Statistics

Correlation

In French: Corrélation

Correlation measures the strength of the link between two quantities that vary together. It is summarised by a coefficient between −1 and 1, and is never read without the scatter plot it was drawn from.

What the coefficient says

The linear correlation coefficient is 1 when the points are perfectly aligned in the increasing direction, −1 when they are in the decreasing direction, and 0 when no alignment emerges. In between, it quantifies the spread around that alignment.

Its sign and its strength are read separately. A coefficient of −0.8 describes a strong link where one quantity decreases as the other increases; it is neither better nor worse than +0.8, only oriented the other way. It is a frequent confusion among those discovering the indicator.

The coefficient is symmetrical: it does not distinguish which of the two quantities would be the cause and which the effect. That neutrality is a property, not a limitation — it reminds you that the causal order is never deduced from the calculation, but from knowledge of the process.

Why the scatter plot comes before the figure

A coefficient close to zero does not mean there is no link: it means there is no linear link. A bell-shaped relationship, where the output improves then degrades, produces an almost nil coefficient even though the link is strong and perfectly usable. The plot shows it instantly; the figure hides it.

Conversely, a high coefficient may be carried by only a few extreme points. Removing two outliers is sometimes enough to halve it, which means that the observed relationship rested on special cases and not on the usual behaviour of the process.

A third case regularly misleads: two distinct populations, each with no internal link, together produce an apparent correlation simply because they occupy different areas of the chart. The scatter plot reveals the two clusters; the coefficient returns only a single, convincing value.

The practical rule comes down to one sentence: plot first, calculate next. A coefficient presented without its chart is not a verifiable result, it is an assertion.

What distorts the reading

The observed range. A link measured over a narrow interval looks weak even when it is real: if the parameter varied by only a few per cent during the period, the output variation it causes drowns in the noise.

The number of points. On about ten measurements, an apparently high coefficient frequently arises by chance. On several hundred, a weak coefficient can be perfectly real while having no practical bearing.

The hidden common factor. Two quantities that both depend on a third vary together without having any direct link. It is the mechanism behind most spectacular associations, and it is not detected in the data: it is detected by knowing the process.

The common mistakes

Reading a coefficient without having plotted the scatter. It is the single mistake that by itself explains most of the false conclusions drawn from a correlation, because a single figure cannot signal a curved relationship, an outlier or two mixed populations.

Searching for the correlations of one variable against all the others and keeping the strongest. By testing enough pairs, high links due to chance alone are always found; what comes out of that fishing requires confirmation on new data before being presented.

Concluding there is nothing because the coefficient is close to zero, without having checked the range of variation. A parameter that stayed almost constant during the observed period cannot show its influence, whatever it is.

On the shop floor — Food processing

A strong correlation linked the temperature of a line to the scrap rate, which seemed to point to the thermal setting. The scatter plot showed two clearly separated groups of points, corresponding to two production shifts. Within each group, the link disappeared: temperature merely betrayed the shift, and the real difference lay elsewhere.

The other tools illustrated by this trade: food and beverage.

Frequently asked questions

From what value is a correlation strong?

There is no universal threshold, and ready-made reading grids mislead. The same coefficient can be remarkable on very noisy human data and disappointing on a physical process where a clean relationship would be expected. What counts is the comparison with what the field allows one to hope for, not with a generic scale.

What should be done when two variables are strongly correlated with each other?

Be wary before using them together in the same model: they largely carry the same information, and the coefficients obtained become unstable, to the point of changing sign if a few observations are removed. The usual approach is to keep one, chosen for its business relevance or its ease of measurement.

Can a correlation be calculated on ordered non-numerical data?

Yes, by working on the ranks rather than on the values. That calculation detects any monotonic relationship, including a curved one, and withstands extreme values far better than the linear coefficient. It is indicated as soon as the data are rankings, scores or measurements whose distribution is very unbalanced.

Is a correlation enough to justify an action plan?

It is enough to justify a trial, never a roll-out. The observed link may come from an unmeasured common factor, and only deliberately varying the suspected parameter can settle it. That is exactly what a design of experiments produces, and that is why an analysis phase normally leads to trials rather than to conclusions.