# Bivariate Visualization - Bryn Mawr Bivariate Visualization CMSC 120: Visualizing Information 3/20/08 Types of Analysis

A single attribute Characterize Observations Number Type Similarity Are two groups the same?

Comparing Two Groups (A) (B) t-test (Normal Distributions) Nonparameterics

Mann-Whitney U 175.00, p = 0.008 Types of Analysis A single attribute Two attributes

Characterize Observations Number Type Similarity Describe Associations

How variables simultaneously change together Are two groups the same? Is there a relationship? What is the nature of the

relationship? Types of Data Qualitative: pertaining to fundamental or distinctive characteristics

Nominal: unordered (e.g., names, types) Ordinal: ordered (e.g., cold, warm, hot) Quantitative: pertaining to an amount of anything Discrete: isolated intervals Continuous: unbroken, immediate connection

Types of Comparisons Qualitative Quantitative Qualitative

Contingency Table Quantitative One-Way Analysis Area Chart Bar Chart

Continuous Discrete Line Plot Scatter Plot Qualitative versus

Qualitative Contingency Table Contingency: dependent on chance Represents number of observations that exhibit pairings of potential qualitative values (e.g., rainy

and windy, sunny and dry) Contingency Table: Example Are certain types of organisms more or less likely to be threatened by extinction? The data: biodiversity list of British Columbia

List of species Two variates: organism type, risk assessment Contingency Table: Example Chi-Squared (2) test: are the values randomly

distributed in the table cells? Qualitative v Quantitative Bar Chart

Area Chart One Way Analysis Comparison of Means ANOVA Paired t-tests or other non-parametric test

Quantitative v Quantitative Line Plot Use when both values are continuous Indicates a flow or connectedness from one point

to another Used to visualize a trend, or prevailing tendency Time Distance Line and Scatter Plot Use when at least one value is continuous

Indicates a flow or connectedness from one point to another Scatter emphasizes that measurements are taken at discrete intervals

Example: Diversity Gradients Example: Average Dinosaur Body Size thru Time How to Lie: Smoothing

How to Lie: Filtering Scatter Plot Can use whether data are discrete or continuous Implies data are discrete Used to visualize relationships How two variables co-vary

How two variables are correlated Describes a how a change in one variable is related to a change in another, but does not show a cause and effect Covariation

Describes the degree of similarity between two variables (X, and Y) Measure of how two variables vary together If, when X is greater than its mean, Y tends to be greater than its mean, the covariance is positive if, when X is greater than its mean, Y tends to be lesser,

the covariance is negative Units: units of X * units of Y Covariation Correlation Describes the degree of similarity between two

variables (X, and Y) Indicates strength and directionality of a linear relationship between X and Y Departure of relationship from independence

No Units Correlation