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Research Methods: 2 M.Sc. Physiotherapy/Podiatry/Pain

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Title: Research Methods: 2 M.Sc. Physiotherapy/Podiatry/Pain


1
Research Methods 2M.Sc. Physiotherapy/Podiatry/P
ain
  • Correlation and Regression

2
Relationships Between Variables
  • Exploring relationships between variables
  • What happens to one variable as another changes

3
Relationships Between Variables
  • Correlationthe strength of the linear
    relationship between two variables.
  • Regression the nature of that relationship, in
    terms of a mathematical equation.
  • In this module we are only concerned with linear
    relationships between variables.

4
Correlation
5
Correlation
Correlation Coefficient r -1 ? r ? 1
6
Correlation r 1, perfect positive correlation
7
Correlation r -1, perfect negative correlation
8
Correlation 0 lt r lt 1, positive correlation
9
Correlation -1 lt r lt 0, negative correlation
10
Correlation r ? 0, no linear relationship
11
Correlation r ? 0, no linear relationship
12
Correlation
  • Closer to ? 1 the stronger
  • Relationships do not necessarily mean what you
    think, i.e. non-causal relationships

13
Spurious Correlation
  • Coincidental Correlation chance relationships
  • Indirect Correlation related through some third
    variable
  • Infant mortality and temperature in country of
    birth are linearly related, but the poorest
    countries are closest to the equator.
  • .

14
Putting a value on the Linear Relationship
  • Pearsons Product Moment Correlation Coefficient
    (PPM)
  • Parametric data - Quantitative data where it can
    be assumed both variables are normally
    distributed, r

15
Putting a value on the Linear Relationship
  • Spearmans Rank Correlation Coefficient
  • Non parametric - Ordinal data or quantitative
    data where one (or both) variables are not
    normally distributed. Calculated from the ranked
    data ? (rho)

16
Regression
  • Identify the nature of the relationship
  • Predict one variable from the other
  • The independent variable (plotted on the x-axis)
    determines the dependant variable (plotted on the
    y-axis)

17
The Regression line
The Method of Least Squares (the smallest sum of
the squared distances)
18
The Regression equation
Y bX a Y the y-axis value X the x-axis
value b the gradient (slope) of the line a
the intercept point with the y - axis
19
The Regression prediction ?
  • Residuals
  • Coefficient of Determination
  • Coefficient of Determination 100
  • R squared (R2)
  • How good a fit the equation (and the line) is to
    the data
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