Representativeness in Statistical Reasoning: Identifying and Assessing Misconceptions

Figures & data

Table 1. Distribution of Participants' Majors

Major	n	Percent
Psychology	69	26.2
Social Sciences	48	18.3
Natural/Physical Sciences	34	12.9
Engineering	32	12.2
Education	27	10.3
Statistics	20	7.6
Food Science/Nutrition	12	4.6
Pharmacy/Health	11	4.2
Non-Matriculated/Other	10	3.8
Total	263	100%

Table 2. Distribution of Correct Responses

# Correct Responses	n	Percent	Cumulative Percent
0	2	0.8	0.8
1	5	1.9	2.7
2	10	3.8	6.5
3	13	4.9	11.4
4	8	3.0	14.4
5	11	4.2	18.6
6	17	6.5	25.1
7	16	6.1	31.2
8	11	4.2	35.4
9	20	7.6	43.0
10	22	8.4	51.0
11	19	7.2	58.2
12	23	8.7	66.9
13	33	12.4	79.3
14	53	20.2	99.5

Table 3. Distribution of Misconception Responses

# Misconception Responses	n	Percent	Cumulative Percent
0	93	35.4	35.4
1	28	10.6	46.0
2	21	8.0	54.0
3	24	9.1	63.1
4	14	5.3	68.4
5	22	8.4	76.8
6	21	8.0	84.8
7	13	4.9	89.7
8	9	3.4	93.1
9	3	1.1	94.2
10	10	3.8	98.0
11	2	0.8	98.8
12	1	0.4	99.2
13	1	0.4	99.6
14	1	0.4	100.0

Table 4. Item Characteristics of Test Questions

Question #	Type of Item	Difficulty: Proportion Correct	Misconception Responses (%)
1 a	open-ended	.97
1 b	open-ended	.87
1 c	open-ended	.86
2 a	open-ended	.94
2 b	open-ended	.78
2 c	open-ended	.79
3	multiple-choice	.79	5
4	multiple-choice	.81	8
5	multiple-choice	.81	10
6	multiple-choice	.81	10
7	multiple-choice	.44	29
8	multiple-choice	.48	31
9	multiple-choice	.68	26
10	multiple-choice	.61	33
11	multiple-choice	.61	35
12	multiple-choice	.57	41
13	multiple-choice	.75	21
14	multiple-choice	.73	20
15	multiple-choice	.68	30
16	multiple-choice	.76	13

Table 5. Test Performance (Pass/Fail) and Formal Experience with Probability and Statistics

	Test Performance
Number of Statistics Courses	Passed (%)	Failed (%)	Total
0	13 (32%)	28 (68%)	41
1	68 (45%)	82 (55%)	150
2	20 (59%)	14 (41%)	34
3 or more	27 (71%)	11 (29%)	38
Total	135	128	263

Table 6. Misconceptions of Representativeness and Formal Experience with Probability and Statistics

	Misconceptions
Number of Statistics Courses	Yes (%)	No (%)	Total
0	28 (68%)	13 (32%)	41
1	87 (58%)	63 (42%)	150
2	15 (44%)	19 (56%)	34
3 or more	12 (32%)	28 (68%)	38
Total	135	128	263