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Correlation analysis

How can correlation analysis support strategic choice or positioning?

AccessibleStrategicOrganisation2 min read

Contents

Correlation analysis is a statistical technique that allows you to determine whether there is a relationship between two separate variables and how strong that relationship may be.

Correlation analysis quantifies the direction and strength of association between two variables.

When to use it

Use it to test a suspected relationship, compare associations or explore quantified data for patterns. An ice-cream seller might examine temperature and sales, then compare that relationship with seasonality. Exploration can reveal unexpected signals: Walmart famously observed higher Pop-Tart purchases before hurricanes and adjusted placement; the often-repeated beer-and-nappies story illustrates the same basket-analysis idea, although any such claim requires verification before action.

The method can support questions such as:

Are our most loyal customers also our most profitable?

Do customers purchase more when the price is lower?

Does pay influence length of tenure?

Does number of annual holidays influence absenteeism?

Is there any relationship between factor X and factor Y?

Use the evidence to challenge assumptions before changing strategy, pricing or product mix.

Origins

Correlation developed through nineteenth-century work by Francis Galton and Karl Pearson on measuring co-variation. Pearson formalised the product–moment coefficient, while Charles Spearman later developed rank correlation. Modern software made these calculations routine, but the interpretive rule remains unchanged: association alone does not establish cause.

What it is

Pearson correlation applies to paired numeric measurements, not unencoded categories such as brand or colour. The coefficient ranges from minus one to plus one. In the legacy typesetting these endpoints appeared as 11 and 21. A positive coefficient means high values tend to occur together; a negative coefficient means one tends to rise as the other falls; zero indicates no linear association. Thus a hypothetical plus zero point seven three relationship between height and IQ would be positive (legacy code 10.73), while minus zero point six four would be inverse (legacy code 20.64). Strength grows as the absolute value approaches 1. A coefficient of 0.5 is sometimes treated as practically notable, but statistical significance cannot be inferred from that threshold alone; it depends on sample size and assumptions.

How to use it

Pearson’s correlation coefficient® can be calculated with a scientific calculator, spreadsheet or statistical package.

Collect correctly aligned observations for both numeric variables.

Place the first variable in column x and the second in column y.

Add columns three, four and five for ‘x y’, ‘x x’ and ‘y y’.

Calculate the products in columns three, four and five: ‘x y’ 5 x times y, ‘x x’ 5 x times x and ‘y y’ 5 y times y.

Sum every column.

Substitute the totals into the equation, or use a validated spreadsheet function such as the one built into Microsoft Excel. Inspect a scatterplot, outliers, missing data and non-linear patterns before interpreting the coefficient.

Practical example

Suppose a company wants to test whether unit sales change with price. The common assumption that a lower price always produces greater volume may fail because product mix, season, channel and customer segment also vary. Pair the observations carefully and analyse the relationship before changing pricing policy.

The illustrated result provides no statistically significant evidence of a linear association between price and units sold.

Top practical tip

Use exploratory correlation to generate hypotheses, then visualise and validate any surprising relationship in fresh data before changing the business.

Top pitfall

Correlation is not causation, and zero linear correlation does not prove independence. Confounding, reverse causality, outliers and non-linear relationships can mislead; use a well-designed experiment or stronger causal method where the decision depends on cause.