1. Bivariate Relationships
SHARON LAWNER WEINBERG SARAH KNAPP ABRAMOWITZ
Statistics
SPSS
An Integrative Approach
SECOND EDITION
Bivariate Relationships
Using
Chapter 5

2. Summarizing the Relationship Between Two Variables: An Overview
Variable Types
Summary Graphic
Summary Statistic
Both Scale
Scatterplot
Pearson Correlation
Both Ordinal
Spearman Correlation
An Ordinal & A Scale
A Scale & A Dichotomy
Scatterplot or Boxplot
Pearson (point biserial) Correlation
Both Dichotomies
Clustered Bar Graph
Pearson (phi-coefficient) Correlation or Contingency Table

3. The Relationship Between Two Scale Variables What the Scatterplot Tells Us
Whether the relationship appears linear
If it does appear linear, it also tells us:
The direction and nature of the linear relationship
The relative strength of the linear relationship

4. Direction: Look at sign of r (positive or negative).
Quantifying the Linear Relationship between Two Scale Variables: Pearson Product Moment Correlation Coefficient
This summary statistic measures the direction, nature, and strength of the linear relationship.
Direction: Look at sign of r (positive or negative).
Nature: Look at sign of r (positive means that high scores on one variable correspond to high scores on the other and low with low, negative means that low scores on one variable correspond to high on the other and vice versa).
Strength: Look at magnitude (absolute value) of r. In the social sciences, a good rule of thumb comes from Cohen’s scale: r < .1 little or no, .1 <= r < .3, weak, .3 <= r < .5 moderate, r >= .5 strong. 4

5. Selection
The table on the following slide provides guidelines for choosing the appropriate statistic(s) and graphs for describing the relationship between two variables.
Other combinations may be correct. 5

6. 6 Levels of measurement Nominal with two categories
Nominal with more than two categories or ordinal with more than two categories but not more than five categories
Ordinal with five or more categories
Scale
Pearson correlation or percentages from crosstabulation and clustered bar graph
Percentages from crosstabulation and clustered bar graph
Spearman correlation and interactive scatterplot or boxplot
Pearson correlation and interactive scatterplot or boxplot
Spearman correlation (if both ordinal) or medians and interactive scatterplot or boxplot
Means or medians (depending on skew) and interactive scatterplot or boxplot
Spearman correlation and scatterplot
Means or medians (depending on skew) and interactive scatterplot or boxplot
Pearson correlation and scatterplot. Correlation should not be used if scatterplot is well fit by a simple curve 6