficient		0.3293
Cramer's V		-0.3487

Fisher's Exact Test


Fisher's Exact Test
Cell (1,1) Frequency (F)	40
Left-sided Pr <= F	<.0001
Right-sided Pr >= F	1.0000

Table Probability (P)	<.0001
Two-sided Pr <= P	<.0001

Effective Sample Size = 257
Frequency Missing = 1

Prediction of Performance in First-year Calculus: Exploratory Sample

Eastern European vs. Middle Eastern

The FREQ Procedure

Table ethnic * tongue

Cross-Tabular Freq Table

Frequency Row Pct

Table of ethnic by tongue
ethnic(Judged Nationality of name)	tongue(Mother Tongue (Eng or Other))
ethnic(Judged Nationality of name)	English	Other	Total
Eastern European	40 63.49	23 36.51	63
Middle-Eastern and Pakistani	50 69.44	22 30.56	72
Total	90	45	135

Statistics for Table of ethnic by tongue

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	1	0.5357	0.4642
Likelihood Ratio Chi-Square	1	0.5352	0.4644
Continuity Adj. Chi-Square	1	0.3013	0.5830
Mantel-Haenszel Chi-Square	1	0.5317	0.4659
Phi Coefficient		-0.0630
Contingency Coefficient		0.0629
Cramer's V		-0.0630

Fisher's Exact Test


Fisher's Exact Test
Cell (1,1) Frequency (F)	40
Left-sided Pr <= F	0.2913
Right-sided Pr >= F	0.8199

Table Probability (P)	0.1112
Two-sided Pr <= P	0.4716

Sample Size = 135

Prediction of Performance in First-year Calculus: Exploratory Sample

Passing the course

The FREQ Procedure

Table sex * passed

Cross-Tabular Freq Table

Frequency Row Pct

Table of sex by passed
sex	passed(Passed the course)
sex	No	Yes	Total
Female	118 44.36	148 55.64	266
Male	138 48.42	147 51.58	285
Total	256	295	551
Frequency Missing = 28

Statistics for Table of sex by passed

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	1	0.9118	0.3396
Likelihood Ratio Chi-Square	1	0.9122	0.3395
Continuity Adj. Chi-Square	1	0.7559	0.3846
Mantel-Haenszel Chi-Square	1	0.9101	0.3401
Phi Coefficient		-0.0407
Contingency Coefficient		0.0406
Cramer's V		-0.0407

Fisher's Exact Test


Fisher's Exact Test
Cell (1,1) Frequency (F)	118
Left-sided Pr <= F	0.1923
Right-sided Pr >= F	0.8509

Table Probability (P)	0.0432
Two-sided Pr <= P	0.3484

Effective Sample Size = 551
Frequency Missing = 28

Table ethnic * passed

Cross-Tabular Freq Table

Frequency Row Pct

Table of ethnic by passed
ethnic(Judged Nationality of name)	passed(Passed the course)
ethnic(Judged Nationality of name)	No	Yes	Total
Asian	65 49.62	66 50.38	131
Eastern European	30 47.62	33 52.38	63
European not Eastern	88 45.13	107 54.87	195
Middle-Eastern and Pakistani	33 45.83	39 54.17	72
East Indian	31 39.74	47 60.26	78
Other and DK	27 67.50	13 32.50	40
Total	274	305	579

Statistics for Table of ethnic by passed

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	5	9.0500	0.1071
Likelihood Ratio Chi-Square	5	9.1556	0.1030
Mantel-Haenszel Chi-Square	1	0.0788	0.7789
Phi Coefficient		0.1250
Contingency Coefficient		0.1241
Cramer's V		0.1250

Sample Size = 579

Table tongue * passed

Cross-Tabular Freq Table

Frequency Row Pct

Table of tongue by passed
tongue(Mother Tongue (Eng or Other))	passed(Passed the course)
tongue(Mother Tongue (Eng or Other))	No	Yes	Total
English	187 46.52	215 53.48	402
Other	69 46.31	80 53.69	149
Total	256	295	551
Frequency Missing = 28

Statistics for Table of tongue by passed

Chi-Square Tests


Statistic	DF	Value	Prob
Chi-Square	1	0.0019	0.9652
Likelihood Ratio Chi-Square	1	0.0019	0.9652
Continuity Adj. Chi-Square	1	0.0000	1.0000
Mantel-Haenszel Chi-Square	1	0.0019	0.9652
Phi Coefficient		0.0019
Contingency Coefficient		0.0019
Cramer's V		0.0019

