Quantitative analysis

“What do my results actually say?”

Reading the few things that change your conclusion, in plain words.

You ran the analysis, or someone ran it for you, and the output is a wall of terms: regression, effect size, post-hoc, MANCOVA. Half of it you don’t follow, so you have quietly trusted the conclusions. You do not need to become a statistician. You need to read four things.

By Heidi Andersén, MD, PhD · Updated 18 July 2026 · 7 min read

“I am a PhD student, and I don’t understand statistical studies. Ok… I said it. Since I don’t understand half of the results, I have to trust in the correctness of the conclusions.” — a doctoral student, saying it out loud

The problemTrusting a conclusion you can’t read is a risk, not a shortcut.

The honest thing that student admitted, trusting the conclusions because the results are opaque, is extremely common, and it is where errors hide. If you cannot read your own output, you cannot tell a strong finding from a fragile one, and you cannot catch the mistake that turns a significant result non-significant. For most theses, four ideas carry nearly all the meaning, and none needs an equation.

You will also have to defend numbers you did not fully read. At a viva or in review, someone will ask what a result means, not how the software computed it. “What does this effect size tell us in practice?” is answerable in a sentence if you have read the four things, and terrifying if you have not.

Common mistakesFour misreadings to avoid

Reading significance as importance. “p < 0.05” says the effect is probably not zero, not that it is large or that it matters.
Reading non-significance as “no effect”. It often means the study was too small to be sure: absence of evidence, not evidence of absence.
Ignoring the confidence interval. The interval, not the point estimate, tells you how much you actually know.
Reporting only the p-value. A finding without an effect size and interval is half a sentence, and reviewers notice the missing half.

The four thingsWhat changes the meaning

Effect size is the number that matters most and gets read least. It answers “how much?”, how large the difference or association is in units you can picture, and a tiny effect can be statistically significant in a large sample while meaning nothing in practice.

Significance, the p-value, tells you how surprising your result would be if there were truly no effect. A small one says “unlikely if nothing were going on”, not “big” or “important” or “definitely real”, so read it alongside the effect size, never alone.

The confidence interval is the range of values compatible with your data, not a verdict. A narrow one means you have pinned the effect down; a wide one crossing zero means you do not yet know the direction.

What to report is all three together, effect size first, then interval, then p-value, with one plain sentence on what the effect means. That habit answers most viva questions before they are asked.

Worked exampleReading one result aloud

From output to a sentence

Take a result: mean difference 2.1 points, 95% CI 0.3 to 3.9, p = 0.02. Read plainly, that is: the intervention group scored about 2 points higher on average; the data are compatible with a true difference anywhere from about 0.3 to 3.9 points, so the direction is fairly clear but the size is uncertain; and a difference this large would be unlikely if there were really no effect. Whether 2 points matters is a judgement about the scale, not a statistical one.

Notice what you just did. You read the size, the range, and the significance, and you separated “is it there?” from “does it matter?”

ChecklistRead any result

Four questions per result

Effect size: how big is it, in units you can picture, and does that size matter in practice?
Confidence interval: how wide, and does it cross zero (or 1 for ratios)?
p-value: read alongside the effect size, not alone.
Can you say the result in one plain sentence, separating “is it there?” from “does it matter?” If not, flag it for the statistician early.

When to call the statisticianSooner than you think

Ask for help early, and specifically, when the model itself is in question (which test, which covariates), when results shift depending on choices you don’t understand, or when a reviewer challenges the analysis. Bring the four things you can read and name exactly what you cannot. “I can read the effect size and interval, but I don’t understand why this covariate changes the result” gets you a useful answer; “I don’t understand any of it” gets you a lecture.

Related guidesRead next

There is no Vahtian tool that reads your statistics for you; that judgement stays with you, and with your statistician when it gets hard. If the next step is designing a study whose statistics are answerable from the start, StudyVahti Vault keeps the question, estimand, and analysis plan in one place before any data arrives.