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United States Department of Agriculture

Agricultural Research Service

Probit Download
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Probit analysis programs

These programs are used for statistical analysis of data from bioassay studies, such as determining the effects of insecticides on insect mortality. The programs are written in the Mathematica language. You must have the Wolfram Mathematica or Wolfram Player Pro software on your computer to run these programs. Note: to determine whether you have free access to Mathematica, visit the Mathematica web site (www.wolfram.com) and the web site will automatically notify you if you have a site license. If you don’t have a site license, the Player Pro software package is more economical to purchase if you will only be using the software to run the probit programs that I have written. Player Pro is not a full implementation of the Mathematica software package, but it will allow you to run programs written in the Mathematica language. If you do not have a site license or do not have the Mathematica or Player Pro software package on your computer, you will not be able to run the programs that I have written.

Note: The programs were updated in June 2013 so that the programs will run in either Wolfram Mathematica 9 or Wolfram Player Pro.


Use the following links to download the programs (zip files). Descriptions of the programs are given below.
  • Time-mortality programs – tmprogs.zip
  • Backtransformation programs – btprogs.zip
  • Accessory programs – accprogs.zip
  • Descriptions of numerical methods used – methods.zip
  • Download all programs – all.zip

  • Instructions for downloading and installing files
    1. Click above to download the .zip files that you want.
    2. Extract the .zip file to your Documents folder (this is the default directory where Mathematica looks for files), and then delete the .zip file (a Windows zip utility can be found at www.winzip.com).
    3. The programs are ready to run in Mathematica (see instructions for running the programs below).

      Time-mortality programs

      The PROBIT program is used to analyze bioassay data when multiple observations over time were made on the same groups of organisms at one dose of a stimulus. If you made multiple observations over time at more than one dose in a single study, don't use this program to analyze those data. Instead, use the program by Preisler and Robertson (1989. Journal of Economic Entomology 82: 1534-1542). Our program gives you the option of using any of six possible transformations of the data (probit, logit, CLL [complementary log-log], log-probit, log-logit, log-CLL). All information for complete reporting of probit analyses is provided by the program, including: the slopes and intercepts, with their variances and covariance; the chi-square for goodness-of-fit of the regression line; and lethal time values, with confidence limits. The program PROBIT2 does the same thing, but will calculate all six possible transformations at one time.

      Backtransformation programs

      The backtransformation programs use output from the PROBIT program, or from any other probit analysis program. The BACKTRAN program can be used to transform probit-, logit-, or CLL-transformed data back to the original units (proportion organisms responding to the stimulus) to help assess goodness of fit. The program will also calculate residuals and standardized residuals of proportion organisms responding to the stimulus. The program outputs time or dose, the observed and predicted proportion organisms responding at each time or dose, and the residual and standardized residual corresponding to each time or dose. The program also outputs the observed and predicted probit-transformed (or logit- or CLL-transformed) data corresponding to each time or dose. These data can be used to plot observed vs. predicted proportion organisms responding to the stimulus, or the corresponding probits, to assess goodness-of-fit. These graphs are also automatically generated by the BACKTRAN program. BACKTRAN should be used only for data that are correlated i.e., you looked at the same insects over several time periods. If your data consist of independent observations - i.e., a different batch of organisms for every observation time or for each dose - use BACKTRN2.

      Accessory programs

      The accessory programs use output from the PROBIT program, or from any other probit analysis program. The SLOPE program is used to calculate whether slopes and intercepts from two regression lines differ. The RELPOT program is used to calculate relative potency of two stimuli, including confidence limits on relative potency.


      Instructions for running the programs

      1. To run any of the six programs (PROBIT.nb, PROBIT2.nb, BACKTRAN.nb, BACKTRN2.nb, RELPOT.nb, SLOPE.nb), you first need to edit the appropriate input file (PRinput, PR2input, BTinput, BT2input, RPinput, SLinput, respectively) using a text editor such as Notepad (don’t save the input files as Word Processor files), and then save the input file using the original name for the input file. The files PRinput.txt, PR2input.txt, BTinput.txt, BT2input.txt, RPinput.txt, and SLinput.txt describe the input data required to run the programs, and can be viewed in Notepad. No changes should be made to the Mathematica notebook files (.nb files).
      2. To run one of the programs, ensure that both the modified input file and the notebook file are both in the Documents directory using Windows Explorer. Then double-click the notebook file to open the notebook in Mathematica or Player Pro automatically. Then select “Evaluation”, “Evaluate Notebook” from the toolbar to run the program. If you are running one of the programs that produces graphs, the graphs will be shown at the bottom of the program window. You can click on a graph to select it and then print or save it, or right-click on the selected graph to copy it to the clipboard and then paste the graph into Word, PowerPoint, or another program. The last line of the program window shows the file where output was written. You can open the output file with Notepad to view your output.

        PDF files describing the numerical techniques used in the programs are also available for downloading (methods.zip).


        Papers describing the techniques used:
         pdf icon PDF   Throne, J. E., Weaver, D. K., Chew, V., and Baker, J. E. 1995. Probit analysis of correlated data: Multiple observations over time at one concentration. J. Econ. Entomol. 88: 1510-1512.
         pdf icon PDF   Throne, J. E., Weaver, D. K., and Baker, J. E. 1995. Probit analysis: Assessing goodness-of-fit based on backtransformation and residuals. J. Econ. Entomol. 88: 1513-1516.

      Contact Dr. James Throne with questions or comments.
      Mention of a proprietary product does not constitute an endorsement or a recommendation for its use by USDA.

      Last Modified: 2/24/2014