Fisher's Exact Test


Fisher's Exact Test
Cell (1,1) Frequency (F)	187
Left-sided Pr <= F	0.5552
Right-sided Pr >= F	0.5214

Table Probability (P)	0.0765
Two-sided Pr <= P	1.0000

Effective Sample Size = 551
Frequency Missing = 28

Table course * passed

Cross-Tabular Freq Table

Frequency Row Pct

Table of course by passed
course	passed(Passed the course)
course	No	Yes	Total
Catch-up	44 74.58	15 25.42	59
Mainstrm	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 course 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

Effective Sample Size = 471
Frequency Missing = 108

WARNING: 19% of the data are missing.

Prediction of Performance in First-year Calculus: Exploratory Sample

Sex and Grade

The GLM Procedure

Data

Class Levels


Class Level Information
Class	Levels	Values
gender	2	0 1

Number of Observations


Number of Observations Read	579
Number of Observations Used	383

Prediction of Performance in First-year Calculus: Exploratory Sample

Sex and Grade

The GLM Procedure

Dependent Variable: grade Final mark (if any)

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
gender	1	110.7945190	110.7945190	0.30	0.5870

Type III Model ANOVA


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

Box Plot

Fit Plot for Final mark (if any) by gender

Prediction of Performance in First-year Calculus: Exploratory Sample

Ethnic and Grade

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

Prediction of Performance in First-year Calculus: Exploratory Sample

Ethnic and Grade

The GLM Procedure

Dependent Variable: grade Final mark (if any)

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 (if any) by Judged Nationality of name

Prediction of Performance in First-year Calculus: Exploratory Sample

Mother tongue and Grade

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

Prediction of Performance in First-year Calculus: Exploratory Sample

Mother tongue and Grade

The GLM Procedure

Dependent Variable: grade Final mark (if any)

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 (if any) by Mother Tongue (Eng or Other)

Prediction of Performance in First-year Calculus: Exploratory Sample

Mother tongue and Grade

The GLM Procedure

Means

tongue

grade

Distribution of grade by tongue

Means


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

Prediction of Performance in First-year Calculus: Exploratory Sample

Course and Grade

The GLM Procedure

Data

Class Levels


Class Level Information
Class	Levels	Values
course	3	Catch-up Elite Mainstrm

Number of Observations


Number of Observations Read	579
Number of Observations Used	346

Prediction of Performance in First-year Calculus: Exploratory Sample

Course and Grade

The GLM Procedure

Dependent Variable: grade Final mark (if any)

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
course	2	612.6623710	306.3311855	0.84	0.4317

Type III Model ANOVA


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

Box Plot

Fit Plot for Final mark (if any) by course

Prediction of Performance in First-year Calculus: Exploratory Sample

Correlations between quantitative variables

The CORR Procedure

Variables Information


9 Variables:	hsgpa hscalc hsengl calc precalc totscore diff grade passed

Simple Statistics


Simple Statistics
Variable	N	Mean	Std Dev	Sum	Minimum	Maximum	Label
hsgpa	466	79.26910	6.03849	36939	65.00000	97.30000	High School GPA
hscalc	448	75.44420	12.19185	33799	50.00000	100.00000	HS Calculus
hsengl	480	75.83542	8.71804	36401	50.00000	96.00000	HS English
calc	480	3.31875	2.49184	1593	0	11.00000	Number calculus correct
precalc	480	4.40208	1.76216	2113	0	9.00000	Number precalculus correct
totscore	480	7.72083	3.70369	3706	0	20.00000	Total # right on diagnostic test
diff	480	18.74158	21.25534	8996	-41.41414	70.70707	Percentage correct: Precalc minus calc
grade	393	58.73791	19.18319	23084	1.00000	99.00000	Final mark (if any)
passed	579	0.52677	0.49971	305.00000	0	1.00000	Passed the course

