MODULE 01

Measurement Levels

Two questions decide almost every method choice: what kind of variable is this? and what role does it play in my research question? They are different questions.

Research question
Variables (trained here)
Variable roles (trained here)
Measurement levels (trained here)
Method choice
Statistical logic
SPSS workflow
Output interpretation
Defensible conclusion

Understand

Three levels, two yes/no questions

Ask two things about a variable's values: can they be ordered, and is the numerical distance between them meaningful? The answers give the measurement level, and the level limits which statistics make sense.

Nominal

different kinds, no order

Categories have an order?: –
Distances are meaningful?: –

e.g. religion, gender, settlement type

Allows: frequencies, mode, crosstab, χ², Cramer's V

Ordinal

ranked categories, unknown distances

Categories have an order?: ✓
Distances are meaningful?: –

e.g. political interest 1–4, age groups, education level

Allows: + median, percentiles, Spearman's rank correlation

Continuous / Scale

numbers with meaningful distances

Categories have an order?: ✓
Distances are meaningful?: ✓

e.g. age in years, working hours, number of children

Allows: + mean, standard deviation, Pearson's r, t-tests

Numbers in the data file are not automatically numeric

SPSS stores almost everything as numbers. Gender might be coded 1 and 2, political interest 1 to 4. The codes tell you nothing about the measurement level; the meaning of the categories does.

Try

Classify the variables

Pick a level for each variable. The feedback tells you whether an order exists and whether distances are meaningful.

Classify each variable

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Gender
man · woman · other
Age in years
18, 19, 20 … 94
Age groups
18–29 · 30–44 · 45–59 · 60+
Political interest
1 not at all … 4 very interested
Happiness
0 extremely unhappy … 10 extremely happy
Number of children
0, 1, 2, 3 …
Religion
Catholic · Protestant · Jewish · Muslim · none · other
Working hours per week
0 … 80
Trust in parliament
0 no trust at all … 10 complete trust
Cigarettes smoked per day
0, 1, 2 … 40
Type of settlement
capital · county seat · town · village

Understand

Measurement level is not variable role

The role of a variable comes from the research question: Xindependent, Ydependent or Zcontrol. The measurement level comes from how the variable was measured. Change the question and the role changes; the level does not.

Measurement level

A property of the variable.

Nominal, ordinal or scale. Fixed once the variable is measured.

Variable role

A property of the research design.

X, Y or Z. It changes with the research question.

Age can be an independent variable in one research question and a control variable in another. Its role depends on the research design. Its measurement level does not.

Same variable, three research questions

“Is age associated with trust in parliament?”

XAgelevel: scale

YTrust in parliament

Role of age: independent variable (X). It changed because the research question changed.

Measurement level of age in years: scale, in every question. It is a property of how age was measured.

Your turn: what is the role of education?

Education (highest completed level, 5 categories)

Measurement level: Ordinal in every question

1Is education associated with trust in parliament?
2Do men and women differ in their highest level of education?
3Does the association between age and political participation hold after controlling for education?
4Is parents' education related to the respondent's own education?

SPSS

Where SPSS records the measurement level

Before any analysis, check Variable View: the Measure column, the value labels and the missing-value codes.

Before you open SPSS

1What is the research question?Which variables will I analyse, and how?
2What are X and Y?Decide the roles from the question, not from the data file.
3What are their measurement levels?Check the categories' meaning, not the codes.
4Which codes are not valid answers?Don't know, refused, not applicable → define as missing.

Data Editor›Variable View›Measure column

Variable View (excerpt)
Name	Label	Values	Missing	Measure
gender	Gender	{1, man}…	None	Nominal
polint	Political interest	{1, not at all}…	8, 9	Ordinal
agey	Age in years	None	999	Scale
trustprl	Trust in parliament	{0, no trust}…	88, 99	Scale

1Measure is metadata you set. It does not change the data, but it should match the real measurement level.
2Nonresponse codes (don't know, refused) must be declared as missing, or they will be treated as real answers.

Test yourself

Mastery check

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Classify variable

Political interest is coded 1 = not at all, 2 = not very, 3 = fairly, 4 = very interested. What is its measurement level?

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