Skip to content
Theoria home
Log in

For upper secondary and university students, and anyone who wants to understand the numbers in studies

Understanding statistics in studies: p-value, effect size and confidence interval

Almost every study contains details such as "significant (p < 0.05)" or "95% confidence interval". They help determine what a result means, and they are often misunderstood. This guide explains the three most important ones without formulas and shows what to look out for when reading.

Updated on 28 October 2026

The question

What do the p-value, effect size and confidence interval in a study mean, and how do I read them correctly?

In short

The p-value shows how well the data fit the assumption that there is no effect: the smaller it is, the worse they fit. Only the effect size shows how large an effect is, and whether it matters is something you judge in context. The confidence interval indicates which values are compatible with the data; the wider it is, the more uncertain the result.

Step by step

  1. Step 1

    Understand the measurement first

    Before you read any numbers: what was compared, and how was it measured? A number only makes sense if you know what it refers to, for example hours per day, points on a test or a percentage.

    In Theoria: Deep Insights explains a paper at a depth you choose from 1 to 10: a low depth gives an overview, a higher depth explains methods and background.

  2. Step 2

    Read the p-value correctly

    The p-value shows how well the data fit the assumption that there is no effect: the smaller it is, the worse they fit. A small p-value, often below 0.05, is called "statistically significant": if there were no effect, data like these would be rather surprising. But it does not tell you how likely a hypothesis is to be true, nor how large the effect is.

  3. Step 3

    Look at the effect size

    The effect size describes how strong a difference or association is, for example as a difference in hours or as a correlation. With very large samples, even a tiny effect can be significant. So always ask whether the effect is large enough to matter in everyday life.

  4. Step 4

    Read the confidence interval

    A 95% confidence interval gives the range of values that agree well with the data. A narrow interval points to a precise result, a wide one to a lot of uncertainty. If the interval for a difference includes zero, "no difference" is also compatible with the data. An example from a study on phone rules at schools: for wellbeing, the adjusted difference between schools with and without a ban was -0.48 points, 95% confidence interval -2.05 to 1.06 (p = 0.62). For phone time during school hours, it was -0.67 hours, interval -0.92 to -0.43. Only the second interval excludes zero.

  5. Step 5

    Do not read too much into a single result

    A significant result can be a chance finding, and a non-significant one does not prove that there is no effect. Check whether other studies reach the same result.

    In Theoria: AI Peer Review lists strengths and limitations of a paper as a starting point for your own check.

Worked example

100 studies, run again

In 2015 the Open Science Collaboration published a large project in Science: researchers repeated 100 experiments and correlational studies from three psychology journals, using designs with high statistical power and, where possible, the original materials. The results show why a p-value on its own says little.

p-values
97 percent of the original studies had a statistically significant result; in the replications it was 36 percent.
Effect sizes
On average, the effects in the replications were only half as large as in the original studies.
Confidence intervals
47 percent of the original effect sizes fell within the 95% confidence interval of the replication.
What predicted success
Whether a replication succeeded was linked more to the strength of the original evidence than to characteristics of the research teams.
What the project does not show
That the original studies were wrong. A replication can also fail because of differences in the sample or the procedure. But it does show that a single significant result is no guarantee that it can be replicated.

A significant result is a start, not proof. Pay attention to the size of the effect, to the uncertainty and to whether others have been able to repeat the result.

Where AI reaches its limits

  • AI can explain statistics wrongly or mix up numbers. Check every number you use against the results section of the original.
  • AI summaries often only say whether a result is significant. You will usually find the effect size and confidence interval only in the paper itself.
  • The statistics do not tell you whether a study was well planned. Check the design, sample and measurement as well.
  • Theoria's explanations are generated by AI and can contain mistakes. Check important claims against the linked source.

Read the numbers in a real paper

Open a paper in Theoria on a topic that interests you and look for the p-value, effect size and confidence interval in the results section. "Ask Theoria", Deep Insights and AI Peer Review need a free account; some tools have monthly limits on the free plan.

Start for freeHow reliable is a study?

Sources

  1. Open Science Collaboration (2015). Estimating the reproducibility of psychological science. Science, 349(6251), aac4716. https://doi.org/10.1126/science.aac4716Basis of the worked example.
  2. Wasserstein, R. L., & Lazar, N. A. (2016). The ASA Statement on p-Values: Context, Process, and Purpose. The American Statistician, 70(2), 129-133. https://doi.org/10.1080/00031305.2016.1154108Statement by the American Statistical Association on the meaning and limits of the p-value.
  3. Goodyear, V. A., et al. (2025). School phone policies and their association with mental wellbeing, phone use, and social media use (SMART Schools): a cross-sectional observational study. The Lancet Regional Health - Europe, 51, 101211. https://doi.org/10.1016/j.lanepe.2025.101211Source of the confidence interval figures in step 4. Open access.

Publication details checked against Crossref and arXiv on 27 October 2026.

Other guides

All guides