Binomial Test: How to Run It Online and Report It in APA7
The binomial test checks whether the proportion of "successes" in a sample differs from a proportion you expected in advance.
What is Binomial Test?
The binomial test checks whether the proportion of "successes" in a sample differs from a proportion you expected in advance.
When to use it
Use it for a yes/no outcome in one sample, for example whether the share of customers who prefer a product differs from 50%.
Example question: Did more than half of the 50 participants choose option A?
Preparing your data
Either the number of successes and the total number of trials, or one column with two categories (such as yes and no), one row per participant.
Example dataset (simulated; first rows of 50): id, choice (A or B); 36 participants chose A and 14 chose B; test value = .50.
| id | choice |
|---|---|
| 1 | A |
| 2 | A |
| 3 | A |
| 4 | A |
| 5 | A |
| 6 | A |
Download the full example CSV to practise. If the tool asks for a different layout, follow the instructions on its page.
How to run it on StatFas
- Open the Binomial Test tool. You do not need an account to run an analysis.
- Enter your data or upload your file, laid out as described in Preparing your data.
- Select your variables. Choose the category that counts as a success, enter the number of trials and the hypothesised proportion (for example .50).
- Choose any options the tool offers (for example the confidence level, a post hoc test or the error bar type) and run the analysis.
- Read the results on the page. Check the assumptions first, then the test statistic, the p-value and the effect size.
- To save your results, log in or create a free account. Every analysis stays free; the account is only needed to download.
Assumptions and checks
- Each trial has exactly two outcomes.
- Trials are independent and the sample size is fixed in advance.
- The probability of success is the same on every trial.
- The hypothesised proportion is chosen before looking at the data.
Key numbers to look at
- Observed count and proportion of successes.
- Exact p-value (two-sided unless a direction was predicted).
- Confidence interval for the proportion (the exact Clopper–Pearson interval is common).
- Hypothesised proportion used in the test.
Effect size
Report the observed proportion with its confidence interval. Cohen's h can describe the difference from the hypothesised proportion.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Binomial Test in APA7 style
Template
Worked example (simulated data)
The numbers below were computed from the example CSV above, so you can reproduce them. They illustrate the format and are not real findings.
APA7 reminders: italicise statistical symbols (M, SD, t, F, p, r), report exact p-values to two or three decimals (use p < .001 for very small values), omit the leading zero for values that cannot exceed 1 (.45, not 0.45), and put degrees of freedom in parentheses. See the APA7 cheat sheet.
Common mistakes
- Using it for outcomes with more than two categories (use a chi-squared goodness-of-fit test).
- Counting several responses per person as independent trials.
- Switching to a one-sided test after seeing the direction of the result.
Related analyses and alternatives
- Chi-squared Test: Two or more categories, or two categorical variables.
- One sample t-Test: If the outcome is continuous.
- Frequency Analysis: To count the categories first.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
Why is it called exact?
It computes the probability from the binomial distribution directly, without a normal approximation, so it is valid for small samples.
How do I choose the hypothesised proportion?
Use a value that comes from theory, prior research or chance (for example .50 for a two-option choice) and decide it before collecting data.
References
American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
This guide is for learning and for preparing results for your own reports. You remain responsible for choosing an appropriate analysis, checking its assumptions and interpreting the results. Follow the formatting rules of your journal or institution where they differ from APA7.