What predicts whether a student passes or fails, whether a patient adheres to treatment, or whether an employee intends to leave? When the outcome has two categories, linear regression is the wrong tool and logistic regression is the standard choice. The output is easy to produce in SPSS, but the odds ratio in the Exp(B) column is regularly described as a probability or a percentage chance, which it is not.
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This guide explains odds and odds ratios in plain terms, the assumptions, the SPSS steps, how to read the six main output tables, and how to report the model in APA style.
What is binary logistic regression? It is a regression model for a dependent variable with two categories (coded 0 and 1). It models the natural logarithm of the odds of the outcome coded 1 as a linear combination of predictors, which can be continuous or categorical. Exponentiating each coefficient gives an odds ratio: the multiplicative change in the odds of the outcome for a one-unit increase in that predictor, holding the other predictors constant.
What is the difference between probability, odds and an odds ratio?
| Concept | Formula | Example |
|---|---|---|
| Probability | Events ÷ all cases | 60 passes out of 80 students = .75 |
| Odds | Probability ÷ (1 − probability) | .75 ÷ .25 = 3, read as “3 to 1” |
| Odds ratio | Odds in group A ÷ odds in group B | Odds 3 in one group and 1.5 in another give OR = 2.00 |
An odds ratio of 2.00 means the odds are doubled. It does not mean the probability is doubled, and it does not mean “a 2% higher chance”. When the outcome is common, odds ratios overstate the relative change in probability, so describe them as odds.
When should you use logistic regression?
Use binary logistic regression when the outcome has exactly two categories (pass/fail, yes/no, adopted/did not adopt) and you want to estimate how one or more predictors relate to it. For outcomes with three or more unordered categories use multinomial logistic regression; for ordered categories, ordinal regression. For two categorical variables with no other predictors, the chi-square test may be sufficient.
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What are the assumptions of logistic regression?
- A binary dependent variable, coded 0 and 1, with the event of interest coded 1.
- Independent observations: no repeated measurements of the same people.
- Linearity in the logit for continuous predictors. A common check is the Box-Tidwell approach: add the interaction of each continuous predictor with its own natural log and check that it is not significant.
- No strong multicollinearity, checked with tolerance and VIF from a linear regression run on the same predictors (VIF above about 10 is a common warning sign, many authors use 5).
- No highly influential cases, checked with standardized residuals and Cook’s distance saved from the model.
- Enough events per predictor. Peduzzi et al. (1996) found that fewer than about 10 events per variable (the smaller outcome group divided by the number of predictor terms) produced biased estimates. With 60 failures, plan for no more than about six predictor terms.
How do you run logistic regression in SPSS?
- Analyze, then Regression, then Binary Logistic.
- Move the outcome to Dependent and the predictors to Covariates.
- Click Categorical and declare every categorical predictor. Choose the reference category (First or Last) deliberately, because every odds ratio for that variable is compared with it.
- Under Options, tick Hosmer-Lemeshow goodness-of-fit and CI for exp(B) at 95%.
- Under Save, tick Cook’s and Standardized residuals if you want to check influential cases.
- Keep the Enter method unless your theory justifies a hierarchical (block) entry. Stepwise selection is widely criticized for theory-driven research.
How do you read the six output tables?
- Dependent Variable Encoding confirms which category SPSS treats as 1. Every odds ratio refers to this category.
- Categorical Variables Codings shows the reference category of each categorical predictor (the row with all zeros).
- Block 0 Classification Table shows the accuracy of a model with no predictors, which simply predicts the larger group. It is the baseline.
- Omnibus Tests of Model Coefficients tests whether the model with predictors fits better than the baseline. Report the chi-square, df and p.
- Model Summary and Hosmer-Lemeshow test: Cox and Snell and Nagelkerke R² are pseudo R² values and should not be read as variance explained. A non-significant Hosmer-Lemeshow test indicates acceptable fit, though it is sensitive to sample size.
- Variables in the Equation is the core table: B, S.E., Wald, df, Sig., Exp(B) and the 95% CI for Exp(B).
How do you interpret odds ratios in logistic regression?
