Purpose

   Probit Analysis is a method of analyzing the relationship between a stimulus (dose) and the quantal (all or nothing) response. Quantitative responses are almost always preferred, but in many situations they are not practical. In these cases, it is only possible to determine if a certain response (such as death) has occurred. In a typical quantal response experiment, groups of animals are given different doses of a drug. The percent dying at each dose level is recorded. These data may then be analyzed using Probit Analysis.
    StatPlus realizes 2 different methods of probit analysis. This page contains description of Finney method  due the popularity of this method.
    The Probit Model assumes that the percent response is related to the log dose as the cumulative normal distribution. That is, the log doses may be used as variables to read the percent dying from the cumulative normal. Using the normal distribution, rather than other probability distributions, influences the predicted response rate at the high and low ends of possible doses, but has little influence near the middle. Hence, much of the comparison of different drugs is done using response rates of fifty percent. The probit model may be expressed mathematically as follows:

where P is five plus the inverse normal transform of the response rate (called the Probit). The five is added to reduce the possibility of negative probits, a situation that caused confusion when solving the problem by hand.
    When using of Finney method the regression line is created for logs of dozes. Some programs in Finney method adjust 0 % and 100 % lethality under the formula 49%/N, instead of 25%/N. You can change percents correction method in Service→Parameters...: Other.

Preparations

    Run Statistics→Survival Analysis→Probit analysis....

Results

    Doses are shown in the first column. Lethality percents are shown in the second column. In other columns probites, weights and some of auxiliary quantities are shown.

    LD50, LD50 Error, LD16, LD84, LD100, lower and upper confidence limits are calculated.
    Dose - the dose level.
    Actual Percent - the ratio of the count to the sample size (R/N).
    Probit Percent - the estimated ratio (R/N) based on the probit model.
    N - the sample size.
    R - the count (number responding).
    E(R) - the expected count based on the probit model.
    Difference - the difference between the actual and the expected counts.
    Chi-Square - the Chi-Square statistic for testing the significance (non-zero) of the difference. Since these are single degree of freedom tests, the value should be greater than 3.81 to be significant at the 0.05 level.
    Chi-Square - the total of the Chi-Square values, used to test the overall significance of the differences from the model.
    Degrees of freedom - the degrees of freedom of the Chi-Square test.

     If the data for a cumulative operation estimation was specified then LD50 for cumulative action and the cumulation coefficient are calculated.