P0 (baseline probability): The probability that Y=1 when all explanatory variables are set to their mean value.If X1 is quantitative and has a normal distribution, the parameters of the approximation are: Power is computed using an approximation which depends on the type of variable. That means that the X1 explanatory variable has no effect on the model.Ĭalculation of the statistical power for logistic regression P is equal to: P = exp(β0 + β1X1 + … + βkXk) / We have: log(P/(1-P)) = β0 + β1X1 + … + βkXk The test used in XLSTAT-Power is based on the null hypothesis that the β1 coefficient is equal to 0. In the general framework of logistic regression model, the goal is to explain and predict the probability P that an event appends (usually Y=1). The main application of power calculations is to estimate the number of observations necessary to properly conduct an experiment. The statistical power calculations are usually done before the experiment is conducted. For a given power, it also allows to calculate the sample size that is necessary to reach that power. The XLSTAT-Power module calculates the power (and beta) when other parameters are known. We therefore wish to maximize the power of the test. The power of a test is calculated as 1-beta and represents the probability that we reject the null hypothesis when it is false. We cannot fix it up front, but based on other parameters of the model we can try to minimize it.
In fact, it represents the probability that one does not reject the null hypothesis when it is false. The type II error or beta is less studied but is of great importance. It is set a priori for each test and is 5%. It occurs when one rejects the null hypothesis when it is true.
When testing a hypothesis using a statistical test, there are several decisions to take: XLSTAT-Power estimates the power or calculates the necessary number of observations associated with this model. XLSTAT-Base offers a tool to apply logistic regression. Statistical Power for Logistic regression
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