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Research Methods: 1 M.Sc. Physiotherapy/Podiatry/Pain

Research Methods: 1 M.Sc. Physiotherapy/Podiatry/Pain. Correlation, Regression and Basic Probability. Relationships Between Variables. Exploring relationships between variables What happens to one variable as another changes. Relationships Between Variables.

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Research Methods: 1 M.Sc. Physiotherapy/Podiatry/Pain

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  1. Research Methods: 1M.Sc. Physiotherapy/Podiatry/Pain Correlation, Regression and Basic Probability

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

  3. 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.

  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 < r < 1, positive correlation

  9. Correlation; -1 < r < 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 • .

  14. 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

  15. Putting a value on the Linear Relationship • Spearmans Rank Correlation Coefficient • Non parametric - Ordinal dataor 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

  20. Basic Probability

  21. Chance, possibilities and luck! • How likely is anything to happen, is one outcome more likely than any other? • What are the odds of one particular outcome occurring? • If you toss a dice what is the probability of getting a six ?

  22. Probability • p(Six) + p(Not Six) = 1 • p(Six)1/6 + p(NotSix) 5/6 =1 • If an event is certain to occur p = 1 • If an event is impossible p = 0 • All other events fall somewhere between 0 and 1, 0 < p < 1

  23. Probability • p(Event) = • Theoretical and Relative frequencies

  24. Probability • 100 students attend a statistics lecture and 40 of them fall asleep within 10 minutes. • What is the probability that one of the students chosen at random will fall asleep within 10 minutes? • Pr (sleep) = 40/100 = 0.4 p = 0.4/40%

  25. Probability • 100 students attend a statistics lecture and 40 of them fall asleep within 10 minutes. • What is the probability that one of the students chosen at random will not fall asleep within 10 minutes? • Pr (not sleep) = 60/100 = 0.6 p = 0.6/60%

  26. Probability • Complimentary rule of Probability • Pr (not event) = 1 - Pr (event) • Addition rule of Probability • Pr(A or B) = Pr(A) + Pr(B) where A and B are mutually exclusive events

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