# Probit Regression

This procedure measures the relationship between the strength of a stimulus and the proportion of cases exhibiting a certain response to the stimulus. It is useful for situations where you have a dichotomous output that is thought to be influenced or caused by levels of some independent variable(s) and is particularly well suited to experimental data. This procedure will allow you to estimate the strength of a stimulus required to induce a certain proportion of responses, such as the median effective dose.

Example. How effective is a new pesticide at killing ants, and what is an appropriate concentration to use? You might perform an experiment in which you expose samples of ants to different concentrations of the pesticide and then record the number of ants killed and the number of ants exposed. Applying probit regression to these data, you can determine the strength of the relationship between concentration and killing, and you can determine what the appropriate concentration of pesticide would be if you wanted to be sure to kill, say, 95% of exposed ants.

Statistics. Regression coefficients and standard errors, intercept and standard error, Pearson goodness-of-fit chi-square, observed and expected frequencies, and confidence intervals for effective levels of independent variable(s). Plots: transformed response plots.

## Probit Regression data considerations

Data. For each value of the independent variable (or each combination of values for multiple independent variables), your response variable should be a count of the number of cases with those values that show the response of interest, and the total observed variable should be a count of the total number of cases with those values for the independent variable. The factor variable should be categorical, coded as integers.

Assumptions. Observations should be independent. If you have a large number of values for the independent variables relative to the number of observations, as you might in an observational study, the chi-square and goodness-of-fit statistics may not be valid.

Related procedures. Probit analysis is closely related to logistic regression; in fact, if you choose the logit transformation, this procedure will essentially compute a logistic regression. In general, probit analysis is appropriate for designed experiments, whereas logistic regression is more appropriate for observational studies. The differences in output reflect these different emphases. The probit analysis procedure reports estimates of effective values for various rates of response (including median effective dose), while the logistic regression procedure reports estimates of odds ratios for independent variables.

## Obtaining a Probit Regression analysis

This feature requires SPSS® Statistics Standard Edition or the Regression Option.

Analyze > Regression > Probit...

2. Select a response frequency variable. This variable indicates the number of cases exhibiting a response to the test stimulus. The values of this variable cannot be negative.
3. Select a total observed variable. This variable indicates the number of cases to which the stimulus was applied. The values of this variable cannot be negative and cannot be less than the values of the response frequency variable for each case.

Optionally, you can select a Factor variable. If you do, use Define Range to define the range for the groups.

4. Select one or more covariate(s). This variable contains the level of the stimulus applied to each observation. If you want to transform the covariate, select a transformation from the Transform drop-down list. If no transformation is applied and there is a control group, then the control group is included in the analysis.
5. Select either the Probit or Logit model.
Probit Model
Applies the probit transformation (the inverse of the cumulative standard normal distribution function) to the response proportions.
Logit Model
Applies the logit (log odds) transformation to the response proportions.

This procedure pastes PROBIT command syntax.