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Statistical hypothesis testing is considered a mature area within statistics, [25] but a limited amount of development continues. An academic study states that the cookbook method of teaching introductory statistics leaves no time for history, philosophy or controversy. Hypothesis testing has been taught as received unified method.
In experimental design, where a study may be divided into different treatment groups, there may be different sample sizes for each group. Sample sizes may be chosen in several ways: using experience – small samples, though sometimes unavoidable, can result in wide confidence intervals and risk of errors in statistical hypothesis testing.
If the hypothesis summarizes a set of data, there is no value in testing the hypothesis on that set of data. Example: If a study of last year's weather reports indicates that rain in a region falls primarily on weekends, it is only valid to test that null hypothesis on weather reports from any other year.
The hypothesis that a data set in a regression analysis follows the simpler of two proposed linear models that are nested within each other. Multiple-comparison testing is conducted using needed data in already completed F-test, if F-test leads to rejection of null hypothesis and the factor under study has an impact on the dependent variable. [1]
The closed testing principle allows the rejection of any one of these elementary hypotheses, say H i, if all possible intersection hypotheses involving H i can be rejected by using valid local level α tests; the adjusted p-value is the
A thought experiment might also be used to test the hypothesis. In framing a hypothesis, the investigator must not currently know the outcome of a test or that it remains reasonably under continuing investigation. Only in such cases does the experiment, test or study potentially increase the probability of showing the truth of a hypothesis.
In this case a single multivariate test is preferable for hypothesis testing. Fisher's Method for combining multiple tests with alpha reduced for positive correlation among tests is one. Another is Hotelling's T 2 statistic follows a T 2 distribution. However, in practice the distribution is rarely used, since tabulated values for T 2 are hard ...
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.