Assessment of Materials for Engaging Students in Statistical Discovery

Figures & data

Table 1: Activities, Learning Objectives, and Assessment Items

		Assessment Items
Activity	Learning Outcomes	Year 1	Year 2
#2	Distributions and Numerical Summaries	Exam 1: Q1 & Q2	Exam 1: Q1 & Q2
#2	The Normal Model	Exam 1: Q3 & Q4	Exam 1: Q3 & Q4
#3	Regression and correlation	Exam 2: Q1	Exam 2: Q1
#5	Experimental design	Exam 2: Q2	Exam 2: Q2
#3, #5	Connect experimental design with regression and correlation	Project	Project

Table 2: ACT Math Scores

Year 1
Group			Number	Mean	Std. Dev.
Experimental	A		20	29.95	1.701
Control: H M	A		39	28.97	2.134
Control: Reg		B	48	21.90	3.068
Year 2
Group			Number	Mean	Std. Dev.
Experimental	A		16	30.00	2.191
Control: H M	A		17	29.35	1.539
Control: Reg		B	39	21.74	3.354

Table 3: Year 1 Overall Measure of Student Performance (54 pts max)

Group			Number	Mean	Std. Dev.
Experimental	A		20	40.35	5.29
Control: H M	A		39	39.90	5.60
Control: Reg		B	48	31.23	8.11

Table 4: Year 1 ANCOVA Results for Overall Measure of Student Performance

R^2	Significant Variable	Coefficient	P-value
55.9%	ACT Math	0.7439	<0.0001
	Cumulative College GPA	5.5152	<0.0001
	Pretest Skill 1	1.7416	0.0205

Table 5: Year 1 - Distributions & Numerical Summaries (Exam 1, Questions 1 and 2 combined, out of 18 points).

Group			Number	Mean	Std. Dev.
Experimental		B	20	13.45	1.432
Control: H M	A		39	16.05	1.849
Control: Reg		B	48	13.33	4.184

Table 6: Year 1 - Normal model (Exam 1, Questions 3 and 4 combined, out of 6 points).

Group			Number	Mean	Std. Dev.
Experimental	A		20	4.60	1.465
Control: H M	A		39	4.15	1.461
Control: Reg		B	48	2.04	1.701

Table 7: Year 1 - Regression (Exam 2, Question 1, out of 20 points)

Group				Number	Mean	Std. Dev.
Experimental	A			20	14.20	3.172
Control: H M		B		39	11.77	3.232
Control: Reg			C	48	9.21	3.984

Table 8: Year 1 - Experiments (Exam 2, Question 2, out of 10 points)

Group			Number	Mean	Std. Dev.
Experimental	A		20	8.10	1.373
Control: H M	A		39	7.92	1.707
Control: Reg		B	48	6.65	1.564

Table 9: Year 1 - ANCOVA Models

Assessment	R^2	Significant Variable	Coefficient	P-value
Distributions Numerical Summaries	29.3%	Group(C-E) ACT Math Cummulative College GPA	1.5496 0.2925 1.7616	0.0001 0.0006 0.0010
Normal Model	45.8%	ACT Comp ACT Math Pretest Skill 2	0.1665 0.1210 0.6120	0.0028 0.0151 0.0374
Regression	46.9%	Group(C-E) ACT Math Cumulative College GPA Pretest Skill 1	−0.8791 0.2130 2.6132 1.1296	0.0374 0.0080 <0.0001 0.0070
Experiments	18.9%	Cumulative College GPA Pretest Skill 3	0.7444 0.2619	0.0068 0.0057

Table 10: Year 1 Project Results (out of 50 points)

Group				Number	Mean	Std. Dev.
Experimental	A			7	46.36	2.48
Control: H M		B		28	40.38	5.82
Control: Reg			C	18	36.25	8.36

Table 11: Year 2 Overall Measure of Student Performance (out of 45 points)

Group				Number	Mean	Std. Dev.
Experimental	A			16	40.06	2.48
Control: H M		B		17	34.71	5.88
Control: Reg			C	39	27.99	7.86

