Essential Mathematical Skills for Introductory Statistics Students Roger

Essential Mathematical Skills for Introductory Statistics Students Roger E. Kirk Tomas P. Carpenter Department of Psychology & Neuroscience Baylor University

Attitudes Toward Taking A Statistics Class “When I realized that I had to take this course, I. . . ” was scared panicked. I have heard horror stories about this course. wanted to die knew I’d have to take it twice Didn’t understand what it had to do with psychology Didn’t have any idea what to expect. Everyone has told me that it’s a killer.

nervous but interested knew it would be hard dreaded it, because of the rumors I heard about the class was apprehensive about the grading scale knew I’d be facing a challenge wanted to cry Wasn’t too thrilled thought that if I wanted to be a psychologist I would have to take it and suffer through it was frightened

Table 2. Representative Items In the Math Skills Test Round the following numbers to three digits 1. 2. 576 = ____ 3. 1. 645 = ____ 6. 16. 25 = ____ Perform the following basic operations 8. – 5 + 2 = ____ 10. – 6 – 3 = ____ 14. 10/(– 2) = ____ 26. 3– 2 = ( )/( )( 29. Factor X 2 – 2 XY + Y 2 = 30. Factor pn – p = 32. 0! = )

Table 2. Continued Remove the parentheses 33. X + (Y – Z) = ______ 35. n. S(1 – R 2) = ______ 36. (X – Y)S + M = ______ Solve the equations and inequalities 37. 3 X – 6 = 12 X = _____ 42. R = ______ 43. b = ______ 44. X =[(n – 1)S]/b S = ______ 45. 2 X – 1 < 3 X < _____

Table 3. Performance of 3, 281 Students on the Ten Most Difficult Items Item Solve for or Fill In % Incorrect b= 75% = 71% <X< 66% <M< 65% 48%

Table 3. Continued Item Solve for or Fill In % Incorrect 46% b≥ 42% = 40% 39% = 37%

Table 4. Performance of 3, 281 Students on the Ten Easiest Items Item Solve for or Fill In % Incorrect = 3% = 4% = 5% = 6%

Table 4. Continued Item Solve for or Fill In % Incorrect = 6% = 7% X= 8% = 9% = 10%

Table 5. Ten Best Predictors of Course Performance Item Solve for or Fill In b≥ Point Biserial r. 26. 25 X= . 24 b= . 24

Table 5. Continued Item Solve for or Fill In Point Biserial r = . 23 X= . 23 <M< . 22 = . 22

Mean Math Skills Test Academic Term Figure 1. Math test means are shown on the Y axis. The X axis is fall and spring semesters beginning in fall 1990 and ending in fall 2011. Error bars are 95% confidence intervals.

Figure 2. Effects of requiring a rigorous math prerequisite on course performance and Math Skills scores.

Mean Math Skills Test F 1994 S 1997 Academic Term Figure 3. The vertical lines at fall 1994 and spring 1997 define the years when a the rigorous math course was required for all psychology majors.

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