Descriptive statistics summarise the data you actually collected, while inferential statistics use that sample to draw conclusions about a larger population you didn't measure. If you're staring at a spreadsheet for your thesis and can't tell whether you need a mean or a t-test, this is the distinction that unlocks everything else — and it's the single most common point where researchers get stuck before they even open their analysis software.
Key Takeaways
- Descriptive statistics describe your sample — think mean, median, standard deviation, and frequency counts. They make no claims beyond the data in front of you.
- Inferential statistics generalise from a sample to a population — using tools like t-tests, ANOVA, chi-square, and correlation to test hypotheses and estimate uncertainty.
- You almost always use both: describe the data first, then run inferential tests to answer your research question.
- The dividing line is the p-value: descriptive stats never produce one; inferential stats do, because they involve probability and sampling error.
- StatRyx picks the right descriptive summaries and inferential test for your data automatically and writes both up in APA 7 format.
What are descriptive statistics?
Descriptive statistics are numbers that summarise and organise a dataset without inferring anything beyond it. If you measured the exam scores of 30 students, descriptive statistics tell you the average score, how spread out the scores were, and what the highest and lowest were — nothing more, nothing less.
They fall into three families:
- Measures of central tendency: mean, median, and mode — the "typical" value.
- Measures of dispersion: range, variance, standard deviation, and interquartile range — how spread out the data is.
- Measures of frequency and shape: counts, percentages, skewness, and kurtosis.
For example, suppose you collect anxiety scores from 30 participants and find a mean of M = 42.6 with a standard deviation of SD = 8.1. That's a purely descriptive statement: it describes those 30 people and claims nothing about anyone else. Descriptive statistics are the honest, foundational layer of any analysis — you should always report them before running a single test.
What are inferential statistics?
Inferential statistics use a sample of data to make probability-based conclusions about a wider population. Because you rarely measure everyone, you measure a sample and then ask: "How confident can I be that what I see here holds true in general?"
Inferential statistics account for sampling error — the random variation you'd expect just from picking a different set of people. They produce p-values, confidence intervals, and effect sizes that quantify how likely your result is to reflect a real effect rather than chance.
Common inferential tests include:
- t-tests — compare two group means.
- ANOVA — compare three or more group means.
- Chi-square — test associations between categorical variables.
- Correlation and regression — measure and model relationships between variables.
If you're unsure which of these your data calls for, our guide on how to choose the right statistical test walks through it — or StatRyx will simply detect it from your variables.
Descriptive vs inferential statistics: what's the difference?
The clearest way to separate them: descriptive statistics answer "what does my data look like?" while inferential statistics answer "what can I conclude beyond my data?"
| Feature | Descriptive statistics | Inferential statistics |
|---|---|---|
| Purpose | Summarise the sample | Generalise to a population |
| Scope of claim | The data you collected | People/cases you didn't measure |
| Typical outputs | Mean, SD, frequencies, charts | p-values, CIs, effect sizes |
| Involves probability? | No | Yes |
| Example tools | Mean, median, histogram | t-test, ANOVA, regression |
| Produces a p-value? | Never | Always |
| Answers | "What happened here?" | "Does it hold in general?" |
A simple test: if a result comes with a p-value, it's inferential. If it's just describing what you observed, it's descriptive.
A worked example using both together
Imagine a study comparing test anxiety between two teaching methods, with 45 students split into a traditional group (n = 23) and a mindfulness group (n = 22).
Step 1 — Describe the data (descriptive statistics).
You calculate the group means and standard deviations:
- Traditional group: M = 46.2, SD = 7.9
- Mindfulness group: M = 39.4, SD = 8.3
These numbers describe your 45 participants. The mindfulness group looks less anxious, but descriptive statistics alone can't tell you whether that 6.8-point gap is real or just random luck of the sample.
Step 2 — Test the difference (inferential statistics).
You run an independent-samples t-test and get:
t(43) = 2.82, p = .007, d = 0.84, 95% CI [1.94, 11.66]
Here's what each number means:
- t(43) = 2.82 — the test statistic and its degrees of freedom (45 − 2 = 43).
- p = .007 — there's roughly a 0.7% probability of seeing a difference this large if the two methods truly had no effect. Because .007 is below the conventional .05 threshold, the difference is statistically significant.
- d = 0.84 — a large effect size (Cohen's d): the groups differ by about 0.84 standard deviations.
- 95% CI [1.94, 11.66] — you're 95% confident the true mean difference in the population falls between 1.94 and 11.66 points.
The descriptive statistics told you what your sample looked like; the inferential statistics let you conclude the mindfulness method likely reduces anxiety in the broader student population, not just these 45.
How do I report descriptive and inferential statistics in APA 7?
In APA 7, report descriptive statistics first (means and standard deviations), then the inferential test with its statistic, degrees of freedom, exact p-value, and an effect size. Drop the leading zero on p because it can't exceed 1, and italicise all statistical symbols.
A complete APA 7 sentence for the example above:
The mindfulness group reported lower test anxiety (M = 39.4, SD = 8.3) than the traditional group (M = 46.2, SD = 7.9), a statistically significant difference, t(43) = 2.82, p = .007, d = 0.84, 95% CI [1.94, 11.66].
Notice how the descriptive and inferential pieces sit side by side — reviewers expect both. Reporting a p-value without the means, or means without a test, is one of the most common reasons for revise-and-resubmit. StatRyx generates this exact sentence for you, so you don't have to remember which symbols get italicised or where the leading zero disappears.
Which one do I actually need for my research?
You almost certainly need both — descriptive statistics to summarise your data and inferential statistics to answer your hypothesis. The only time you'd stop at descriptive statistics is if you're reporting on an entire population (a census, not a sample) or writing a purely exploratory summary with no hypothesis to test.
If you have a research question that includes words like "does," "is there a difference," "is X related to Y," or "does A predict B," you need inferential statistics. StatRyx reads your variables — how many groups, whether data is continuous or categorical, whether assumptions hold — and selects the correct inferential test automatically, then reports the descriptive statistics alongside it.
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