Stats: Getting Started

Variables

What is a variable?

Values of a variable:

Categories with code numbers

Numerical values

Level of Measurement

Nominal (qualitative categories)

Ordinal (ordered categories)

Interval-ratio (quantitative — meaningful numbers)

Examples of each!

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?)

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.”

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

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.

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).

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.

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!

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).