Bivariate Statistics

1
Bivariate Statistics

• Measures of Association between two variables.

2
Questions we ask

• Do changes in the Independent Variable cause
  changes in the Dependent Variable?
• What is the direction and form of the
  relationship?
• Positive
• Negative
• Perfect
• No Relationships

3
More Questions

• Whats the likelihood that the association is
  caused by bias in the sample instead of actual
  variation in the population?
• At what level of measurement are we working?

4
Association

• Proportional Reduction in Errors

• E Errors
• w/o without knowledge
• w with knowledge

5
What PRE tells us

• Degree of relationship
• How well we predict
• How well the independent variable explains the
  dependent variable

6
Lambda (?)

• PRE for nominal variables
• Measures strength of relationship
• Non-directional
• Values between 0 and 1
• Use PRE formula

7
Gamma (? or G)

• PRE for Ordinal data
• Strength and Direction
• Values from -1 to 1
• Similar/Dissimilar pairs
• P number of concordant pairs
• Q number of discordant pairs

8
Other options for Ordinal Data

• Tau b
• Tau c
• Asymetric d
• Symmetric d

9
Hypothesis Testing

• Part I

10
Hypotheses

• H1 our theoretical hypothesis
• H0 the null hypothesis no actual
  relationship
• Rejecting the Null
• Statistical Significance

11
Hypothesis Errors

• Type I wrongly rejecting null
• Type II failing to reject false null