Table 12: Year 2 ANCOVA Results on Overall Measure of Student Performance

R^2	Significant Variable	Coefficient	P-value
60.53%	Group(C-E) ACT Math Cumulative College GPA	−1.8602 0.7858 3.9522	0.0474 <0.0001 0.0015

Table 13: Year 2 - ANOVA Results

Distributions and Numerical Summaries (Exam 1, Questions 1 & 2, out of 16 points)
Group			Number	Mean	Std. Dev.
Experimental	A		16	13.66	1.62
Control: H M	A		17	12.53	2.54
Control: Reg		B	39	9.28	3.22
Normal Model (Exam 1, Questions 3 & 4, out of 10 points)
Group			Number	Mean	Std. Dev.
Experimental	A		16	9.72	0.55
Control: H M	A		17	8.76	2.36
Control: Reg		B	39	6.90	2.98
Regression (Exam 2, Question 1, out of 12 points)
Group			Number	Mean	Std. Dev.
Experimental	A		16	10.38	1.16
Control: H M		B	17	7.53	2.05
Control: Reg		B	39	6.51	2.42
Experiments (Exam 2, Question 2, out of 7 points)
Group			Number	Mean	Std. Dev.
Experimental	A		16	6.31	0.57
Control: H M	A	B	17	5.88	0.91
Control: Reg		B	39	5.29	1.29

Table 14: Year 2 - ANCOVA Results}

Assessment	R^2	Significant Variable	Coefficient	P-value
Distributions and Numerical Summaries	58.1%	ACT Math Pretest Skill 3	0.3836 0.5443	<0.0001 0.0142
Normal Model	34.4%	Cummulative College GPA Pretest Skill 3	1.2015 0.7739	0.0102 <0.0001
Regression	52.6%	Group (C-E) Cumulative College GPA	−1.3614 1.9991	<0.0001 <0.0001
Experiments	21.8%	ACT Math Cumulative College GPA	0.0642 0.5534	0.0229 0.0147

Table 15: Year 2 Project Results (out of 50 points)

Group			Number	Mean	Std. Dev.
Experimental	A		6	38.67	4.46
Control: H M	A		10	31.80	8.57
Control: Reg	A		11	33.91	8.95

Table 16: Year 2 SATS Survey Results

		Pre-course				Post-course
SATS Component	Group			Mean	Std. Dev			Mean	Std. Dev.
Affect	Experimental Control: H M Control: Reg	A A	B	5.04 4.91 4.03	1.02 0.79 1.02	A A	B	5.43 5.25 3.97	1.11 0.92 1.27
Cognitive Competence	Experimental Control: H M Control: Reg	A A	B	5.57 5.84 4.97	0.71 0.75 0.90	A A	B	5.83 5.98 4.69	0.93 0.67 1.20
Value	Experimental Control: H M Control: Reg	A	B B	5.74 5.11 4.94	0.77 0.93 0.89	A A	B	5.42 5.15 4.52	0.88 1.14 1.01
Difficulty	Experimental Control: H M Control: Reg	A A A		3.95 4.27 3.89	0.62 0.63 0.61	A A A		4.28 4.44 3.86	0.72 0.77 1.00
Interest	Experimental Control: H M Control: Reg	A	B B	5.36 4.53 4.19	1.08 1.14 1.09	A A	B	5.02 4.56 3.73	1.42 1.43 1.34
Effort	Experimental Control: H M Control: Reg	A A	B	6.25 5.66 6.31	0.94 0.75 0.69	A A	B B	5.75 5.33 6.04	0.90 0.69 1.10

Table 17: Year 2 ANCOVA Model with SATS

Significant Variable	Coefficient	P-value
Group(C-E) ACT Math Cumulative College GPA Post Cognitive Competence	−2.0865 0.4703 3.2214 2.2945	0.0168 0.0094 0.0052 0.0006

Table

Day	Temp	Day	Temp	Day	Temp	Day	Temp	Day	Temp
1	52	7	26	13	35	19	16	25	27
2	60	8	31	14	40	20	23	26	21
3	34	9	26	15	38	21	46	27	15
4	21	10	31	16	34	22	19	28	5
5	11	11	49	17	34	23	53	29	2
6	16	12	45	18	27	24	25	30	2
								31	14