Essential Mathematical Skills for Introductory Statistics Students

Essential Mathematical Skills for Introductory Statistics

Students

Roger E. KirkTomas P. Carpenter

Department of Psychology & NeuroscienceBaylor 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 operations8. –5 + 2 = ________

10. –6 –3 = ________14. 10/(–2) = ________ 26. 3–2 = ( )/( )( )

29. Factor X 2 – 2XY + Y

2 =30. Factor pn – p = 32. 0! =

Table 2. Continued Remove the parentheses

33. X + (Y – Z) = ____________35. nS(1 – R2) = ____________ 36. (X – Y)S + M = ____________

Solve the equations and inequalities37. 3X – 6 = 12 X = _________42. R = ____________43. b = ____________ 44. X =[(n – 1)S]/b S = ____________45. 2X – 1 < 3 X < _________

S =R / 2n

S =a 1−b2

46. −3<

16−X7

<5 < X < ____________

Table 3. Performance of 3,281 Students on the Ten Most Difficult Items

Item Solve for or Fill In % Incorrect

43. S =a 1−b2 b = 75%

32. 0! = 71%

46. −3<

16−X7

<5 < X < 66%

47. −z<

X −MS

< z < M < 65%

28. 3 15 48% = ( )15

Table 3. Continued

Item Solve for or Fill In % Incorrect

b ≥ 42%

= 40%

39%

= 37%

48. [(n −1)S] / b≤X

16. 9 / 0

26. 3−2

29. Factor X 2 −2XY+Y2

27. 32 / 34 46%

=( ) / ( )( )

=( )( )

Table 4. Performance of 3,281 Students on the Ten Easiest Items

Item Solve for or Fill In % Incorrect

8. −5+2 = 3%

10. −6−3 = 4%

14. 10 / (−2) = 4%

11. 5−(−1) = 5%

13. (−2)(−6) = 6%

Table 4. Continued

Item Solve for or Fill In % Incorrect

= 7%

X = 8%

= 9%

= 10%

12. −9−(−4)

37. 3X −6 =12

23. ( X )( X )2

9. 3−2+4−8 = 6%

15. 0 / 6

Table 5. Ten Best Predictors of Course Performance

Item Solve for or Fill In Point Biserial r

b ≥ .26 48. [(n −1)S] / b≤X

.25 26. 3−2 =( ) / ( )( )

.25 25. 2−1 =( ) / ( )

X = .24 41. Y =a+bX

43. S =a 1−b2 b = .24

Table 5. Continued

Item Solve for or Fill In Point Biserial r

47. −z<

X −MS

< z < M < .22

= .22 29. Factor X 2 −2XY+Y2

= .23 30. Factor np −p

X = .23

27. 32 / 34 .23 =( )( )

40. z =(X −Y)/ S

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.

Mea

n M

ath

Ski

lls T

est

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

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.

Mea

n M

ath

Ski

lls T

est F 1994 S 1997

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