The formula for the test statistic depends on whether the population standard deviation (σ) is known or unknown. If σ is known, our hypothesis test is known as a z test and we use the z distribution. If σ is unknown, our hypothesis test is known as a t test and we use the t distribution. Use of the t distribution relies on the degrees of freedom, which is equal to the sample size minus one. Furthermore, if the population standard deviation σ is unknown, the sample standard deviation s is used instead. To switch from σ known to σ unknown, click on $\boxed$, reject $H_0$. When conducting a hypothesis test, there is always a chance that you come to the wrong conclusion. There are two types of errors you can make: Type I Error and Type II Error. A Type I Error is committed if you reject the null hypothesis when the null hypothesis is true. Ideally, we'd like to accept the null hypothesis when the null hypothesis is true. A Type II Error is committed if you accept the null hypothesis when the alternative hypothesis is true. Hence, it has become a common practice to take the following steps in hypothesis testing. Ideally, we'd like to reject the null hypothesis when the alternative hypothesis is true. State the statistical hypotheses in terms of the fold change ( ratio) of the means. Transform this into hypotheses about a difference by taking logarithms. Analyze the logged datathat is, do the analysis in terms of the difference. Hypothesis testing is closely related to the statistical area of confidence intervals. If the hypothesized value of the population mean is outside of the confidence interval, we can reject the null hypothesis. Confidence intervals can be found using the Confidence Interval Calculator. The calculator on this page does hypothesis tests for one population mean. Sometimes we're interest in hypothesis tests about two population means. These can be solved using the Two Population Calculator. The probability of a Type II Error can be calculated by clicking on the link at the bottom of the page.The goal of the test proposed by Page (1963) is to allow analyzing rigorously the results of a study carried out within the framework of a complete design, to verify if a series of several treatments should be considered as not different, or if alternatively a ranking of the treatment makes sense.
The Page test is a nonparametric method, thus not making any assumption on the distribution of the measurements. This test differs from the Friedman test by the fact that the alternative hypothesis is a ranking of the treatments and not only a difference. If the p-value is such that the H0 hypothesis has to be rejected, then at least one treatment is different from another. If t1, t2, …, tk correspond to the k treatments, the null and alternative hypotheses used in the test are: This test has been extended to the case of incomplete blocks by Alvo and Cabilio (2005). This hypothesis could be tested using normality tests. H0 : The k treatments are not significantly different.The TOST test uses Students test to check the equivalence between the means of two samples. A detailed description of such tests can be found in the chapter dedicated to t tests. XLSTAT offers two equivalent methods to test equivalence using the TOST test. To compute the p-values corresponding to the various statistics, XLSTAT offers two alternative methods: Where, for the alternative hypotheses, at least one inequality is strict. Asymptotic method: The p-value is obtained using the asymptotic approximation of the distribution of the z statistics.The reliability of the approximation depends on the number of treatments and on the number of blocks. Monte Carlo method: The computation of the p-value is based on random resamplings.The user must set the number of resamplings. A confidence interval on the p-value is provided. The more resamplings are performed, the better the estimation of the p-value. In order to avoid freezing Excel because of too long computations, it is possible with the two latter methods to set the maximum time that should be spent computing the p-value. To identify which treatment(s) is/are responsible for rejecting H0, a multiple comparison procedure can be used, XLSTAT allows using the procedure suggested by Cabilio and Peng (2008), with two alternative ways to compute the p-value of the paired comparisons. Ce tutoriel explique comment calculer et interprter un test non-paramtrique de Cochran-Mantel-Haenszel CMH avec Excel en utilisant XLSTAT. It can either use the normal approximation of a Monte Carlo based -pvalue.
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