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200702P - CORRELATION ANALYSIS

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Presented in the Biostatistics module of the Clinical Research Coordinators Course on June 23, 2020 11.00-12.00 by Professor Omar Hasan Kasule MB ChB (MUK), MPH (Harvard), DrPH (Harvard)  Professor of Epidemiology and Bioethics King Fahad Medical City


FIGURE 1: CORRELATION MATRIX


WHAT IS CORRELATION?

  • Correlation analysis is used as preliminary data analysis before applying more sophisticated methods. 
  • Correlation describes the relation between 2 random variables (bivariate relation) about the same person or object with no prior evidence of inter-dependence.
  • Correlation indicates only association; the association is not necessarily causative
  • Correlation measures linear relation and not variability.


OBJECTIVES OF CORRELATION

  • A correlation matrix is used to explore for pairs of variables likely to be associated.
  • Correlation analysis has the objectives of describing the relation between x and y
  • Correlation predicts y if x is known
  • Correlation predicts x if y is known
  • Correlation can study trends


FIGURE 2: SCATTERPLOT: visual impression of the data and identifying outliers






THE PEARSON COEFFICIENT OF LINEAR CORRELATION, r

• Then Pearson coefficient of correlation, r, is the commonest statistic for linear correlation. 

• The Pearson coefficient of linear correlation essentially measures the scatter of the data

• The Pearson coefficient has a complicated formula but can be computed easily by modern computers.

• Its values range from 0.0 (no correlation) to 1.0(perfect correlation)

• It can take negative values if there is a correlation but in the opposite direction.


FIGURE 3: POSITIVE CORRELATION




FIGURE 4: NEGATIVE CORRELATION





INTERPRETATION OF THE PEARSON LINEAR CORRELATION COEFFICIENT, r

• r= 0.25 - 0.50 indicate a fair degree of association. 

• r= 0.50 - 0.75 indicate moderate to fair relation. 

• r= > 0.75 indicate good to excellent relation. 

• r = 0 indicate either no correlation or non-linear correlation

• r=1.0 is perfect positive linear correlation

• r=-1.0 is perfect negative linear correlation

• Very high correlations above 0.9 are suspicious (something wrong with the data)


SITUATIONS IN WHICH THE PEARSON LINEAR CORRELATION COEFFICIENT IS NOT USED/IS MISLEADING

• Relation between x and y is non-linear

• The data has outliers

• Observations are clustered

• One of the variables is fixed


ALTERNATIVES TO PEARSON COEFFICIENT (NOT USED REGULARLY)

• Coefficient of partial correlation = relation between x and y is influenced by a third variable

• Correlation ratio is used for curvilinear relations

• biserial or tetrachoric correlation coefficient is used in linear relations when one variable is quantitative and the other is qualitative

• contingency coefficient is used  for 2 qualitative nominals (ie unordered) variables each of which has 2 or more categories

• The coefficient of mean square contingency is used when both variables are qualitative

• The multiple correlation coefficient is used to describe the relationship in which a given variable is being correlated with several other variables.

• The square of the linear correlation coefficient is called the coefficient of determination.


NON-PARAMETRIC CORRELATION COEFFICIENTS (USED FOR DATA THAT IS NOT NORMAL ie BELL SHAPED)

• The Spearman is the non-parametric equivalent of the Pearson correlation

• The Spearman rank correlation coefficient is used for non-normal data for which the Pearson linear correlation coefficient would be invalid.