SPSS command: SPSS PROBIT

Probit analysis for dose-response data

Q: Probit or logit model?

They usually give very similar effective doses. Probit is traditional in toxicology and assumes normally distributed tolerances; logit has heavier tails and gives odds-ratio slopes. Compare the Pearson goodness-of-fit results if unsure.

Q: Why log-transform the dose?

Biological tolerance is often log-normally distributed, so the curve is symmetric in log dose. With Log base 10 or Natural log selected, the limits are still reported back on the original dose scale.

Q: What is the heterogeneity factor?

If the Pearson goodness-of-fit p is below .150, responses vary more than the binomial model allows. The limits are then widened using the Pearson chi-square per df and a t critical value, and a footnote says so.

Q: Why are fiducial limits missing?

Fiducial limits exist only when the dose effect is clearly different from zero (g < 1). If the slope is imprecise the table explains that the limits are not available; more doses or subjects usually fix it.

Q: How do I read relative median potency?

A vs. B = 0.70 means A needs only 0.70 times the dose of B for the same 50% response, so A is more potent. It is valid when the parallelism test does not reject a common slope.

Probit analysis fits an S-shaped curve to grouped yes/no responses — how many of n subjects responded at each dose — and turns it into effective doses such as the ED50 with fiducial confidence limits.

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Free · No account · Files stay on your device · Updated 18 October 2026

What it tells you

Crosstabs runs the SPSS PROBIT procedure on your device with probit or logit models, log-transformed doses, an optional natural response rate and relative median potency between groups.

How steeply the response probability rises with dose (the slope on the probit or logit scale) and its standard error.
The dose that produces any response rate from 1% to 99%, including the ED50, with 95% fiducial limits on the original dose scale.
Whether the model fits the grouped data (Pearson goodness-of-fit test) and whether a heterogeneity factor is needed.
With a grouping factor, whether the dose-response lines are parallel and how many times more potent one preparation is than another.

When to use it

Use it when

Toxicology, pharmacology or agronomy bioassays where each row is a dose with the number tested and the number responding.
You need effective doses (ED50, ED90, LD50) with confidence limits rather than just regression coefficients.
Comparing two or more compounds or batches on a common slope (relative median potency).
Some subjects respond even at zero dose and you want to estimate or fix that natural response rate.

Use something else when

Each row is one individual with a 0/1 outcome and several predictors: binary logistic regression or GENLIN with a binomial probit link is more natural.
The response is a continuous measurement rather than a count of responders: use nonlinear regression for a dose-response curve.
You need effective-dose limits with several covariates: the confidence limits table is produced for a single covariate only.

How to run it in Crosstabs

01
Arrange grouped data
One row per dose (and group), with a column for the number responding, one for the number tested and the dose itself. Open it in Statistics mode.
02
Choose Probit analysis
In the Regression group, pick Probit analysis (PROBIT).
03
Assign the variables
Set Response frequency to the responder count and Total observed to the number tested, tick the dose under Covariates (up to six), and optionally choose a Factor (optional) for groups.
04
Choose the model
Under Model choose Probit or Logit, set Transform covariate to None, Log base 10 or Natural log, and set Natural response rate to None, Calculate from data or Specify value.
05
Run and read the limits
Click Run. The ED50 is the row with probability .50 in Confidence Limits, back-transformed to the original dose scale.

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Worked example

Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.

Try with example data

Data

Two synthetic formulations (A, B) are each tested at doses 1, 2, 4, 8, 16 and 32 on 40 subjects per dose; responded counts how many reacted. Responses are binomial draws from a probit curve in log10(dose), with B shifted to need a higher dose; the seed is fixed. Transform covariate = Log base 10, Factor = formulation.

