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

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Research Methods 1M.Sc. Physiotherapy/Podiatry/P
ain

• Correlation, Regression and Basic Probability

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Relationships Between Variables

• Exploring relationships between variables
• What happens to one variable as another changes

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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.

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Correlation
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Correlation
Correlation Coefficient r -1 ? r ? 1
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Correlation r 1, perfect positive correlation
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Correlation r -1, perfect negative correlation
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Correlation 0 lt r lt 1, positive correlation
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Correlation -1 lt r lt 0, negative correlation
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Correlation r ? 0, no linear relationship
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Correlation r ? 0, no linear relationship
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Correlation

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

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Spurious Correlation

• Coincidental Correlation chance relationships
• Indirect Correlation related through some third
  variable
• .

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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

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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)

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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)

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

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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 ?

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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 lt p lt 1

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Probability

• p(Event)
• Theoretical and Relative frequencies

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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

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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

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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