Logistic Regression: How to Run It Online and Report It in APA7
Logistic regression models the probability of a yes/no (binary) outcome from one or more predictors and reports effects as odds ratios.
What is Logistic Regression?
Logistic regression models the probability of a yes/no (binary) outcome from one or more predictors and reports effects as odds ratios.
When to use it
Use it when the outcome has two categories, such as pass/fail, disease/no disease or purchased/not purchased, and you want to know which predictors change the odds of the outcome.
Example question: Do study hours and prior GPA predict whether a student passes?
Preparing your data
One row per participant. The outcome column is coded 0 and 1 (1 = the event you are modelling). Each predictor is its own column.
Example dataset (simulated; first rows of 150): id, study_hours, prior_gpa (predictors), passed (0 = failed, 1 = passed).
| id | study_hours | prior_gpa | passed |
|---|---|---|---|
| 1.0 | 15.3 | 3.75 | 1.0 |
| 2.0 | 6.9 | 2.91 | 0.0 |
| 3.0 | 8.7 | 2.68 | 0.0 |
| 4.0 | 6.0 | 3.56 | 0.0 |
| 5.0 | 5.7 | 3.26 | 0.0 |
| 6.0 | 4.2 | 2.85 | 0.0 |
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 Logistic Regression 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 binary outcome and one or more predictors. State which category is coded 1.
- 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
- The outcome is binary and its categories are mutually exclusive.
- Observations are independent.
- Continuous predictors have a linear relationship with the log odds of the outcome.
- No severe multicollinearity among predictors.
- Enough events: roughly at least 10 cases of the less frequent outcome per predictor.
- No perfect separation, where a predictor splits the outcome perfectly.
Key numbers to look at
- Omnibus (likelihood-ratio) χ² test of the whole model.
- Pseudo-R2 such as Nagelkerke, which is not the same as linear R2.
- Coefficients B (log odds), standard errors, Wald statistics and p-values.
- Odds ratio, Exp(B), with its 95% CI.
- Classification table (accuracy, sensitivity, specificity) as supporting information.
Effect size
The odds ratio is the effect size. OR = 1 means no effect; OR above 1 means higher odds of the event; OR below 1 means lower odds. As a rough guide, ORs of about 1.5, 2.5 and 4.3 are small, medium and large.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Logistic Regression 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.
| Predictor | B | SE | Wald | p | OR | 95% CI for OR |
|---|---|---|---|---|---|---|
| study hours | 0.48 | 0.08 | 34.88 | < .001 | 1.62 | [1.38, 1.90] |
| prior gpa | 1.07 | 0.56 | 3.73 | .054 | 2.93 | [0.98, 8.70] |
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
- Interpreting odds ratios as risk ratios; the two differ when the outcome is common.
- Using too few events for the number of predictors.
- Reporting accuracy alone, which can look good simply because one outcome is much more common.
Related analyses and alternatives
- Linear Regression: If the outcome is continuous.
- Chi-squared Test: To associate two categorical variables without modelling.
- Regression Analysis: For the regression overview.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
How do I interpret an odds ratio of 2.0?
Each one-unit increase in the predictor doubles the odds of the event, holding other predictors constant.
What is Nagelkerke R²?
A pseudo-R2 that is scaled to range from 0 to 1. It is a rough indication of model fit, not literally the variance explained.
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.