![]() Their principle is simple, it consists of alternating between a conventional estimation using linear regression or ANOVA and a monotonic transformation of the dependent variables (after searching for optimal scaling transformations). These methods are based on iterative algorithms based on the ALS (alternating least squares) algorithm. They are based on linear regression in the first case, and on the ANOVA model in the second. We then obtain the size N such that the test has a power as close as possible to the desired power.Monotone regression and the MONANOVA model differ only in the fact that the explanatory variables are either quantitative or qualitative. This algorithm is adapted to the case where the derivatives of the function are not known. It is called the Van Wijngaarden-Dekker-Brent algorithm (Brent, 1973). To calculate the number of observations required, XLSTAT uses an algorithm that searches for the root of a function. Calculating sample size for changes in R² in linear regression The power of this test is obtained using the non-central Fisher distribution with degrees of freedom equal to: DF1 is the number of tested variables DF2 is the sample size from which the total number of explanatory variables included in model plus one is subtracted and the non-centrality parameter is: NCP = f²N. For this specific case we will use the Fisher non-central distribution to compute the power. The power of a test is usually obtained by using the associated non-central distribution. Calculations of the Statistical Power for changes in R² in linear regression Once the effect size is defined, power and necessary sample size can be computed. We have: f² = CorrYT * CorrX-1 * CorrY / (1 - = CorrYT * CorrX-1 * CorrY)
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