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Stats: Getting Started
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Variables
What is a variable?
Values of a variable:
Categories with code numbers
Numerical values
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Level of Measurement
Nominal (qualitative categories)
Ordinal (ordered categories)
Interval-ratio (quantitative — meaningful numbers)
Examples of each!
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Categoric or Continuous?
Categories (nominal, ordinal): Code numbers Continuous (sub-dividable, numerical values)
“In-between” Discrete; whole numbers or counts Scale variables (Are they really ordinal?)
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Dichotomous (Binary) Variables
Give examples.
The mean of a dichotomous variable (proportion of cases coded 1).
It is often useful to recode variables with many categories into dichotomous variables.
A multi-category variable can be “broken up” into dichotomous “dummy variables.”
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Conceptual and Operational Variables
Examples: Wealth, religious intensity, quality of education, democracy (country)
Can you propose an operational variable —a measurement procedure — for each of these?
Valid and reliable measures
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IV and DV
Which is the independent variable?
Which is the dependent variable?
Is it always clear? Examples, yes and no.
Difference between an independent variable and a cause.
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It’s Not a Cause Unless—
Association/correlation. The variables “go together,” and their distributions are related to each other.
Time sequence: The cause precedes (or is concurrent with) the effect. A cause cannot follow an effect.
Not a spurious relationship: Remember lemonade sales and drowning accidents (Garner, 2010).
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Predictor Variables
A predictor variable enables us to conclude something about an outcome variable.
The predictor variable is not necessarily a cause of the outcome.
A day with hot temperatures is likely to have more drowning accidents (prediction), although the drowning accidents are not directly caused by heat.
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Statistical Causality
A higher probability of an outcome.
Outcome is not determined — “guaranteed” — by a single cause in every instance.
Statistical causality: Rates are different.
Durkheim: Higher suicide rates of Protestants compared to Catholics.
Smokers have a higher rate of illness, premature mortality, and other health concerns — but NOT all smokers!
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What Are the Cases?
Individuals
Organizations or places where individual-level data are aggregated (e.g., crime rate of a city, suicide rate of a country, per cent below the poverty line in a city, or unemployment rate of a state or province)
For place-level data, qualitative measures (nominal) become the basis of quantitative, interval-ratio variables (e.g., % in poverty or % male).