Descriptive statistics summarise the data you actually collected; inferential statistics use that sample to draw conclusions about the wider population it came from. Descriptives describe what is in front of you, while inferentials let you generalise beyond it. A complete results chapter needs both, in that order.
Why your chapter needs both, and in what order
Descriptive and inferential statistics answer different questions, so they are not interchangeable. You lead with descriptives to show the reader what your sample looks like, the means, spread, and shape of each variable, then move to inferential tests to answer your research questions. Skipping the descriptive layer leaves your supervisor unable to judge whether your inferential results are even plausible, and it hides problems like outliers that should have been addressed in data cleaning. To produce that opening summary, the descriptive statistics calculator returns the mean, spread, shape, and a confidence interval from a pasted column.
What descriptive statistics cover
Descriptives fall into three groups. Measures of central tendency (mean, median, mode) say where the centre of your data sits. Measures of spread (standard deviation, variance, range, interquartile range) say how dispersed it is. Measures of shape (skewness and kurtosis) say whether it is symmetric, which feeds directly into testing for normality. Frequencies and percentages handle your categorical variables.
What inferential statistics add
Inferential methods quantify how confident you can be that a pattern in your sample reflects the real population rather than chance. This is the territory of hypothesis tests, p-values, confidence intervals, and the tests you choose in choosing a statistical test. Every inferential result carries uncertainty, which is precisely why you report a confidence interval or significance level alongside it.
| Descriptive | Inferential | |
|---|---|---|
| Purpose | Summarise the sample | Generalise to the population |
| Typical output | Mean, SD, frequencies, charts | p-values, confidence intervals, test statistics |
| Answers | What does my data look like? | Is the effect likely real beyond my sample? |
One dataset, both layers in sequence
A short example shows how the two layers connect. Imagine you have measured exam scores for forty students, twenty taught online and twenty in person. The descriptive layer comes first: you report that the online group scored a mean of 68.4 with a standard deviation of 9.1, the in-person group a mean of 73.2 with a standard deviation of 8.6, and you note the frequencies of any missing or repeated cases. At this point you have described exactly what is in your sample and nothing more.
The gap of roughly five points is a fact about these forty students; it is not yet a claim about students in general. To make that leap you move to the inferential layer and run an independent-samples t-test, which asks whether a difference of this size is likely to reflect a real population effect or could plausibly arise from sampling variation. The descriptive numbers feed the test directly: the means supply the difference, the standard deviations and sample sizes supply the uncertainty around it. The descriptive layer is not a warm-up you can skip; it is the input the inferential test runs on. If you want this sequence built end to end on your own data, that is the work in dissertation data analysis help.
The parameter and statistic distinction
One precise idea underpins the whole split. A parameter is a true value for the entire population, usually unknown; a statistic is the estimate of it from your sample. Inferential statistics is the bridge between the two: it uses your sample statistic to make a defensible claim about the population parameter you cannot measure directly. Keeping these terms straight prevents the common slip of describing a sample result as though it were a settled population fact.
Putting it together in your write-up
Present descriptives first in a clear table, then report each inferential result with its effect size and interpretation, following how to report statistics in APA style. If you are working to a tight master's deadline, see master's thesis statistics for a proportionate version of this, and for doctoral work that needs advanced inferential modelling, see PhD statistics help.