Research Methods: 2 M.Sc. Physiotherapy/Podiatry/Pain Correlation and Regression

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

Relationships Between Variables Correlation;the 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.

Correlation

Correlation Coefficient = r -1  r  1

Correlation; r = +1, perfect positive correlation

Correlation; r = -1, perfect negative correlation

Correlation; 0 < r < 1, positive correlation

Correlation; -1 < r < 0, negative correlation

Correlation; r  0, no linear relationship

Correlation Closer to  1 the stronger Relationships do not necessarily mean what you think, i.e. non-causal relationships

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..

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

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)

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)

The Regression line The Method of Least Squares (the smallest sum of the squared distances)

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

The Regression prediction ? Residuals Coefficient of Determination Coefficient of Determination * 100 = R squared (R 2 ) How good a fit the equation (and the line) is to the data