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

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

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

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

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 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