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Simple back-of-the-envelope test takes the sample maximum and minimum and computes their z-score, or more properly t-statistic (number of sample standard deviations that a sample is above or below the sample mean), and compares it to the 68–95–99.7 rule: if one has a 3σ event (properly, a 3s event) and substantially fewer than 300 samples, or a 4s event and substantially fewer than 15,000 ...
A t-test can be used to account for the uncertainty in the sample variance when the data are exactly normal. Difference between Z-test and t-test: Z-test is used when sample size is large (n>50), or the population variance is known. t-test is used when sample size is small (n<50) and population variance is unknown. There is no universal ...
Lilliefors test is a normality test based on the Kolmogorov–Smirnov test.It is used to test the null hypothesis that data come from a normally distributed population, when the null hypothesis does not specify which normal distribution; i.e., it does not specify the expected value and variance of the distribution. [1]
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...
The Shapiro–Wilk test tests the null hypothesis that a sample x 1, ..., x n came from a normally distributed population. The test statistic is = (= ()) = (¯), where with parentheses enclosing the subscript index i is the ith order statistic, i.e., the ith-smallest number in the sample (not to be confused with ).
Derive the distribution of the test statistic under the null hypothesis from the assumptions. In standard cases this will be a well-known result. For example, the test statistic might follow a Student's t distribution with known degrees of freedom, or a normal distribution with known mean and variance.
This test procedure is based on the statistic whose sampling distribution is approximately a Chi-Square distribution with (k − 1) degrees of freedom, where k is the number of random samples, which may vary in size and are each drawn from independent normal distributions. Bartlett's test is sensitive to departures from normality.
The Anderson–Darling test is a statistical test of whether a given sample of data is drawn from a given probability distribution. In its basic form, the test assumes that there are no parameters to be estimated in the distribution being tested, in which case the test and its set of critical values is distribution-free.