How Much Math Do Students Need to Succeed in Business and Economics Statistics? An Ordered Probit Analysis

Figures & data

Table 1. Grade Distribution for Students Enrolled in Business Statistics: Fall 2001 — Summer 2006

Grade	Percent of Total Grades	Cumulative Percent (F to A)
A- To A	21.10 %	100 %
B- to B+	28.64	78.91
C- to C+	25.16	50.28
D- to D+	13.88	25.12
F	11.24	11.24
Number of Students	2162

Table 2. MATHS Course Sequences for Business Statistics Students

Prerequisite Sequences			Acceptable Alternative Sequences
Prior to Fall 2004	Fall 2004 — Spring 2005 ^12	Spring 2005 — Summer 2006	Throughout the Entire Period
108	108	108	108 (or 111)	108
131	131	135	112	111
132			161	112
				165
Number of Students in Our Study Who Used Each Sequence
929	277	241	179	58

Table 3. Alternative Math Courses and Topics

A. Preliminary Math Courses
Topic	MATHS
	108	111	112
Factoring	X
Quadratic equations	X	X
Inequalities	X	X
Relations and functions	X
Rational exponents	X
Systems of linear systems	X	X
Exponential and logarithmic functions	X	X
Determinants		X
Mathematical induction		X
Binomial theorem		X
Permutations, combinations and progressions		X
Trigonometric functions, identities and equations			X
Graphs of trigonometric and inverse trigonometric			X
Solution of right and general triangles			X
Polar coordinates			X
Complex numbers			X

B. Alternative Prerequisite/Acceptable Math Courses for Business Statistics
Topic	MATHS
	131	132	135	161	165
Mathematics of finance	X		X
Probability	X		X
Matrix algebra	X
Linear programming
Differential calculus		X	X	X	X
Integral calculus		X		X	X

Table 4. Ordered Probit Estimated Business Statistics Grade Equation

Dependent Variable: STAT

Included Observations: 1684

variable	Coefficient ^24	Std. Error	z-Statistic	Prob.
D131	0.067	0.221	0.302	0.763
D135	−0.304	0.256	−1.188	0.235
D161	0.056**	0.276	0.203	0.839
D165	1.742*	0.478	3.642	0.000
MATH	0.275*	0.044	6.300	0.000
D131M	−0.053	0.083	−0.634	0.526
D135M	0.095	0.100	0.941	0.347
D161M	0.071**	0.100	0.715	0.475
D165M	−0.550*	0.179	−3.077	0.002
GPA	1.057*	0.095	11.067	0.000
ACC	0.196*	0.039	4.970	0.000
ECON	0.106*	0.041	2.584	0.010
SUMMER	0.639*	0.087	7.343	0.000
Limit Points
LIMIT_1:C(14)	3.072	0.192	15.982	0.000
LIMIT_2:C(15)	3.782	0.195	19.428	0.000
LIMIT_3:C(16)	4.717	0.203	23.256	0.000
LIMIT_4:C(17)	5.889	0.216	27.269	0.000
Pseudo R-squared	0.178	Akaike info criterion		2.559
Schwarz criterion	2.614	Log likelihood		−2137.907
Hannan-Quinn criter.	2.580	Restr. log likelihood		−2600.528
LR statistic	925.242	Avg. log likelihood		−1.270
Prob(LR	0.000

Table 5. Model Predictions for Values of the Dependent Variable STAT

Estimates from Probit Model
Dep. Value	Obs.	Correct	Incorrect	% Correct	% Incorrect
0	176	63	113	35.795	64.205
1	231	0	231	0.000	100.000
2	418	196	222	46.890	53.110
3	501	267	234	53.293	46.707
4	358	214	144	59.777	40.223
Total	1684	740	944	43.943	56.057

Table 6. Predicted Probabilities of Statistics Grades for Alternative Math Courses and Grades

	MATHS 131	Grade in MATHS 131
Stat Grades	Overall	A- to A	B- to B+	C- to C+	D- to D+
A- to A	15.54 %	41.13 %	17.07 %	7.17 %	2.15 %
B- to B+	29.67	37.95	35.96	25.90	13.66
C- to C+	27.28	15.70	28.22	32.05	27.30
D- to D+	15.08	3.97	12.05	19.58	24.73
F	12.44	1.24	6.70	15.30	32.16
Number	277	45	101	89	42

