Using the R² (in the case H0: R²=0): We enter the estimated square multiple correlation value (called rho²) to define the size of the effect.With varExplained being the variance explained by the explanatory variables that we wish to test and varError being the variance of the error or residual variance, we have: f² = varExplained/ varError.
Using variances: We can use the variances of the model to define the size of the effect.XLSTAT-Power allows you to enter directly the effect size but also allows entering parameters of the model that will help calculating the effect size. In the context of a linear regression, conventions of magnitude of the effect size are: The effect size is a quantity that will allow you to calculate the power of a test without entering any parameters but will tell if the effect to be tested is weak or strong. Indeed, Cohen (1988) developed this concept. This concept is very important in power calculations. H0: Increase in R² is equal to 0 / Ha: Increase in R² is different from 0.Įffect size for the variation of R² in linear regression.
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.
XLSTAT-Power estimates the power or calculates the necessary number of observations associated with variations of R ² in the framework of a linear regression. XLSTAT-Pro offers a tool to apply a linear regression model.
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