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The term " Z -test" is often used to refer specifically to the one-sample location test comparing the mean of a set of measurements to a given constant when the sample variance is known. For example, if the observed data X1, ..., Xn are (i) independent, (ii) have a common mean μ, and (iii) have a common variance σ 2, then the sample average X ...
Normality test. In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed. More precisely, the tests are a form of model selection, and can be interpreted several ways, depending on one's ...
A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently supports a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical value or equivalently by evaluating a ...
Kruskal–Wallis test. The Kruskal–Wallis test by ranks, Kruskal–Wallis test[1] (named after William Kruskal and W. Allen Wallis), or one-way ANOVA on ranks[1] is a non-parametric statistical test for testing whether samples originate from the same distribution. [2][3][4] It is used for comparing two or more independent samples of equal or ...
Multiple comparisons problem. An example of coincidence produced by data dredging (uncorrected multiple comparisons) showing a correlation between the number of letters in a spelling bee's winning word and the number of people in the United States killed by venomous spiders. Given a large enough pool of variables for the same time period, it is ...
Usage. Pearson's chi-squared test is used to assess three types of comparison: goodness of fit, homogeneity, and independence. A test of goodness of fit establishes whether an observed frequency distribution differs from a theoretical distribution. A test of homogeneity compares the distribution of counts for two or more groups using the same ...
Illustration of the Kolmogorov–Smirnov statistic. The red line is a model CDF, the blue line is an empirical CDF, and the black arrow is the KS statistic.. Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), one-dimensional probability distributions that can be used to test whether a sample came from a ...
Chi-squared distribution, showing χ2 on the x -axis and p -value (right tail probability) on the y -axis. A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical ...
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