Statistics Workshop B ivariate Descriptive Statistics J-Term 2009 Bert Kritzer

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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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### Statistics WorkshopBivariate Descriptive StatisticsJ-Term 2009Bert Kritzer

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

Paired Values

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

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

Feeling Thermometer

Source: http://www.laits.utexas.edu/txp_media/html/poll/features/feeling/slide1.html

(visited September 4, 2008)

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 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
• Eyeball
• Split medians
• Minimize sum of errors
• Minimize sum of absolute errors
• Minimize sum of squared errors

(“Least Squares”)

The Fitted Regression Line

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

Y = 12.89 – 0.10X

Correlation
• 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

Other Ways of Computing r

Cope’s 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

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

ONE PREDICTOR:

TWO PREDICTORS:

or

k PREDICTORS:

or

TortReformIndex = 13.032 – 0.062∙Citizen – 0.040∙Elite

R2 = 0.264

1884

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