MKTG90011 · Marketing Research
Measures of Association
Association answers three questions about a relationship — is there one (presence), which way does it go (direction, + or −), and how strong is it (strength) — and the test you choose is decided entirely by the measurement scale of the two variables. Two categorical (nominal) variables → chi-square test of independence. At least one ordinal variable → Spearman rank correlation. Two metric variables in a linear relationship → Pearson correlation. The selection matrix is the whole game: chi-square handles any pair that includes a nominal variable; Spearman covers the ordinal cases; Pearson is reserved for two interval/ratio variables. Correlation coefficients run from −1 to +1 — the sign is direction, the magnitude is strength — while chi-square compares observed to expected counts in a contingency table. The cardinal rule, and a guaranteed exam point: association is never causation. In the project this chapter is H1 (chi-square on two categorical variables) plus the mandated correlation.
What this chapter covers
- 019.1 Presence, direction and strength of association
- 02The association selection matrix (scale × scale → test)
- 03Chi-square test of independence (two categorical variables)
- 04Observed vs expected counts and the contingency table
- 05Pearson correlation (two metric variables, linear)
- 06Spearman rank correlation (ordinal or non-normal)
- 07Reading r: sign = direction, magnitude = strength; association ≠ causation
Worked example: pick the association test from the scales
- +1(a) Two nominal variables → chi-square. Both store and gender are categorical labels, so test independence with chi-square on the contingency table.
- +1(b) Two metric variables → Pearson. Both are interval/ratio and the relationship is assumed linear, so Pearson's r measures direction and strength.
- +1(c) At least one ordinal variable → Spearman. Education and loyalty are ranks, so Spearman's rank correlation is the legal choice (Pearson would be invalid).
Key terms
- Association
- A relationship between two variables described by presence, direction and strength. It is symmetric and does not imply that one variable causes the other.
- Chi-square test of independence
- The association test for two categorical (nominal) variables. It compares the observed counts in a contingency table to the counts expected if the variables were independent; a significant result means they are related.
- Pearson correlation (r)
- A measure of the linear association between two metric variables, ranging from −1 to +1. The sign gives direction; the magnitude gives strength (0 = none, ±1 = perfect).
- Spearman rank correlation
- A correlation computed on the ranks of the data, used when at least one variable is ordinal or the relationship is non-linear/non-normal. It assesses monotonic association rather than strictly linear.
- Association is not causation
- A correlation or significant chi-square shows variables move together, not that one causes the other — the relationship can be reversed or driven by a third variable. A staple caveat in every association answer.
Measures of Association FAQ
How do I decide between chi-square, Pearson and Spearman?
By the scales of the two variables. Two categorical (nominal) variables → chi-square. Two metric (interval/ratio) variables in a linear relationship → Pearson. At least one ordinal variable (or non-normal/non-linear data) → Spearman. Label each variable N/O/I/R, then read the selection matrix.
What does the correlation coefficient r actually tell me?
Two things at once: the sign gives the direction (+ means they rise together, − means one rises as the other falls) and the magnitude gives the strength, from 0 (no linear association) to ±1 (perfect). Always interpret both — a strong negative correlation is just as informative as a strong positive one.
Why is ‘association is not causation’ so important?
Because a relationship between two variables can arise from reverse causation or a lurking third variable, not from one causing the other. Stating this caveat is almost always worth a mark, and forgetting it is the classic over-claim — only a controlled experiment, not a correlation or chi-square, supports a causal conclusion.
When do I use Spearman instead of Pearson?
Use Spearman when at least one variable is ordinal (ranked), or when two metric variables have a non-linear or non-normal relationship. Pearson assumes two metric variables with a linear association and approximate normality; if those assumptions fail, Spearman on the ranks is the safe, legal choice.
Exam move
Commit the association selection matrix to memory — chi-square wherever a nominal variable appears, Spearman for ordinal, Pearson for two metric — because the exam's single-best-answer items are decided by it alone. Practise the routine: identify the two variables, label each scale N/O/I/R, match to the test, then interpret r by sign (direction) and magnitude (strength). Finish every association answer with the not causation caveat — it is nearly free marks. This chapter is your project's H1 (chi-square) and mandated correlation, so the drill doubles as project prep.
