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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