![]() ![]() If the value of the test statistic is less extreme than the one calculated from the null hypothesis, then you can infer no statistically significant relationship between the predictor and outcome variables. If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then you can infer a statistically significant relationship between the predictor and outcome variables. The p-value estimates how likely it is that you would see the difference described by the test statistic if the null hypothesis of no relationship were true. It then calculates a p value (probability value). Statistical tests work by calculating a test statistic– a number that describes how much the relationship between variables in your test differs from the null hypothesis of no relationship. Frequently asked questions about statistical tests.Choosing a parametric test: regression, comparison, or correlation.XLSTAT allows entering the effect size directly. In the context of comparisons of means, the 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. We then obtain the size N such that the test has a power as close as possible to the desired power. 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 using the statistical power of a test ![]() The calculation is done using the F distribution with the ratio of the variances as parameter and the sample sizes – 1 as degrees of freedom. The power computation will give the proportion of experiments that reject the null hypothesis. Ha: The difference between the variances is different from 0.H0: The difference between the variances is equal to 0.Several hypotheses can be tested, but the most common are the following (two-tailed): The power of a test is usually obtained by using the associated non-central distribution. ![]() Calculation for the Statistical Power analysis for the comparison of variances XLSTAT allows you to compare two variances. 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. XLSTAT is able to compute 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 upfront, 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.
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