Title: Research Methods: 2 M.Sc. Physiotherapy/Podiatry/Pain
1Research Methods 2M.Sc. Physiotherapy/Podiatry/P
ain
- Correlation and Regression
2Relationships Between Variables
- Exploring relationships between variables
- What happens to one variable as another changes
3Relationships 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.
4Correlation
5Correlation
Correlation Coefficient r -1 ? r ? 1
6Correlation r 1, perfect positive correlation
7Correlation r -1, perfect negative correlation
8Correlation 0 lt r lt 1, positive correlation
9Correlation -1 lt r lt 0, negative correlation
10Correlation r ? 0, no linear relationship
11Correlation r ? 0, no linear relationship
12Correlation
- Closer to ? 1 the stronger
- Relationships do not necessarily mean what you
think, i.e. non-causal relationships
13Spurious 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. - .
14Putting 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
15Putting 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)
16Regression
- 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)
17The Regression line
The Method of Least Squares (the smallest sum of
the squared distances)
18The 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
19The 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