Tags: statistics concept

Descriptive vs Inferential Statistics

Date: 2026-08-17

---

Descriptive statistics summarise what you measured. Inferential statistics claim something about what you didn’t. The distinction decides whether a number needs a confidence interval — and most analytics reporting mixes the two without noticing which it’s doing.

---

The two claims

DESCRIPTIVE                          INFERENTIAL

"In March, 3.2% of sessions          "Our conversion rate is 3.2%"
 converted"
                                     a claim about a population you
a fact about 412,000 sessions        did not measure — including
you actually recorded                 April's sessions, which don't
                                      exist yet
exact. no uncertainty.
no interval needed.                  uncertain. needs an interval.

The same number, 3.2%, is doing two completely different jobs. The first is arithmetic on data you have. The second is a bet about data you don’t.

Why this matters in practice

The confusion runs in both directions, and both are expensive.

Treating an inference as a description — the more common error:

"Mobile converts at 2.1%, desktop at 3.4%. Mobile is worse."

if these are last month's complete figures, that's descriptive
and true — those visitors did convert at those rates.

but the sentence is being used to predict next month, and to
justify spending money. that's an inference, and it needs:
  · how many sessions in each? (2.1% of 400 is not 2.1% of 400,000)
  · what's the interval on each?
  · are the two groups otherwise comparable? — Confounding Variables

That third bullet is asking whether a confounder explains the gap — Confounding Variables.

Treating a description as an inference — less common, quietly wasteful:

"Last quarter's revenue was £4.2m ± £180,000"

no. last quarter's revenue was £4.2m. exactly.
you have every order. there is no sampling uncertainty
in a number you counted completely.

Putting an interval on a completed count implies a randomness that isn’t there, and it trains people to discount figures that are actually exact.

The awkward middle: do you have the population?

This is where it gets genuinely subtle, and where the honest answer is usually “it depends what you’re claiming”.

you have every session in March.        is that the population?

claim: "3.2% of March sessions converted"
  → March sessions ARE the population. descriptive. exact.

claim: "our site converts at 3.2%"
  → the population is all sessions your site could receive,
    under similar conditions. March is a SAMPLE of that.
    inferential. needs an interval.

claim: "the redesign will convert at 3.2%"
  → not even an inference from this data. a forecast, with
    assumptions that need stating separately.

The population is usually hypothetical — a superpopulation of “visits under conditions like these” — which is why an interval is warranted even when you counted everything. The test is whether the number is being used to describe the past or to predict, and reporting nearly always does the second while claiming the authority of the first — Populations and Samples.

What each toolkit contains

	Descriptive	Inferential
Centre	Mean Median and Mode	Estimates of a population parameter
Spread	Variance and Standard Deviation, Percentiles and Quantiles	Standard Error — how much the estimate would bounce
Comparison	”A is bigger than B, in this data”	Hypothesis Testing, Confidence Intervals
Relationship	Correlation as computed	Whether it holds beyond this sample
Presentation	Tables, distributions, charts	Intervals, p-values, effect sizes
Requires	Only the data	An assumption about how the data was sampled

The last row is the whole difference. Inference is only valid if the sample relates to the population in a describable way — and in web analytics it usually doesn’t, because the data is a convenience sample of whoever happened to visit, filtered by consent, ad blocking and bot removal — Sampling Methods.

The practical position

• Report descriptively by default. “In March, X” is honest, exact, and rarely misleading
• Add an interval whenever the number is being used to decide something about the future — which is most of the time in practice
• Say which you’re doing when the audience might act on it
• Never put an interval on a complete count of a fixed past period being described as such
• Segment sizes decide which mode you’re in. A segment of 90 sessions is descriptively fine and inferentially worthless — Dashboard Design

Where it interacts

• Populations and Samples — the distinction underneath this one, and where “the population” gets defined
• Communicating Uncertainty — the presentation problem: people want the descriptive number’s precision with the inferential number’s reach
• Sampling Error — the size of the gap inference has to account for
• Benchmarking — an industry figure is descriptive of someone else’s data and gets used inferentially about yours, which is two errors at once