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The above image shows a table with some of the most common test statistics and their corresponding tests or models. A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently supports a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic.
Test statistic is a quantity derived from the sample for statistical hypothesis testing. [1] A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.
Illustration of the power of a statistical test, for a two sided test, through the probability distribution of the test statistic under the null and alternative hypothesis. α is shown as the blue area , the probability of rejection under null, while the red area shows power, 1 − β , the probability of correctly rejecting under the alternative.
The likelihood-ratio test, also known as Wilks test, [2] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. [3] In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent.
The bootstrap may also be used for constructing hypothesis tests. [5] It is often used as an alternative to statistical inference based on the assumption of a parametric model when that assumption is in doubt, or where parametric inference is impossible or requires complicated formulas for the calculation of standard errors.
It is usually determined on the basis of the cost, time or convenience of data collection and the need for sufficient statistical power. For example, if a proportion is being estimated, one may wish to have the 95% confidence interval be less than 0.06 units wide. Alternatively, sample size may be assessed based on the power of a hypothesis ...
Since the procedure is step-down, we first test = (), which has the smallest p-value = =. The p-value is compared to α / 4 = 0.0125 {\displaystyle \alpha /4=0.0125} , the null hypothesis is rejected and we continue to the next one.
An f-test pdf with d1 and d2 = 10, at a significance level of 0.05. (Red shaded region indicates the critical region) An F-test is a statistical test that compares variances. It's used to determine if the variances of two samples, or if the ratios of variances among multiple samples, are significantly different.