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In statistical hypothesis testing, there are various notions of so-called type III errors (or errors of the third kind), and sometimes type IV errors or higher, by analogy with the type I and type II errors of Jerzy Neyman and Egon Pearson. Fundamentally, type III errors occur when researchers provide the right answer to the wrong question, i.e ...
A hypothesis is rejected at level α if and only if its adjusted p-value is less than α. In the earlier example using equal weights, the adjusted p -values are 0.03, 0.06, 0.06, and 0.02. This is another way to see that using α = 0.05, only hypotheses one and four are rejected by this procedure.
The Breusch–Godfrey test is a test for autocorrelation in the errors in a regression model. It makes use of the residuals from the model being considered in a regression analysis, and a test statistic is derived from these. The null hypothesis is that there is no serial correlation of any order up to p. [3]
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 statistics, particularly in hypothesis testing, the Hotelling's T-squared distribution (T 2), proposed by Harold Hotelling, [1] is a multivariate probability distribution that is tightly related to the F-distribution and is most notable for arising as the distribution of a set of sample statistics that are natural generalizations of the statistics underlying the Student's t-distribution.
With respect to FWER control, the Bonferroni correction can be conservative if there are a large number of tests and/or the test statistics are positively correlated. [9] Multiple-testing corrections, including the Bonferroni procedure, increase the probability of Type II errors when null hypotheses are false, i.e., they reduce statistical power.
Under the null hypothesis = ‖ ′ ‖, and the asymptotic distribution of Q n is a quadratic form of centered Gaussian random variables. Under an alternative hypothesis, Q n tends to infinity stochastically, and thus determines a statistically consistent test. For most applications the exponent 1 (Euclidean distance) can be applied.
[68] [69] For example, the hypothesis might be that "Unemployment has no effect on inflation", which relates to an economics concept called the Phillips Curve. [70] Hypothesis testing involves considering the likelihood of Type I and type II errors, which relate to whether the data supports accepting or rejecting the hypothesis. [71] [72]