Descriptive statistics for research: choosing summaries and reporting them

What should descriptive statistics explain?

Before testing a hypothesis, show who contributed data, how the variables were scored and what the observed values look like. Descriptive statistics summarize the records available for analysis. They do not, by themselves, establish a population difference, an association or a causal effect.

This guide follows the undergraduate research example. It connects the table to its source data so you can check what each number represents. The results chapter guide covers how to integrate this description with hypothesis tests.

Choose a summary that fits the variable

The NIST guide to location explains the mean and median. The mean uses every value and is sensitive to extreme observations; the median describes the middle of the ordered data. NIST's spread guide distinguishes standard deviation from range and interquartile range. Pair a summary with a suitable plot rather than choosing from a normality-test p-value alone.

A single ordered item and a score formed from several items are different variables. In this example, each construct is represented by the mean of five forward-keyed items with responses from 1 to 5. That scoring decision is specified in the study materials; it is not a general rule for every questionnaire. Check the instrument and scale reliability before combining items.

Worked table: two questionnaire scores

There are 180 records, one per student, with no missing responses. The table below was recalculated from the published prepared data. Standard deviations use the sample formula with denominator n − 1. Values are rounded only for presentation.

Each score has 180 observations. The observed range is 1.20–5.00 for academic self-efficacy and 1.20–4.60 for learning persistence.

The possible score range is 1–5; the observed range describes this sample. These similar means do not establish that the constructs are equivalent. The SD describes variation between students' scores, not uncertainty around the mean. Do not label a standard error as SD or treat either as a confidence interval.

Describe the sample with an explicit denominator

The d1 variable identifies year of undergraduate study. Of the 180 students, 56 were in the first year (31.1%), 63 in the second (35.0%) and 61 in the third (33.9%). The denominator is all 180 records because none is missing this variable. Percentages are rounded to one decimal place.

For a different dataset, distinguish all records, valid responses for a variable and complete cases for a particular analysis. Report missing counts and say which denominator was used. A code such as 99 meaning “no response” must not be treated as a substantive score. The data preparation guide includes a reusable codebook template and checklist.

A reporting paragraph you can trace

“The sample included 180 undergraduate students: 56 in their first year (31.1%), 63 in their second (35.0%) and 61 in their third (33.9%). Mean academic self-efficacy was 2.99 (SD = 0.75), and mean learning persistence was 2.98 (SD = 0.73). Each score was the mean of five items scored from 1 to 5. No responses were missing.”

Adapt the structure to your actual variables and study; do not copy the numbers into another report. Avoid assigning labels such as “high” or “low” without a justified interpretation rule. Describing these scores does not test the study's association hypothesis.

Check the files and the next decision

Compare the questionnaire, variable dictionary, prepared data and complete findings chapter. The worked table here adds medians and observed ranges to help explain the data; it is an editorial calculation from the same CSV, not a claim that every displayed column appears in the generated findings chapter.

Once the description is clear, use the test-selection guide to connect the research question to an appropriate analysis. The statistical analysis service explains possible deliverables and their scope. The website currently offers content and examples; consultation and ordering remain closed. See service availability.

See the complete research examples

Follow the research questions through the input files, analysis plan and outputs. Each example includes the consultation report, itemized illustrative price and generated files.