- Exp(B) above 1: higher values of the predictor are associated with higher odds of the outcome. An Exp(B) of 1.35 for hours of study means each extra hour multiplies the odds of passing by 1.35, that is, a 35% increase in the odds.
- Exp(B) below 1: lower odds. An Exp(B) of 0.70 means a 30% decrease in the odds per unit.
- Exp(B) for a categorical predictor: the odds in that category compared with the reference category.
- The confidence interval: if the 95% CI for Exp(B) includes 1, the predictor is not significant at the .05 level. A very wide interval signals a small subgroup or separation problems.
Watch the unit. If a predictor is income in single currency units, an odds ratio of 1.0002 can still be important; rescale it (for example, per 1,000) before interpretation.
Worked example (illustrative)
The numbers are an illustrative scenario, not results from a real study. A logistic regression with 240 students predicts passing (1) versus failing (0) from weekly study hours and attendance at a revision workshop (attended versus not attended, reference = not attended).
| Predictor | B | SE | Wald | p | Exp(B) | 95% CI |
|---|---|---|---|---|---|---|
| Study hours | 0.30 | 0.08 | 14.06 | < .001 | 1.35 | [1.15, 1.58] |
| Workshop (attended) | 0.69 | 0.31 | 4.95 | .026 | 1.99 | [1.09, 3.66] |
APA sentence: “Each additional weekly study hour was associated with 1.35 times higher odds of passing, OR = 1.35, 95% CI [1.15, 1.58], p < .001, and attending the workshop roughly doubled the odds of passing compared with not attending, OR = 1.99, 95% CI [1.09, 3.66], p = .026.” Add the omnibus test, Nagelkerke R² and the classification accuracy compared with the baseline.
Which mistakes appear most often?
- Describing an odds ratio as a probability or a “percentage chance”.
- Not checking which category is coded 1 and which is the reference, which inverts the interpretation.
- Too many predictors for the number of events.
- Treating Nagelkerke R² as variance explained.
- Reporting B without Exp(B) and its confidence interval.
- Ignoring huge standard errors and enormous odds ratios, often caused by a category in which everyone has the same outcome (complete separation).
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Frequently asked questions
What is the difference between linear and logistic regression?
Linear regression predicts a continuous outcome directly. Logistic regression predicts the log odds of a two-category outcome, so its coefficients are read through odds ratios rather than as changes in the outcome’s units.
What sample size do I need?
A widely cited guide is at least 10 events per predictor term (Peduzzi et al., 1996), counted in the smaller outcome group. Later studies suggest the rule is approximate, so a larger sample is safer when predictors are correlated or categories are rare.
Should I report B or Exp(B)?
Report both in the table, with the standard error, Wald statistic, *p* and the 95% CI for Exp(B). In the text, odds ratios are easier for readers to understand.
Why does SPSS exclude cases from the model?
Logistic regression uses listwise deletion: a case missing on any predictor is dropped. Check the Case Processing Summary and report the final N. If many cases are lost, discuss how missing data were handled.
Is the Hosmer-Lemeshow test required?
It is commonly reported but not mandatory. In large samples it flags trivial misfit, and in small samples it has little power. Report it alongside the omnibus test and the classification table rather than alone.
Sources
- Hosmer, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied Logistic Regression (3rd ed.). Wiley.
- Peng, C.-Y. J., Lee, K. L., & Ingersoll, G. M. (2002). An introduction to logistic regression analysis and reporting. The Journal of Educational Research, 96(1), 3–14. https://doi.org/10.1080/00220670209598786
- Peduzzi, P., Concato, J., Kemper, E., Holford, T. R., & Feinstein, A. R. (1996). A simulation study of the number of events per variable in logistic regression analysis. Journal of Clinical Epidemiology, 49(12), 1373–1379. https://doi.org/10.1016/S0895-4356(96)00236-3
- Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE.
- Laerd Statistics. Binomial logistic regression using SPSS Statistics. https://statistics.laerd.com/spss-tutorials/binomial-logistic-regression-using-spss-statistics.php
Sources last checked: November 2026. This article is general educational guidance and does not replace your university regulations or your supervisor’s instructions. How we prepare our content.