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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 ...
A two-tailed test applied to the normal distribution. A one-tailed test, showing the p -value as the size of one tail. 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.
Standard normal table. In statistics, a standard normal table, also called the unit normal table or Z table, [1] is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal ...
The non-central t -distribution is asymmetric unless μ is zero, i.e., a central t -distribution. In addition, the asymmetry becomes smaller the larger degree of freedom. The right tail will be heavier than the left when μ > 0, and vice versa. However, the usual skewness is not generally a good measure of asymmetry for this distribution ...
If there are no ties – or the ties occur within a particular sample (which does not affect the value of the test statistic) – exact tables of S are available; for example, Jonckheere [1] provided selected tables for values of k from 3 to 6 and equal samples sizes (m) from 2 to 5. Leach presented critical values of S for k = 3 with sample ...
The sign test is a statistical test for consistent differences between pairs of observations, such as the weight of subjects before and after treatment. Given pairs of observations (such as weight pre- and post-treatment) for each subject, the sign test determines if one member of the pair (such as pre-treatment) tends to be greater than (or less than) the other member of the pair (such as ...
About 68% of values drawn from a normal distribution are within one standard deviation σ from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. [6] This fact is known as the 68–95–99.7 (empirical) rule, or the 3-sigma rule.
In probability and statistics, studentized range distribution is the continuous probability distribution of the studentized range of an i.i.d. sample from a normally distributed population. Suppose that we take a sample of size n from each of k populations with the same normal distribution N (μ, σ2) and suppose that is the smallest of these ...