Parameter Estimates

Item	Parameter	Estimate	Std. Error	Z	Sig.	Lower Bound	Upper Bound
PROBIT	dose (log10)	2.787	0.206	13.499	<.001	2.382	3.191
	Intercept [formulation=A]	−1.899	0.179	−10.633	<.001	−2.249	−1.549
	Intercept [formulation=B]	−2.332	0.203	−11.511	<.001	−2.729	−1.935

Chi-Square Tests

Item	Category	Chi-Square	df	Sig.
PROBIT	Pearson Goodness-of-Fit Test	10.613	9	.303
	Parallelism Test	0.037	1	.847

Confidence Limits

formulation	Probability	Estimate	Lower Bound	Upper Bound
A	0.100	1.665	1.282	2.066
A	0.500	4.801	4.016	5.736
A	0.900	13.842	11.175	17.937
B	0.100	2.381	1.840	2.947
B	0.500	6.865	5.746	8.210
B	0.900	19.793	15.938	25.752

Fiducial limits use the normal critical value 1.96. Only probabilities .10, .50 and .90 are shown here; the panel lists .01 to .99.

Relative Median Potency Estimates

formulation	Estimate	Lower Bound	Upper Bound
A vs. B	0.699	0.525	0.904
B vs. A	1.430	1.106	1.904

Potency is back-transformed to a ratio of doses on the original scale.

How to read it

On the log10 dose scale the common probit slope is 2.787 (SE 0.206). The Pearson goodness-of-fit test gives χ²(9) = 10.61, p = .303, and the parallelism test (p = .847) does not reject equal slopes, so comparing the two lines by a horizontal shift is reasonable. The median effective dose (ED50) is 4.80 for A and 6.87 for B; the relative median potency A vs. B is 0.699 (95% fiducial limits 0.525 to 0.904).

Output tables explained

Parameter Estimates: The slope for each covariate and one intercept per group, with standard error, Z, significance and confidence interval; the model equation is footnoted.
Natural Response Rate: Shown when the rate is estimated from data or fixed: the background response proportion included in the model.
Chi-Square Tests: Pearson goodness-of-fit test and, with a factor, the parallelism test. When the Pearson p is below .150, a heterogeneity factor widens the confidence limits.
Cell Counts and Residuals: For each dose: subjects, observed and expected responses, residual and fitted probability.
Confidence Limits: Estimated dose for probabilities .01 to .99 with 95% fiducial limits, on the transformed and original scales.
Relative Median Potency Estimates: With a factor and parallel lines: the ratio of median effective doses for each pair of groups with 95% confidence limits.

Assumptions and notes

Subjects respond independently, so the count at each dose is binomial; extra variation shows up as a significant Pearson test.
The response probability follows a normal (probit) or logistic (logit) curve in the chosen dose scale, usually log dose.
Doses must be positive for a log transform; rows that cannot be transformed or have invalid counts are excluded with a note.
Relative potency is meaningful only when the parallelism test supports a common slope.

How the results are validated

PROBIT is checked against a statsmodels binomial GLM with a probit or logit link and an independent NumPy implementation of the SPSS fiducial-limit and relative-potency formulas. With a grouping factor and log10 dose, estimates agree within 1e-7, standard errors within 1e-6, the Pearson statistic within 1e-7, and fiducial limits and relative median potency within 1e-6; a logit model without a factor also checks the heterogeneity-factor limits, and the estimated natural response rate agrees within 1e-5. Validation evidence

Questions

Probit or logit model?

They usually give very similar effective doses. Probit is traditional in toxicology and assumes normally distributed tolerances; logit has heavier tails and gives odds-ratio slopes. Compare the Pearson goodness-of-fit results if unsure.

Why log-transform the dose?

Biological tolerance is often log-normally distributed, so the curve is symmetric in log dose. With Log base 10 or Natural log selected, the limits are still reported back on the original dose scale.

What is the heterogeneity factor?

If the Pearson goodness-of-fit p is below .150, responses vary more than the binomial model allows. The limits are then widened using the Pearson chi-square per df and a t critical value, and a footnote says so.

Why are fiducial limits missing?

Fiducial limits exist only when the dose effect is clearly different from zero (g < 1). If the slope is imprecise the table explains that the limits are not available; more doses or subjects usually fix it.

How do I read relative median potency?

A vs. B = 0.70 means A needs only 0.70 times the dose of B for the same 50% response, so A is more potent. It is valid when the parallelism test does not reject a common slope.

Run Probit Analysis on your own data

Open a .sav, CSV or Excel file. Everything runs in your browser; the file never leaves your device.

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