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.
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.
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.
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.
If you treated one batch of organisms with one dose of a stimulus (e.g., a pesticide or drug) and looked at response (e.g., mortality) of that one batch of organisms several times after exposure, click here for time-mortality analysis of correlated data. (E.g., you treated one batch of 100 insects with one dose of an insecticide, and then checked mortality of that one batch of insects at 24, 48, 72, 96, and 120 h.)
If you treated several batches of organisms with one dose of a stimulus (e.g., a pesticide or drug) and at a series of times looked at response (e.g., mortality) of one of those batches of organisms, click here for time-mortality analysis of independent data. (E.g., you treated 5 batches of 100 insects with one dose of an insecticide, and then checked mortality of 1 batch at 24 h, another batch at 48 h, another batch at 72 h, another batch at 96 h, and another batch at 120 h.)
If you treated several batches of organisms with different doses of a stimulus (e.g., a pesticide or drug) and looked at response (e.g., mortality) after a fixed period of time, click here for dose- mortality analysis of independent data. (E.g., you treated 5 batches of 100 insects with 10, 20, 30, 40, and 50 ppm of an insecticide, and then checked mortality at 24 h.)
Additional utilities are available below, but use of these utilities requires that you have access to the Mathematica software program. Note: To determine whether you have free access to Mathematica, visit the Mathematica web site (www.mathematica.com) and the web site will automatically notify you if you have a site license. If you do not have a site license or do not have the Mathematica software package on your computer, you will not be able to run the programs that I have written.
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.
Download Backtransformation programs here
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.
Download Accessory programs here
The tools you select depend on your analysis needs and your comfort level with programming. We recommend that inexperienced users begin with the tools that do not require programming expertise. A menu-driven package (CADStat) will allow you to conduct several types of data visualization and statistical analyses using a menu-driven interface. The Species Sensitivity Distribution (SSD) Generator provides detailed instructions and macros to generate SSDs. Users with knowledge of command-line statistical programming can begin with the more complex, analytically flexible tools.
CADStat is a menu-driven package of several data visualization and statistical methods. It is based on a Java Graphical User Interface to R. Methods in this package include: scatterplots, box plots, correlation analysis, linear regression, quantile regression, conditional probability analysis, and tools for predicting environmental conditions from biological observations. See the Helpful Links box for links to the CADStat installation instructions and Java GUI Interface to R.
The SSD Generator can be downloaded from the Helpful Links box. More information on using SSDs in causal analysis can be found on the Species Sensitivity Distribution page (follow the link in the helpful links box).
Before beginning any computations, it is helpful to first set up a working directory. Using Windows Explorer (or any other comparable method), make a new folder for storing your work. Then, after launching R, select File: Change dir...
Variable names in R can be composed of combinations of letters, numbers, underscores, and periods. They are case sensitive. Note that in this and all subsequent sections, R commands can be run by cutting and pasting text directly into the R Console window.
When biological responses are plotted against their causal stimuli (or logarithms of them) they often form a sigmoid curve. Sigmoid relationships can be linearized by transformations such as logit, probit and angular. For most systems the probit (normal sigmoid) and logit (logistic sigmoid) give the most closely fitting result. Logistic methods are useful in Epidemiology because odds ratios can be determined easily from differences between fitted logits (see logistic regression). In biological assay work, however, probit analysis is preferred (Finney, 1971, 1978). Curves produced by these methods are very similar, with maximum variation occurring within 10% of the upper and lower asymptotes.
Your data are entered as dose levels, number of subjects tested at each dose level and number responding at each dose level. At the time of running the analysis you may enter a control result for the number of subjects responding in the absence of dose/stimulus; this provides a global adjustment for natural mortality/responsiveness. You may also specify automatic log transformation of the dose levels at run time if appropriate (this should be supported by good evidence of a log-probit relationship for your type of study).
The fitted model is assessed by statistics for heterogeneity which follow a chi-square distribution. If the heterogeneity statistics are significant then your observed values deviate from the fitted curve too much for reliable inference to be made (Finney, 1971, 1978).
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