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Circular Descriptive Statistic for Describing Students Sleeping
Time
Cici Suhaeni, M.Si
Dr. I Made Sumertajaya
Bogor Agricultural University
(IPB)
Presented : 10th Okct 2015, ICSMTR 2015
What is circular DATA? • Representated by directions • Directions are measured by angles ranging from 0 to
360 degree. • Periodic or cyclic • Taken from compass and clock as a measuring
instrument • Circular data was taken from clock, must be convert
to angles • Circular data is taken from compass : wind direction
and directions of migrating bird • Circular data is taken from the clock : arrival time
Number line
Linear Data
-∞ ∞ 0 -1 1 ... ...
Circular Data
Linear and Circular Data
Circle
Treat the
circular
data as
linear data
is not
relevant.
Why MUST CIRCULAR STATISTICS?
Ex :
Data : 30° and 300° Mean =...? Linear : mean = 165 Circular :
Mean direction =−15°
𝛼 0 = arctanS
C
S = sin𝛼𝑖
𝑛
𝑖=1
C = cos𝛼𝑖
𝑛
𝑖=1
Mean ≠ mean direction
Descriptif Statistic
Statistic Linear Circular
Central tendency
Mean Mean direction
Median Median direction
Dispersion Variance Circular Variance Concentration Parameter
Why does students sleeping time?
• The sleep quality of college students seems poor, and going to Participation
Exercises Class turns out to be main way of doing exercise (Chang S.P et al,
2013).
• There is correlation between duration of sleep with academic performance.
The students with adequate sleep have a high academic performance
(Marpaung et al, 2013)
• Amount of sleep per night have positive correlation with GPA of college
students (Lowry, M. et al, 2010)
• Short sleepers have lower overall grade-point averages than did long
sleepers (Kelly, W.E. et al, 2001)
• Hours of sleep is associated with a variety of health-risk behaviors
(McKnight_Eily et al, 2011)
Sleep problem is very important to be discussed
In the previous studies about “sleeping” case,
the measured variable generally is the
duration or quality of sleep. So, make sleeping
time as a variable is a special issue in the
statistical analysis world. This variable is a
different perspective in view of the quality of
one’s sleep.
Studying sleeping time by circular statistics is something interesting and important..
Why does Descriptive Statistics?
•Studies on the circular statistics have not been so much done
•Start the study from the simple method : descriptive statistics
The purpose of this Study
To apply circular descriptive statistics for describing students sleeping time.
To compare circular descriptive statistic and linear descriptive statistic.
Data
Generated from Von Mises Distribution
For small(k=0.05) ,
middle (k=5) ,
big kappa (k=20)
Simulation Data
Student sleeping time
Bachelor students in 5th semester from Dept. of Statistics IPB
Real Data
Convert time to angle
𝛼° =𝑥
𝑘× 360°
1 hour = 15o 1o = 4 minutes
Jam Derajat
0 0
1 15
3 45
6 90
12 180
18 270
21 315
24 360
Description of Simulation Data
Circular data plot and rose diagram for simulation data with mean direction 0 and kappa 0,05, n=100
Circular data plot and rose diagram for simulation data with mean direction 0 and kappa 20, n=100
For small concentration
parameter, data spread around the
circle
For large concentration
parameter, data gather in certain point in the circle
Comparation between linear statistic and circular statistic
→ Mean direction
→ Mean
→ Median direction
→ Median
(i) n=10, 𝜅 = 0.05 (ii) n=10, 𝜅 = 5 (iii) n=10, 𝜅 = 20
(iv) n=100, 𝜅 = 0.05 (v) n=100, 𝜅 = 5 (v) n=100, 𝜅 = 20
Analyze circular data using linear statistics is not very very relevant.
So, use circular statistics to analyze circular data!
Description of Students Sleeping Time
Statistic
All Female Male
Circular Time Circular Time Circular Time
mean
direction 351.103 11:24 pm 351.493 11:26 pm 350.186 11:21 pm
mean 245.176 04:20 pm 240.500 04:02 pm 256.359 05:05 pm
median
direction 345 23.000 345 23.000 345 23.000
concentration
parameter 12.647 11.269 18.062
circular
varians 0.040 0.045 0.028
Conclusion
• Linear descriptive statistic have very different value with circular linear statistic. So, use circular statistics to analyze circular data.
• Mean of sleeping time of 5th semester students from Dept. of Statistics IPB is at 11:24 pm, the female students is at 11:26 pm, and the male students is 11:21 pm.
• Variability of sleeping time data is relative large.
Reference
• Chang, S.P., Huang, S.C., Chen, Y.H., Wright, R., Lung-Chuan, Liao. The relationship between Sleep
Quality and the Exercise Participation Behavior of College Students in the Central Taiwan Region.
International Journal of Sport and Exercise Science (2013), 5(2): 13-18.
• Fisher NI. 1995. Statistical Analysis of Circular Data. Cambridge : Cambridge University Press.
• Jammalamadaka SR, SenGupta A. 2001. Topics in Circular Statistics. Singapore: World Scientific.
• Lowry, M., Dean, K., and Manders, K. The Link Between Sleep Quality and Academic Performance for
the College Student. Sentience : The University of Minnesota Undergraduate Journal of Psychology
(2010), Volume 3.
• Mardia KV, Jupp PE. 2000. Directional Statistics. West Sussex : John Wiley & Sons.
• Marpaung, P.P, Supit, S., and Nancy, J. Gambaran Lama Tidur terhadap Prestasi Belajar Siswa.
Journal e-Biomedik(eBM), Volume 1 Nomor 1, Maret 2013, hlm. 543-549.
• McKnight-Eily, L.R., Eaton, D.K, Lowry, R., Croft, J.B., Presley-Cantrell, L., and Perry, G.S. Relationship
between Hours of Sleep and Health-risk Behaviors in US Adolescent Students. Preventive Medicine
(2011), doi: 10.1016/j.ypmed.2011.06.020.