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Probit Analysis

Probit analysis operates like multiple regression with dependent or response variables that are binary. The term probit was coined to refer to “probability unit.” The statistic was originally developed to deal with the issues of what percentage of a pest would be killed by a particular dose of pesticide. The particular issue that Chester Bliss wrote about in 1934 was the challenge of determining the best pesticide to reduce insects that were feeding on grape leaves. In response to this consideration, he created a technique that became known as probit analysis. The goal of the model was to create a means of converting the data to a representation that could be viewed as a linear function. The procedure treats the same problems and issues as logistic regression. The original goal was to provide an estimate of what would happen if a given pesticide was used under specified conditions (e.g., weather, terrain, dosage, duration) and the amount of pests (e.g., measured in terms of percentage) that would be removed. In this case, the dependent variable is considered binary (the particular pest is either alive or dead) and the contribution or impact of each specified condition becomes a part of the degree to which the method is successful (or how successful in achieving the outcome). This entry explores the application of probit analysis in the social sciences, the assumptions underpinning probit analysis, probit analysis’ comparison to other statistical measures, and probit analysis’ strengths.

Probit Analysis in the Social Sciences

Probit analysis can also be applied in social science research. For example, suppose the goal involves evaluating whether or not a particular set of communication practices predicts whether or not a romantic couple get married. The dependent variable is binary: the couple either gets married or does not. The various elements of prediction operate in combination (with appropriate adjustments) to provide a prediction that can be compared (correlated) to the actual outcome. The research outcomes consider the accuracy of the prediction (the probability of predicting whether or not the couple gets married) as well as the strength of the contribution of individual predictors in the equation. Consider the various methods of computer or other matched dating systems where two persons fill out information and are “matched” based on the answers. The belief is that certain matching characteristics (either similarities or complementary differences) provide the best basis for continuing and mutually satisfactory relationships. The goal is figuring out what combination of values provides the best outcome, and this logic to a large degree resembles the underlying rationale for using probit analysis.

The challenge of a binary dependent variable reflects the difficulty of an outcome that has only two values (in the aforementioned example, the two values were married or unmarried). Mathematically, the values typically used to refer to such states are 1 or 0. Most statistical procedures assume a normal distribution (with a mean, median, mode, variance, and standard deviation), something really not possible in a system with only two values. What happens is that the measures of central tendency (mean, median, mode), while technically capable of mathematical estimation, provide a misleading or difficult to evaluate set of answers. The problem is that for a data set with only 1 and 0, a mean of .50 (assuming the number of 1s and 0s are identical) represents no real entry in the data set. No person has a value of .50, even if the distribution is divided perfectly into 50% halves.

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