Variables, measurement and causation

Variable• Any personal or physical characteristic that..

.– Can change– The change must be measurable

• Examples of “variables”

– Height: a physical characteristic• It changes and changes can be measured with an instrument

– Weight: a physical characteristic• It changes and changes can be measured with an instrument

– Temperature: a physical characteristic• It changes and changes can be measured with a thermometer

– Knowledge about a topic: a personal characteristic• It changes and changes can be measured with a test

• When we measure a variable, we obtain its “value”, “score” or “level”.– These terms are interchangeable

• Categorical variables– Nominal: Mutually exclusive groups or “categories”

• Gender (M/F), color (Red/White/Black), etc.– Ordinal: Implied rank order

• Example: Low/medium/high• Sometimes treated as continuous variables

• Continuous variables: Can take on an infinite number of values– Can specify the precise distance between adjoining scores or

values (distance between 1 & 2 cm. same as between 8 & 9 cm.)– Length, height, weight, temperature, etc.– There are “interval” and “ratio” continuous variables. The

difference (presence/absence of an absolute zero) is not important.

Measuring variables

Issues in Measurement

• Validity: Method of measuring a variable (scaling and categorization) accurately reflects how the “real” world works

• Reliability: System of measuring is “reproducible”– Consistently yields the same value for a variable even

when measured by others

• Operational definition: precise method that must be followed to obtain the value of a variable, according to the system of measurement in use

Causation and hypotheses

• Conditional statement of cause and effect– If [causal variable], then [effect variable]– Changes in height cause changes in weight

• Causal variable is called the “independent” variable– Usual position on the left (e.g., height)

• Effect variable is called the “dependent” variable– Usual position on the right (e.g., weight)

• One and two-tailed hypotheses– Two-tailed simply predicts change: changes in calorie intake cause

changes in weight– One-tailed predicts change and specifies its direction:

Consuming more calories increases a person’s weight• Direction of a relationship

– Positive: Scores on the variables rise and fall together– Negative: Scores on the variables move in opposite directions

Hypotheses

H1: Increased pressure on the accelerator increases speed (+ relationship)

H2: Increased pressure on the brake reduces speed (- relationship)

CauseEffect (speed)

measured with a speedometer

Independent variable

Dependent variable measured with a pressure gauge or by changes in angle of pedal

Causation v. correlation

• Causation

– Must demonstrate more than just an association between variables (“correlation”)

– In nature and society, many variables that have nothing to do with each other are mathematically correlated

• Lunar cycles and homicide

– Must begin with a plausible hypothesis

• Narrowly specified, measurable variables

• Based on a thorough literature review– Nothing is “new”

• Causal order

– Cause (change in an independent variable) must precede effect (change in a dependent variable)

Testing a hypothesis - example

• Hypothesis: Poverty Crime– Which is the independent variable?– How would we measure it?– Which is the dependent variable?– How would we measure it?

• Are these variables “associated”? Do they “vary” or change together?• A simple way of analyzing a relationship between two variables is to

make both categorical– Measure poverty: Low or High income– Measure crime: Arrest record or No record

• From the same population, draw equal-size random samples of persons at each value of the independent variable– 100 Low income– 100 High income

• Then code each case for its scores or values on the variables

Low

Income

High

Income

No prior

Arrest

20 80

Prior

Arrest

80 20

Is a criminal record associated with one’s economic situation?

BUT - is it possible that criminal record is NOT associated with one’s economic situation? Could there be another independent variable at work?

Income

Arrest

An alternative hypothesis...

• It only LOOKS like Poverty Crime• The REAL cause of crime is poor education

– Poverty seems to be the cause because poor people get poor education, and wealthy people get good education

– So whenever we measure poverty, we are really measuring one’s education level

• Is this true?– Make educational level a categorical variable: Less than high

school, High school +– Code each case (all 200 persons) for education

• Repeat the original test, but this time “control” for the new independent variable: educational level– We “stratify” our sample into two groups – one for each value of

the “control” variable

Less than high school High school and above

Poverty Crime – or – Education Crime?

Low

Income

High

Income

No prior

Arrest

20 40

Prior

Arrest

30 20

Low

Income

High

Income

No prior

Arrest

10 30

Prior

Arrest

40 10

Low

Income

High

Income

No prior

Arrest

20 80

Prior

Arrest

80 20

Original tableOne result

Income Education Crime

Low

Income

High

Income

No prior

Arrest

20 20

Prior

Arrest

30 30

Low

Income

High

Income

No prior

Arrest

30 30

Prior

Arrest

20 20

Less than high school High school and above

What is the REAL cause of crime – Poverty or Education?Could the causal chain be complex?

Low

Income

High

Income

No prior

Arrest

20 80

Prior

Arrest

80 20

Original tableAnotherresult