Statistics: Item analysis of spring 2009 midterm

Overall performance on the MS 150 Statistics midterm was strong with a course wide average success rate on the questions of 72%. That is, 57 students correctly answered 72% of the questions posed. The individual item analysis indicated strength in basic statistics, frequency tables, and calculating the slope and intercept for two variable data.

The students had more difficulty when called to make an inference, such as determining whether a z-value was an extraordinary z-value or whether a two-variable relationship was linear or non-linear.

qn	Test two spring 2009	corr	perc
1	level of measurement	43	0.75
2	sample size	56	0.98
3	minimum	57	1.00
4	maximum	57	1.00
5	range	57	1.00
6	midrange	56	0.98
7	mode	56	0.98
8	median	57	1.00
9	mean	48	0.84
10	standard deviation	57	1.00
11	coefficient of variation	48	0.84
12	width	50	0.88
13	frequency table	42	0.74
14	frequency histogram	30	0.53
15	shape of histogram	36	0.63
16	probability	15	0.26
17	z-score	16	0.28
18	inference	16	0.28
19	inference	13	0.23
20	slope	51	0.89
21	intercept	50	0.88
22	predict y given x	38	0.67
23	predict x given y	37	0.65
24	nature of relation	32	0.56
25	direction of relation	47	0.82
26	correlation r	42	0.74
27	strength of relation	43	0.75
28	coef determination	43	0.75
29	percent variation acct	23	0.40
30	inference	11	0.19

The final question, number 30, asked the students whether linearly projected y-values beyond the domain of the x-values would be valid. Given that the system was non-linear, a linear projection beyond the domain would not yield valid values. All but 11 students missed this inference.

The students excel at making basic single step calculations and do well at well-defined procedures. The students have difficulty when the task requires thinking about the data, analyzing patterns, and making judgment calls based on the data. Finding ways to help the students "step back" from the numbers and make decisions about overall patterns remains a challenge.