Independent Statistics Project at SFU. Used cluster sampling method to collect data and SAS to analyze the dataset.

1. Effect of sex and division on
exercising hours per week
Presented by Selina He

2. Introduction
• Who exercise more often?
• Do women exercise less than men?
• Do people who have more free time exercise
more often?
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3. Objective
• Focus on undergraduate students enrolled in
statistics courses in fall semester 2013 at
Simon Fraser University (SFU)
• Investigate if there is any evidence of
difference in mean exercising hours/week
between male and female students, or
between students in lower division and upper
division
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4. Materials & Methods
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300 305 330 350 430 450 485
100 101 201 203 270 285
Upper Division Classes(N=7)
Lower Division Classes(N=6)

5. Materials & Methods
• Date: Friday, Oct 25, 2013
• Questionnaire
– Circle your Gender
– How many hours per week do you exercise?
– Exercising was defined as the work done in the gym as
well as activities like jogging and brisk walk
• STAT 300: 13 feedbacks (M=4,F=9)
• STAT 201: 105 feedbacks (M=40, F=65)
• Total feedbacks: 108
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6. Materials & Methods
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• Assume every student is self-randomized to sex and
division; therefore, the data could be treated as
complete randomized design (CRD)
Female in
lower
division
Male in
upper
division
Male in
lower
division
Female in
upper
division

7. Materials & Methods
Analysis:
• Exclude students who exercise more than 15
hours/week
– 4 students (M=2, F=2) from STAT 201
– Leaves 114 students
• Two-way CRD ANOVA analysis with fixed
effects on log(hours/week)
• Pairwise comparisons with Tukey-Kramer
adjustment
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8. Fig. 1 Side-by-Side dot plot on hours/week for each
treatment group with jitters
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Results

9. Results
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Fig. 2 Profile plot on hours/week

10. Results
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Sex Division N Mean Std. Dev. Min Max
f high 8 2.9 1.9 0 5
f low 64 4.0 3.1 0 15
m high 4 4.3 2.2 1 6
m low 38 5.0 3.2 0 13
Table 1 Summary statistics on hours/week for each
treatment group
• The standard deviation is proportional to the size of its
mean
• To stabilize the variance, we performed log
transformation on hours/week
– Log(hours/week) = log( hours/week+1)

11. Results
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Table 2 Type III Effect Test
Effect F P-value
Sex 2.04 0.16
Division 0.67 0.41
Sex*Division 0.15 0.70
• No evidence of an interaction in the effects of sex
and division upon the mean log exercising
hours/week was found (F1,110 =0.15, p=0.70)

12. Results
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• There is no evidence of difference in mean log
exercising hours/week between male and female
students (F1,110 =2.04, p=0.16)
• There is no evidence of difference in mean log
exercising hours/week between students in lower
division courses and upper division (F1,110 =0.67,
p=0.41)

13. Results
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Fig. 3 Estimated mean hours/week on sex with 95%
confidence intervals

14. Results
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Fig. 4 Estimated mean hours/week on division
with 95% confidence intervals

15. Results
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Difference in
Ratio
(hours/week)
SE (Ratio) Prob
(if diff. = 0)
f-high vs. f-low 0.79 0.17 0.30
f-high vs. m-high 0.71 0.25 0.34
f-high vs. m-low 0.65 0.14 0.06
f-low vs. m-high 0.89 0.27 0.70
f-low vs. m-low 0.81 0.09 0.10
m-high vs. m-low 0.92 0.28 0.78
f vs. m 0.76 0.14 0.15
high vs. low 0.85 0.16 0.41
Table 3 Pairwise comparison of mean hours/week

16. Discussion
• For undergraduate students enrolled in
statistics courses in fall semester 2013, SFU
• No evidence that the mean hours/week differs
in sex or division
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17. Limitation
• Our sample size (N=114) may not be big
enough to detect the difference
• Assume the std. dev. of hours/week in each
treatment group is 3 hours/week
• With 80% power, alpha level 0.05
• To detect a difference of 1 hours/week in sex
– At least 285 students are needed
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18. Limitation
• Our data is not a good representative sample
• Only a few students (N=13) are sampled for
upper division
• STAT 201 is only for non-statistics and actuarial
science major students; while STAT 300 is only for
statistics and actuarial science major students
• No information about statistics and actuarial
science major students in lower division, and
non-statistics and actuarial science major
students in upper division
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19. Limitation
• Further studies with good representative
samples and increased sample size are needed
to draw a precise conclusion
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