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In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test ...
"Note that since U1 + U2 = n1 n2, the mean n1 n2/2 used in the normal approximation is the mean of the two values of U. Therefore, you can use U and get the same result, the only difference being between a left-tailed test and a right-tailed test.
In the 2009 book Dirty rotten strategies by Ian I. Mitroff and Abraham Silvers described type III and type IV errors providing many examples of both developing good answers to the wrong questions (III) and deliberately selecting the wrong questions for intensive and skilled investigation (IV). Most of the examples have nothing to do with ...
The difference between the two sample means, each denoted by X i, which appears in the numerator for all the two-sample testing approaches discussed above, is ¯ ¯ = The sample standard deviations for the two samples are approximately 0.05 and 0.11, respectively. For such small samples, a test of equality between the two population variances ...
The two-tailed p-value, which considers deviations favoring either heads or tails, may instead be calculated. As the binomial distribution is symmetrical for a fair coin, the two-sided p-value is simply twice the above calculated single-sided p-value: the two-sided p-value is 0.115. In the above example:
In order to consider both the biases, we use a two-tailed test. Note that to do this we cannot simply double the one-tailed p-value unless the probability of the event is 1/2. This is because the binomial distribution becomes asymmetric as that probability deviates from 1/2. There are two methods to define the two-tailed p-value.
Z-test tests the mean of a distribution. For each significance level in the confidence interval, the Z-test has a single critical value (for example, 1.96 for 5% two tailed) which makes it more convenient than the Student's t-test whose critical values are defined by the sample size (through the corresponding degrees of freedom). Both the Z ...
The usefulness of the ρ statistic can be seen in the case of the odd example used above, where two distributions that were significantly different on a Mann–Whitney U test nonetheless had nearly identical medians: the ρ value in this case is approximately 0.723 in favour of the hares, correctly reflecting the fact that even though the ...