The four questions, always in this order.
Panic in a results section comes from starting in the middle, usually at a table of unfamiliar symbols. Start at the beginning instead, and refuse to look at any number until the first two questions are answered.
- What was the question? Find the hypothesis or aim in plain words before reading any output
- What was measured, in whom, and how many of them were there?
- Which test was used, and why that one rather than another?
- What did it find, stated as a direction: higher, lower, related, no difference detected
- How large is the effect, and would a practitioner in your field care about a difference that size?
What a p value is, and the three things it is not.
A p value answers one narrow question: if there were genuinely no effect in the population, how likely would it be to see a result at least as extreme as this one. That is all it does. It is compared against a threshold the study chose in advance, called alpha, which should be stated in the methods section rather than decided once the results are in.
Now the misreadings, all three of which appear regularly in coursework. It is not the probability that your hypothesis is true. It is not a measure of how large or important the effect is, so a very small p value does not mean a big finding. And a result above the threshold does not prove there is no effect; it means this study did not detect one, which is a different and much weaker statement. Sample size influences all of this heavily, which is why the count comes before the p value in the order above.
Effect size and intervals, where the meaning lives.
Statistical significance tells you something was probably not noise. Effect size tells you how much of a difference was found, and it is the number that answers the question a clinician or a manager actually has. A study can be significant and trivial at the same time, which happens routinely when the sample is very large, and that is exactly where careful readers separate themselves from careless ones.
Confidence intervals do similar work in a more readable form, because they show a range of plausible values rather than a single verdict. A narrow interval sitting well away from no-difference tells you the finding is both reasonably precise and meaningful. A very wide interval, or one that includes no difference at all, tells you the study cannot rule much out yet, however the accompanying p value reads.
Reading an output table row by row.
Software prints far more than you need. Whether it comes from a statistics package, from R, from Python or from a spreadsheet, the same handful of items carries the meaning and everything else is supporting detail.
- The sample size, and whether cases were excluded and on what grounds
- The descriptive figures first: group means or counts, so the direction is clear before any test
- The test statistic with its degrees of freedom, which mainly tells you what was run
- The p value, read against the threshold the methods section declared
- The effect size, hunted down even when it is not printed beside the test
- Any assumption checks the analysis required, which are usually reported just above
Writing it up without overclaiming.
Report in the order you read: what you asked, what you did, what you found, and what it means. Use the past tense for what happened and stay inside what the design supports. An observational study finds associations rather than causes, and a single word like caused or proved in your discussion is the most common reason otherwise solid papers come back for revision.
Say plainly when nothing was detected, because a study that finds no difference is a result rather than a failure and reviewers respect it being written that way. Follow whichever style your program requires for presenting numbers, italics and decimal places, since those conventions are marked. If the analysis rather than the writing is the obstacle, our statistics coaching walks through the output with you, quoted free within two hours, and doctoral students planning the project behind the data should read the approvals sequence first.
Common questions.
What is a p value really saying about my data?
How surprising your result would be if there were truly no effect in the population. It is compared against a threshold set in advance and stated in the methods section. It does not tell you the probability that your hypothesis is correct, and it says nothing at all about how large or practically important the finding is. Effect size answers that second question.
Can a result be significant but not meaningful?
Yes, and it happens often with large samples, where even a tiny difference clears the threshold. That is why effect size and confidence intervals belong in every write-up. Ask whether a difference of the size reported would change what a practitioner does. If it would not, say so in your discussion rather than letting significance imply importance it does not have.
What should I do when the result is not significant?
Report it as it stands and resist rewording it into a finding. The accurate statement is that this study did not detect a difference, which is not the same as showing there is none. Discuss what might explain it, including sample size and measurement, and note what a future study would need. Reviewers treat honest null results far better than stretched ones.
Do I need to understand the mathematics to pass a statistics course?
You need to understand what each test is for, what its output means and what it cannot claim. Most graduate courses assess interpretation and reporting rather than derivation, which is why the four-question order in this article carries so much of the work. Run the analysis, read the output in that sequence, and write only what the design actually supports.
