statistics workshop b ivariate descriptive statistics j term 2009 bert kritzer n.
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Statistics Workshop B ivariate Descriptive Statistics J-Term 2009 Bert Kritzer. Describing Relationships Between Two Variables. Variables X Predictor (“independent”) X i as the value for the i th observation Y Response (“dependent”) variables

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describing relationships between two variables
Describing Relationships Between Two Variables
  • Variables
    • X Predictor (“independent”)
      • Xi as the value for the ith observation
    • Y Response (“dependent”) variables
      • Yias the value for the ith observation
  • Depends on nature of two variables (e.g., two nominal, two interval, etc.)
    • Simple table
      • Percentages: the right and the wrong way
    • Difference of means or medians
      • Multiple boxplots
    • Regression: fitting a line through a “scatterplot” of points (Xis and Yis)
  • Correlation: Measuring the strength of the relationship
data spreadsheet
Data Spreadsheet

Paired Values

simple crosstabulation trust in the police
Simple “Crosstabulation”Trust in the Police

Question: How much of the time do you think you can trust the local police?

how not to do percentages
How Not To Do Percentages

Source: Sarver, Kaheny, & Szmer, The Attorney Gender Gap in U.S. Supreme Court Litigation, 91 Judicature 238, 248 (2008).

feeling thermometer
Feeling Thermometer


(visited September 4, 2008)

ft scotus means with standard deviation bars
FT-SCOTUSMeans with Standard Deviation Bars

Note: Red dots represent mean; lines go one standard deviation above and below the mean.

the regression line
The Regression Line

The Line:

An Observation:

A Prediction:

eiis the difference between the actual observed value, Yi, and the value of Y on the line that corresponds with Xi

fitting the line
Fitting the Line
  • Eyeball
  • Split medians
  • Minimize sum of errors
  • Minimize sum of absolute errors
  • Minimize sum of squared errors

(“Least Squares”)

the fitted regression line
The Fitted Regression Line

For every ten point increase in citizen liberalism, one less tort reform was adopted

Y = 12.89 – 0.10X

  • Measure of association; strength of relationship
  • Range: 0 to 1 or -1 to 0 to +1
  • Proportional reduction in error (“PRE”)
    • Determining a prediction method
    • Setting a baseline
  • Non-PRE correlation coefficients
product moment correlation
Product Moment Correlation

Traditional formula for r:

other ways of computing r
Other Ways of Computing r

Cope’s Method

Traditional Method

Sum values of X and sum the values of Y to get ΣX and ΣY

Compute the square of X and Y

Sum the values of X2 and sum the values of Y2 to get ΣX2 and ΣY2

Multiple together each pair of values for X and Y to get the product XY

Sum the values of the product XY to get ΣXY

Use the values in the formula below to get r

eta 2 ft scotus by ideology
eta2FT-SCOTUS by Ideology

Baseline = 332462.11

Alternative = 316208.24

eta2= (332462.11 – 316208.24)/332462.11=.049 eta = .221


Moving Beyond Two Variables

Tort Reform by Citizen Liberalism & Elite Liberalism

multiple regression
Multiple Regression







Multiple Regression: Tort Reform by Citizen and Elite Liberalism

TortReformIndex = 13.032 – 0.062∙Citizen – 0.040∙Elite

R2 = 0.264

descriptive statistics summary
Descriptive Statistics: Summary
  • Summarize and describe data
  • Univariate
    • Central tendency & dispersion
    • Distribution
  • Bivariate
    • Describe the relationship
    • Degree of relationship
  • Multivariate