### 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.