Making Sense of Your Numbers: Reading and Reporting Statistics Clearly

A master’s student once came to us with a completed analysis, dozens of tables of output, and a results chapter that simply restated every number the software had produced. The problem was not the statistics; it was that nowhere did the chapter say what the numbers meant for the research question. Interpreting results is a separate skill from running them, and it is the part examiners actually read for.

This guide walks you through the concepts students most often misread, p-values, significance, and effect sizes, and shows you how to turn raw output into a results section that is correct and easy to follow.

Start with the question, not the output

Before you touch a single table, write your research question and hypotheses at the top of the page. Every statistic you report should earn its place by helping answer that question. If a number does not relate to a hypothesis, it usually belongs in an appendix, not your results chapter.

This discipline also stops the most common beginner error: reporting everything the software prints. Your job is to interpret, not to transcribe.

What a p-value actually tells you

The p-value is the single most misunderstood number in student research. It is not the probability that your hypothesis is true, and it is not the size or importance of an effect.

A p-value answers a narrow question: if there were really no effect, how likely is it that you would see a result at least this extreme by chance? A small p-value (commonly below 0.05) suggests the result is unlikely to be pure chance, so you reject the null hypothesis. That is all it does.

Two cautions worth internalising:

• A “significant” result is not necessarily a large or meaningful one.
• A “non-significant” result does not prove there is no effect; it may just mean your sample was too small to detect one.

Tip from practice: Never write “the result was significant” and stop there. Always follow it with what is significant, in which direction, and how large the effect is. Significance without context tells the reader almost nothing.

Why effect size matters as much as significance

If the p-value tells you whether there is likely an effect, the effect size tells you how big it is, and that is what makes a finding interesting. With a large enough sample, even a trivial difference can be statistically significant. Effect sizes (such as Cohen’s d, correlation r, or eta-squared) put the result on a scale your reader can judge.

Always report an effect size alongside your significance test. It is the difference between “men scored higher (p < .01)” and “men scored higher, a small effect (d = 0.2)”, which is a far more honest and useful sentence.

A quick reference for common terms

Use this table as a sanity check while you write. If you cannot fill in the “what it tells you” column in your own words, that is a signal to revisit the concept before submission.

Term	What it tells you	Common mistake
p-value	How likely your result is under the null hypothesis	Reading it as the probability the hypothesis is true
Significance level (α)	Your threshold for “unlikely enough” (often .05)	Treating .05 as a magic line rather than a convention
Effect size	How large or meaningful the effect is	Omitting it and relying on p alone
Confidence interval	The plausible range for the true value	Ignoring it in favour of a single point estimate
Null result	No detectable effect in this sample	Reporting it as proof that no effect exists

How to report results cleanly

Examiners reward clarity. A strong results section follows a predictable rhythm for each finding:

1. Remind the reader of the hypothesis being tested.
2. State the test you ran and on what data.
3. Report the key statistics in standard format, including the effect size.
4. Interpret the result in one plain sentence tied to the research question.

Keep interpretation in the results section factual; save the broader “what this means for the field” discussion for your discussion chapter. Mixing the two is a frequent reason feedback comes back asking you to “separate findings from interpretation”.

In our coaching practice we often see the cleanest results chapters come from students who decided their reporting format and chose their statistics software before collecting data, rather than wrestling with output afterwards.

Common interpretation traps to avoid

A few mistakes appear again and again, and all of them are easy to catch in a careful review:

• Confusing correlation with causation. A relationship between two variables does not mean one causes the other.
• Cherry-picking significant results and quietly dropping the rest, which undermines the integrity of the whole analysis.
• Over-claiming beyond what your design supports, for example generalising from a small, non-random sample.

Whether your study is quantitative or qualitative shapes what counts as a sound claim, so keep your method’s limits in view as you write.

If you want a second pair of eyes before you submit, our statistics support coaching helps you check that your interpretation is sound and that every claim in your results chapter is one your data can actually carry. Getting this right protects months of careful work from a preventable misread.