Lambda Coefficient Calculator

The first question we will address What is the lambda statistics? The Lambda statistic \(\lambda\) is a statistic used to measure the strength of association between two nominal variables, by assessing the proportional reduction of error (PRE).

This is achieved by considering the independent variable when compared to ignoring the independent variable in the prediction of the dependent variable.

It is extremely useful when dealing with two-way crosstabulations, constructed with categorical variables, for which you want to assess the predictive effect of one variable on the other.

What are the properties of Lambda

The Lambda statistic takes values from 0 to 1. Values close to 0 indicate a weak association between the variables and values close to 1 indicate a strong association between the variables.

The Lambda statistic is a asymmetrical measure, in the sense that its value depends on which variable is considered to be the independent variable.

The Lambda Statistics Formula

The following formula shows how to calculate the lambda statistic by hand using the following formula:

\[\lambda = \frac{E_1 - E_2 }{E_1} \]

where \(E_1\) corresponds to the number of prediction errors made when the independent variable is ignored, and \(E_2\) corresponds to the number of prediction errors made when the prediction is based on the independent variable.

This lambda calculator with steps will show you all the necessary calculations to arrive to lambda. Though it is simple, it requires careful analysis to correctly calculate the measures of error reduction required for lambda.

Crosstabulation Effect Size

The Lambda coefficient is a measure of effect size. Other effect size calculators for two-way tables you may be interested in are our gamma calculator , phi calculator , Cohen's d calculator, Cramer's V, among many others.