Bivariate Visualization

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Bivariate Visualization

• CMSC 120 Visualizing Information
• 3/20/08

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Types of Analysis

• Univariate

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

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Comparing Two Groups
(A)
(B)

• t-test (Normal Distributions)
• Nonparameterics
• Mann-Whitney U 175.00, p 0.008

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Types of Analysis

• Univariate

• Bivariate

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

• Two attributes
• Describe Associations
• How variables simultaneously change together
• Is there a relationship?
• What is the nature of the relationship?

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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

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Types of Comparisons
Qualitative Quantitative
Qualitative Contingency Table
Quantitative One-Way Analysis Area Chart Bar Chart Line Plot Scatter Plot
Continuous Discrete
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Qualitative versus Qualitative
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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)

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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

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Contingency Table Example
Fungus Invertebrate Animal Nonvascular Plant Vascular Plant Vertebrate Animal Totals
Extinct 0 0 0 0 5 5
Red 4 81 213 310 115 723
Blue 1 85 155 308 104 653
Yellow 0 358 453 1733 425 2969
No Status 0 13 0 1 22 36
Exotic 0 34 6 736 45 821
Accidental 0 5 0 0 138 143
Unknown 0 11 1 3 15 30

• Chi-Squared (?2) test are the values randomly
  distributed in the table cells?

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(No Transcript)
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Qualitative v Quantitative
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Bar Chart
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Area Chart
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One Way Analysis

• Comparison of Means
• ANOVA
• Paired t-tests or other non-parametric test

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Quantitative v Quantitative
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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

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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

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

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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

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Covariation
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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

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Correlation