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i =1 ◊ r is unaffected by the units of measurements
◊ The sign of r
◊ The magnitude of r NUS/FOS/DSAP 6 GEM2900 Semester 1, 2009/1010 Evaluate Strength of a Relationship
Through Correlation
√ Some features of correlation coefficient, r…
–1 ≤ r ≤ 1
A positive correlation indicates the values of the two
variables changes towards the same direction . A negative correlation indicates the values of the two
variables changes towards the opposite directions. When r = ± 1… there is a perfect linear relationship
between the two variables; (i.e.) All paired values fall
on the same straight line.
When r = 0… there is no linear relationship between the
two variables; or the best straight line through the
paired values is horizontal. NUS/FOS/DSAP 7 GEM2900 Semester 1, 2009/1010 Evaluate Strength of a Relationship
Through Correlation
Examples:
√ In an article, Marsh and Hand et al. reported that the data on
the heights of a random sample of 200 married couples in
Britain showed a correlation coefficient of 0.36.
The ages of 200 couples were also collected. The correlation
between husbands’ and wives’ age is 0.94. √ A study was conducted by Sport Illustrated magazine to study
the success rates at putting versus the distance of putt among
professional golfers. The correlation was found to be –0.94. NUS/FOS/DSAP 8 GEM2900 Semester 1, 2009/1010 Relationships Can Be Deceiving
√ Illegitimate Correlations: Outliers can substantially inflate or deflate the correlations Groups combined inappropriately may mask the
relationships
√ Correlation Does Not Imply Causation: Relationships found from observational studies can not be
reported as causal relationships A causal relationship between two variables may be
established if an experimental design is possible. NUS/FOS/DSAP 9 GEM2900 Semester 1, 2009/1010 Relationships Can Be Deceiving
Example: Pages vs. Prices of Books...
A college student recorded the number of pages and the prices
for a randomly selected books from the university bookstore.
The correlation was found to be –0.312. The fewer the pages, the more expensive the books?
Pages
104
188
220
264
336 Price
32.95
24.95
49.95
79.95
4.50 Type
H
H
H
H
S Pages
342
378
385
415
417 Price
49.95
4.95
5.99
12.50
32.95 Type
H
S
S
S
H Pages
436
458
466
469
585 Price
5.95
60.95
49.95
6.95
5.95 Type
S
H
H
S
S Missing link… A third variable NUS/FOS/DSAP 10 GEM2900 Semester 1, 2009/1010 Relationships Can Be Deceiving
Example: Dental Health vs. Heart Disease...
An article from Straits Time posted discussed the relationship
between dental health and heart disease. It was implied that some of the bacteria living in our mouth can
cause the heart disease.
The article discussed how infrequently that many Singaporean
visit the dentists, with implication that if they did this more
often they would be less likely to suffer from heart disease.
A causal link is doubtful though not impossible.
An experimental design must be conducted to reach the
conclusion of possible causal relationship NUS/FOS/DSAP 11...
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This note was uploaded on 09/12/2013 for the course SCIENCE GEM2900 taught by Professor Chen during the Fall '10 term at National University of Singapore.
 Fall '10
 CHEN

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