	MATHS 135	Grade in MATHS 135
Stat Grades	Overall	A- to A	B- to B+	C- to C+	D- to D+
A- To A	18.34 %	54.61%	24.95 %	8.24 %	2.15 %
B- to B+	29.57	31.53	37.94	27.40	13.45
C- to C+	25.92	10.37	22.55	31.21	26.52
D- to D+	14.24	2.58	8.90	18.36	24.42
F	11.93	0.91	4.67	14.80	33.46
Number	241	31	68	119	23

	MATHS 132	Grade in MATHS 132
Stat Grades	Overall	A- to A	B- to B+	C- to C+	D- to D+
A- To A	20.04 %	48.22 %	22.96 %	8.43 %	2.81 %
B- to B+	29.70	35.02	36.50	27.13	16.42
C- to C+	25.24	12.61	25.11	31.35	29.22
D- to D+	13.79	3.10	10.12	18.56	24.03
F	11.23	1.05	5.31	14.53	27.52
Number	929	194	272	305	158

	MATHS 161	Grade in MATHS 161
Stat Grades	Overall	A- to A	B- to B+	C- to C+	D- to D+
A- To A	36.85 %	64.25 %	40.32 %	19.77 %	4.44 %
B- to B+	32.13	27.08	38.38	34.37	19.00
C- to C+	17.89	6.95	16.00	26.16	28.77
D- to D+	7.60	1.34	4.03	12.00	22.41
F	5.52	0.38	1.27	7.70	25.39
Number	179	47	62	50	20

	MATHS 165	Grade in MATHS 165
Stat Grades	Overall	A- to A	B- to B+	C- to C+	D- to D+
A- To A	30.71 %	40.65 %	32.63 %	27.44 %	23.01 %
B- to B+	37.74	39.84	36.71	37.04	42.72
C- to C+	20.96	15.30	20.00	22.78	24.89
D- to D+	7.25	3.36	7.15	8.55	7.17
F	3.34	0.85	3.51	4.18	2.20
Number	58	7	23	23	5

Table 7. Marginal Impacts of a One-Unit Change in Selected Explanatory Variables on the Probabilities of the Business Statistics Grade ³⁴

Stat Grade	GPA	D131	D135	D161	D165
A- to A	22.82 %	−4.50 %	−1.70 %	16.81 %	10.67 %
B- to B+	19.26	−.03	−.13	2.43	8.04
C- to C+	−16.47	2.04	.68	−7.35	−4.28
D- to D+	−15.82	1.29	.45	−6.19	−6.54
F	−9.79	1.21	.70	−5.71	−7.89

Table A1: Variables and Definitions Used in Ordered Probit Model

Dependent Variable:

STAT: An ordered index (F = 0; D- to D+ = 1; …; A- to A = 4) for the grade that the student received the first time that he/she completed ECON 221.

Independent Variables:

ACC: The numeric grade (F = 0, D- = .7, …, A- = 3.7, A = 4) that the student received in the principles of accounting course taken prior to first completion of ECON 221.

ECON: The numeric grade (F = 0, D- = .7, …, A- = 3.7, A = 4) that the student received in the principles of microeconomics course taken prior to first completion of ECON 221.

MATH: The numeric grade (F = 0, D- = .7, …, A- = 3.7, A = 4) that the student received in the relevant prerequisite math class.

GPA: The student's cumulative GPA in the semester prior to first completion of ECON 221.

D131: A dummy variable identifying whether the student took MATHS 131 as the prerequisite math course for ECON 221 (Yes = 1; 0 otherwise).

D135: A dummy variable identifying whether the student took MATHS 135 as the prerequisite math course for ECON 221 (Yes = 1; 0 otherwise).

D161: A dummy variable identifying whether the student took MATHS 161 as the prerequisite math course for ECON 221 (Yes = 1; 0 otherwise).

D165: A dummy variable identifying whether the student took MATHS 165 as the prerequisite math course for ECON 221 (Yes = 1; 0 otherwise).

D131M: An interaction term for MATHS 131 (D131M = D131 × MATH).

D135M: An interaction term for MATHS 135 (D135M = D135 × MATH).

D161M: An interaction term for MATHS 161 (D161M = D161 × MATH).

D165M: An interaction term for MATHS 165 (D165M = D165 × MATH).

Summer: A seasonal dummy variable for the term in which ECON 221 was first taken (summer = 1; 0 otherwise).