Lecture slides for HFS3283

1. KNOWLEDGE FOR THE BENEFIT OF HUMANITYKNOWLEDGE FOR THE BENEFIT OF HUMANITY
BIOSTATISTICS (HFS3283)
CORRELATION
Dr.Dr. MohdMohd RazifRazif ShahrilShahril
School of Nutrition & DieteticsSchool of Nutrition & Dietetics
Faculty of Health SciencesFaculty of Health Sciences
UniversitiUniversiti SultanSultan ZainalZainal AbidinAbidin
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2. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Topic Learning Outcomes
At the end of this lecture, students should be able to;
• identify types of correlation analysis and when they are
used.
• explain assumptions to be met when using Pearson and
Spearman correlation.
• perform Pearson and Spearman correlation analysis
using SPSS.
• explain how to interpret the SPSS outputs from Pearson
and Spearman correlation analysis.
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3. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Correlation
• A measurement of the magnitude and direction
of two numerical variables
• The estimated correlation value may not be
100% accurate but the stronger is the
relationship, the more accurate the estimate.
• Involves mainly observation of a certain
relationship
– No control of manipulation imparted
– E.g. what is the correlation between sleeping hours
and BMI among UniSZA students
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4. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Aims for correlation
• To show three (3) important aspects involved in
an association:
– Type of correlation
– Direction of correlation
– Magnitude of correlation
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5. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Uses of correlation
• Prediction
– E.g. The SPM Trial exam results are used as selection
criteria into universities
• Validity
– To ensure an instrument measures what it should measure
– E.g. new digital thermometer vs. clinic thermometer
• Reliability
– To ensure an instrument always give consistent reading (if
other parameters are stable)
• Theory verification
– E.g. is it true that a relationship exists between an
individual’s IQ level and their brain size.
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6. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Bivariate distribution
• A distribution showing the association between
two (2) numerical variables
• Usually illustrated via the Scatter diagram/ plot
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7. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Pearson’s r
• The Pearson’s correlation coefficient, r provides
the magnitude of a correlation.
• According to Pearson’s mathematical procedure,
a correlation is linear.
• r ranges from 0 (no correlation) to +/- 1.0
(strongest correlation)
– The higher the value of r, the stronger is the
magnitude of correlation
– The symbols + or – indicate the direction of the
correlation
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8. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Characteristics of r
• Describes only linear correlation
• Sensitive towards variability (spread) and range
• Can be influenced by sampling variation
• Can be influenced by extreme/ outlier values
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9. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Types of correlation
• Three main types;
– Positive correlation (r = + ; variables change in the
same direction)
– Negative correlation (r = - ; variables change in the
opposite direction)
– Zero correlation (r = 0 ; both variable show no
association and direction)
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10. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Types of correlation (cont.)
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11. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Types of correlation (cont.)
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12. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Interpretation
• A relationship exits between two variables; X & Y
• Does not mean any change in X will also alter Y
• Does not involve causal relationship (e.g. X causes Y to
occur)
• If r = 0.50 does not mean 50% relationship
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13. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Interpretation (cont.)
CorrelationCorrelation InterpretationInterpretation
--1.00 to1.00 to --0.760.76 Strong negative correlationStrong negative correlation
--0.510.51 toto --0.750.75 Good negative correlationGood negative correlation
--0.50 to0.50 to --0.260.26 Fair negative correlationFair negative correlation
--0.25 to 0.010.25 to 0.01 Poor negative correlationPoor negative correlation
00 No correlationNo correlation
0.010.01 to 0.25to 0.25 Poor positive correlationPoor positive correlation
0.26 to 0.500.26 to 0.50 Fair positive correlationFair positive correlation
0.51 to 0.750.51 to 0.75 Good positive correlationGood positive correlation
0.76 to 1.000.76 to 1.00 Strong positive correlationStrong positive correlation
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14. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Linear vs. Non-linear correlation
• Not all correlations are linear
• Sometimes correlation can be non-linear e.g.
Curvilinear
– Score are concentrated on a curved line
• The Pearson’s coefficient is not suitable to
quantify this relationship
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15. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Linear vs. Non-linear correlation
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Positive linear
r = 0.82
Negative linear
r = -0.70
Independent
r = 0.00
Curvilinear
r = 0.00
Curvilinear
r = 0.00

16. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Simple example on correlation
• Research Question: Is sleeping duration (hrs)
correlated with exam score (marks)?
• Null Hypothesis: There is no correlation between
sleeping duration (hrs) and exam score (marks)
• Results: If r = -0.89; p < 0.05; n = 220
• Interpretation: The correlation is negative i.e. as
the sleeping duration increase, the exam score
will decrease and vise versa.
– The large magnitude of correlation (nearing 1.00)
means the association is strong
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17. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Assumptions
• The data is drawn from a random sample of
population.
• The data is independent observation to each
other.
• The variables of interest are having bivariate
normal distribution.
• The relationship between the two variables
must be linear.
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18. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Assumption 3 – Linearity
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19. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Assumption 3 – Linearity (cont.)
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20. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Assumption 3 – Linearity (cont.)
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The relationship between the two variables is linear
based on the elliptical shape.

21. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
If assumptions are not met?
• If both variable does not meet all assumptions,
then use Spearmen’s correlation analysis.
– Values obtained would be Spearmen’s correlation
coefficient  (rho).
• If any one of the variable meet all assumption,
proceed with Pearson’s correlation analysis
– Values obtained is Pearson’s correlation coefficient r.
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22. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Correlation in SPSS
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For normal distribution, we can use Pearson’s test.
For non-normal distribution, we can proceed to Spearman’s test.

23. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
SPSS Output
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24. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
SPSS Output Interpretation
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• In correlation, look at the correlation coefficient
which is the strength of relationship instead of
the p value.
– Even though the coefficient is weak, the p value is
usually significant depending upon the sample size.
• In this analysis the p value is < 0.05, therefore
we reject the null hypothesis.

25. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
SPSS Output Interpretation (cont.)
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• There is a significant (linear) correlation between
sleeping duration and exam score (p< 0.001).
The observed correlation coefficient (r) is 0.337,
which suggests positive and fair correlation. It
suggests that higher the duration of sleeping,
the higher the exam scores.

26. S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Results presentation
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Exam score (marks)
r p value*
Sleeping duration (hrs) 0. 337 < 0.001
* Pearson’s correlation
Table: Correlation between sleeping duration (hrs) and
exam score (marks)

27. Thank YouThank You
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