Once the effect size is defined, power and necessary sample size can be computed. The effect size is then multiplied by f = в€љ1 / (1 вЂ“ ПЃВІ) where ПЃВІ is the theoretical value of the square multiple correlation coefficient associated to the quantitative predictors. When an ANCOVA is performed, a term has to be added to the model in order to take into account the quantitative predictors.We have: f = в€љОЈ i (m i - m)ВІ / k / SD intra with m i mean of group i, m mean of the means, k number of groups and SD intra within-group standard deviation. It is also possible to have groups of different sizes, in this case, you must also select a vector with different sizes (the standard option assumes that all groups have equal size). Using the means of each group (in the case of one-way ANOVA or within subjects repeated measures ANOVA): We select a vector with the averages for each group.For more details on etaВІ, please refer to Cohen (1988, chap. Using the direct approach: We enter the estimated value of etaВІ which is the ratio between the explained variance by the studied factor and the total variance of the model.With var explained being the variance explained by the explanatory factors that we wish to test and var error being the variance of the error or residual variance, we have: f = в€љvar explained / var error 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 you to enter parameters of the model that will calculate the effect size. In the context of an ANOVA-type model, conventions of magnitude of the effect size are: The effect size is a quantity that will allow calculating 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. H a: At least one of the means is different from another:Д®ffect size for ANOVA, ANCOVA and Repeated measures ANOVA.H 0: The means of the groups of the within-between subjects interaction are equal.In the case of repeated measures ANOVA for an interaction between a within-subjects factor and a between-subjects factor:.H 0: Les The means of the groups of the between subjects factor are equal.In the case of repeated measures ANOVA for a between-subjects factor:.H 0: The means of the groups of the within subjects factor are equal.In the case of repeated measures ANOVA for a within-subjects factor:.H a: At least one of the means is different from another.H 0: The means of the groups of the tested factor are equal.In the case of a one-way ANOVA or more fixed factors and interactions, as well as in the case of ANCOVA:.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. The null hypothesis H 0 and the alternative hypothesis H a.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 these models. XLSTAT-Pro offers tools to apply analysis of variance (ANOVA), repeated measures analysis of variance and analysis of covariance (ANCOVA). Statistical Power for ANOVA, ANCOVA and Repeated measures ANOVA

Anova xlstat