Pearson Correlations


Pearson Correlation Coefficients Prob > \|r\| under H0: Rho=0 Number of Observations
	hsgpa	hscalc	hsengl	calc	precalc	totscore	diff	grade	passed
hsgpa High School GPA	1.00000 466	0.62249 <.0001 437	0.54327 <.0001 464	0.33876 <.0001 396	0.33965 <.0001 396	0.39002 <.0001 396	-0.05195 0.3024 396	0.58129 <.0001 337	0.45684 <.0001 466
hscalc HS Calculus	0.62249 <.0001 437	1.00000 448	0.08498 0.0749 440	0.43774 <.0001 384	0.36684 <.0001 384	0.47262 <.0001 384	-0.13979 0.0061 384	0.53272 <.0001 332	0.43152 <.0001 448
hsengl HS English	0.54327 <.0001 464	0.08498 0.0749 440	1.00000 480	0.04272 0.3917 404	0.06543 0.1893 404	0.05995 0.2293 404	0.01445 0.7722 404	0.16441 0.0022 345	0.17492 0.0001 480
calc Number calculus correct	0.33876 <.0001 396	0.43774 <.0001 384	0.04272 0.3917 404	1.00000 480	0.50135 <.0001 480	0.91133 <.0001 480	-0.60394 <.0001 480	0.36247 <.0001 346	0.34069 <.0001 480
precalc Number precalculus correct	0.33965 <.0001 396	0.36684 <.0001 384	0.06543 0.1893 404	0.50135 <.0001 480	1.00000 480	0.81309 <.0001 480	0.38685 <.0001 480	0.37834 <.0001 346	0.39230 <.0001 480
totscore Total # right on diagnostic test	0.39002 <.0001 396	0.47262 <.0001 384	0.05995 0.2293 404	0.91133 <.0001 480	0.81309 <.0001 480	1.00000 480	-0.22227 <.0001 480	0.42847 <.0001 346	0.41587 <.0001 480
diff Percentage correct: Precalc minus calc	-0.05195 0.3024 396	-0.13979 0.0061 384	0.01445 0.7722 404	-0.60394 <.0001 480	0.38685 <.0001 480	-0.22227 <.0001 480	1.00000 480	-0.06639 0.2180 346	-0.00172 0.9700 480
grade Final mark (if any)	0.58129 <.0001 337	0.53272 <.0001 332	0.16441 0.0022 345	0.36247 <.0001 346	0.37834 <.0001 346	0.42847 <.0001 346	-0.06639 0.2180 346	1.00000 393	0.75410 <.0001 393
passed Passed the course	0.45684 <.0001 466	0.43152 <.0001 448	0.17492 0.0001 480	0.34069 <.0001 480	0.39230 <.0001 480	0.41587 <.0001 480	-0.00172 0.9700 480	0.75410 <.0001 393	1.00000 579

Prediction of Performance in First-year Calculus: Exploratory Sample

Preliminary regression on grade try 1: Initial sample size is n=579

The REG Procedure

Model: MODEL1

Dependent Variable: grade Final mark (if any)

The REG Procedure

MODEL1

Fit

grade

Number of Observations


Number of Observations Read	579
Number of Observations Used	287
Number of Observations with Missing Values	292

Analysis of Variance


Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	14	46767	3340.47977	18.15	<.0001
Error	272	50062	184.05293
Corrected Total	286	96829

Fit Statistics


Root MSE	13.56661	R-Square	0.4830
Dependent Mean	60.59582	Adj R-Sq	0.4564
Coeff Var	22.38869

Note:Model is not full rank. Least-squares solutions for the parameters are not unique. Some statistics will be misleading. A reported DF of 0 or B means that the estimate is biased.

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

Dependence Equations


totscore =	calc + precalc

Parameter Estimates


Parameter Estimates
Variable	Label	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	Intercept	1	-62.36496	12.00338	-5.20	<.0001
gender		1	1.81127	1.74763	1.04	0.3009
mtongue	English vs. Other	1	-4.73479	2.19787	-2.15	0.0321
e1	Asian	1	-4.90208	2.81249	-1.74	0.0825
e2	East Eur.	1	-5.23834	3.24067	-1.62	0.1072
e3	Other Eur.	1	-3.68304	2.55945	-1.44	0.1513
e4	Mid. East & Pak.	1	-5.96859	3.23922	-1.84	0.0665
e6	Other/DK	1	-1.35234	5.64402	-0.24	0.8108
c1	Catch-up	1	5.11126	4.38522	1.17	0.2448
c3	Elite	1	-2.26101	2.93938	-0.77	0.4424
hsgpa	High School GPA	1	1.56363	0.22272	7.02	<.0001
hscalc	HS Calculus	1	0.24454	0.10413	2.35	0.0196
hsengl	HS English	1	-0.35793	0.12877	-2.78	0.0058
calc	Number calculus correct	B	0.70710	0.38573	1.83	0.0679
precalc	Number precalculus correct	B	1.78737	0.56837	3.14	0.0018
totscore	Total # right on diagnostic test	0	0	.	.	.