Descriptive Statistics vs. Inferential Statistics

Why the distinction matters in a manuscript, not just a statistics course

Descriptive and inferential statistics answer two different questions, and a manuscript’s Results section needs to be explicit about which one it is answering at each point. Descriptive statistics characterize the data a study actually collected: sample size, means, medians, standard deviations, ranges, and frequencies. They make no claim about anything beyond the observed data. Inferential statistics use that same sample data to estimate or test a claim about a broader population the sample was drawn from — via hypothesis tests, p-values, confidence intervals, or regression coefficients — and every inferential claim carries an explicit or implicit statement of uncertainty.

The practical reason this matters for scholarly writing: a manuscript that reports “Group A scored higher than Group B” based only on observed means, with no inferential test behind it, has made a descriptive statement dressed up as a finding. Peer reviewers and statistical editors treat this as a reporting weakness because the sentence implies a generalizable difference without the statistical machinery to support that claim. Getting the two roles straight — and signaling clearly which one a given sentence is doing — is part of writing a Results section reviewers don’t have to send back for clarification.

Descriptive statistics: summarizing the sample in hand

Descriptive statistics are reported first in most manuscripts, typically in a “Participants” or early Results subsection, and typically include:

• Measures of central tendency — mean, median, mode — describing a typical value in the sample.
• Measures of dispersion — standard deviation, interquartile range, variance — describing how spread out the values are.
• Frequencies and proportions — counts and percentages for categorical variables (e.g., sex, treatment arm, diagnosis category).
• Sample size and demographic composition, usually presented in a “Table 1” baseline characteristics table.

None of these figures, by themselves, say anything about whether an observed pattern would hold in a different sample or in the population the study is meant to speak to. A mean difference between two groups is a fact about the specific participants measured — it is not yet evidence of a real effect.

Inferential statistics: generalizing beyond the sample

Inferential statistics take the sample data and use probability theory to make a claim about the population the sample was drawn from. Common inferential tools in a manuscript’s Results section include:

• Hypothesis tests (t-tests, chi-square tests, ANOVA, regression) that produce a p-value assessing how compatible the observed data are with a null hypothesis of no effect or no association.
• Confidence intervals, which express a range of plausible values for a population parameter (an effect size, a proportion, a mean difference) given the observed data.
• Effect size estimates (odds ratios, Cohen’s d, correlation coefficients) that quantify the magnitude of an association, often reported alongside the p-value rather than in place of it.

Every inferential statistic depends on assumptions about how the sample was drawn — random or representative sampling from a clearly defined population — which is why a manuscript’s methods section needs to establish the population and sampling approach before the Results section can meaningfully use inferential language like “significant” or “associated with.”

Where manuscripts get this wrong

• Reporting a descriptive difference as if it were a finding. Stating that one group’s mean was higher than another’s, without a test statistic, p-value, or confidence interval, describes the sample but does not support a generalizable claim.
• Using inferential language for a purely descriptive result. Phrases like “significantly higher” should be reserved for results that were actually tested; using them loosely to mean “noticeably higher” in a purely descriptive table is a common source of reviewer comments.
• Running inferential tests without a clearly specified population or sampling frame. An inferential claim is only as credible as the sampling approach behind it — see survey research methods for how sampling frame and response rate affect what a survey’s inferential statistics can legitimately claim.
• Conflating statistical and practical significance. A very small p-value from a large sample can accompany a trivially small effect size; descriptive statistics (the effect size itself) and inferential statistics (the p-value) need to be read together, not as substitutes for each other.

How the two relate to variables and study design

Which variables get inferential treatment, and which statistical test is appropriate, depends on how those variables are classified in the study design — see independent vs. dependent variable for how that classification determines the analysis plan. A manuscript’s Methods section should specify, in advance, which descriptive statistics will be reported for which variables and which inferential tests will be applied to which comparisons — reporting this analysis plan clearly is part of what allows a Results section to move cleanly between the two without ambiguity.

Frequently asked questions

Can a manuscript report only descriptive statistics?

Yes — purely descriptive studies (e.g., some case series, prevalence surveys, or exploratory reports) legitimately report only descriptive statistics, as long as the manuscript does not use inferential language (“significant,” “associated with,” “predicts”) to describe those results. The problem is not using descriptive statistics alone; it is describing them with inferential claims they don’t support.

Does a large sample size make descriptive statistics into inferential ones?

No. Sample size affects the precision and power of an inferential test, but a mean or proportion is descriptive regardless of how large the sample is. A large sample makes inferential tests more capable of detecting small effects, but the descriptive/inferential distinction is about the type of claim being made, not the sample size.

Should descriptive and inferential statistics appear in the same table?

Journals vary, but a common convention is to report descriptive statistics (means, SDs, proportions) alongside the inferential results (test statistic, degrees of freedom, p-value, confidence interval) for the same comparison in one results table, so a reader can see both the magnitude of the difference and the statistical evidence for it in one place.