Bivariate and Multivariate Data Analysis

1
Bivariate and Multivariate Data Analysis

• Session 28

2
Linear Bivariate Relationships

• Bivariate two variables, the relationship
  between the two
• Univariate descprition
• Bivariate association
• Linear what is not linear well . . .
  exponential, S-curve, curvilinear . . .
• Scatterplot a tool we can use to evaluate a
  bivariate linear relationship between two
  interval level variables is a scatterplot

3
The Scatterplot

• Too many values in an interval level variable for
  a frequency table, right?
• We actually have a display that contains more
  information the scatterplot
• So specifically?
• Values of one variable are on the Y axis, values
  of the other on the X axis
• Each case is represented by dot
• The pattern of the relationship emerges

4
Example Lobbying

• Is there a relationship between how many years a
  lobbyist has been working as a lobbyist and how
  many legislator the lobbyist knows on a
  first-name basis?
• Yes, scatterplot shows a positive linear
  relationship?
• Outlier a case that is far outside of the range
  of the other cases
• example Son of the former Speaker

5
Possible Relationships

• Scatterplot
• Positive
• Negative
• No Relationship
• Curvilinear
• Outliers
• The next step in bivariate analysis
• Linear regression analysis the last section of
  PSC 412
• A line is estimated based on the position of the
  individual dots

6
As the number of aspirin taken increases from
half an aspirin to 5 aspirin, relief increases.
However, after 5 aspirin, adding more aspirin
doesn't increase relief it decreases it. There
is not a linear relation between aspirin and
relief. Taking 9 aspirin is NOT better than
taking 4 aspirin, as the graph above indicates.
7
Regression Line Shows Strength and Direction
8
Regression Line Shows Strength and Direction
9
Analyzing More Than Two Variables

• Sorting Out Multiple Influences
• Multivariate analysis
• Testing a bivariate relationship requires the
  introduction of control variables to falsify or
  disprove the hypothesis for the bivariate
  relationship
• Multivariate statistical techniques will allow
  you to examine both the separate simultaneous
  effect of each independent variable and the
  combined effects of all the independent variables
  directly on the dependent variable at the same
  time

10
Possible Effects of Control Variables on Original
Relationships

• Refining original relationship holds only under
  certain conditions
• Replicating control variable has no effect on
  original relationship
• Candidate Choice and Gender, Controlling for Age

11

• Reducing original relationship diminishes or
  disappears
• Candidate Choice and Gun Ownership, Controlling
  for Residence
• Revealing original relationship is strengthened
  under certain conditions
• Candidate Choice and Gender, Controlling for
  Income
• Reversal direction of original relationship
  changes from positive to negative
• Candidate Choice and Education, Controlling for
  Country of Birth