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[21] Most two-sample t-tests are robust to all but large deviations from the assumptions. [22] For exactness, the t-test and Z-test require normality of the sample means, and the t-test additionally requires that the sample variance follows a scaled χ 2 distribution, and that the sample mean and sample variance be statistically independent ...
In statistics, the Jonckheere trend test [1] (sometimes called the Jonckheere–Terpstra [2] test) is a test for an ordered alternative hypothesis within an independent samples (between-participants) design. It is similar to the Kruskal-Wallis test in that the null hypothesis is that several independent samples are from the same population ...
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.
If X and Y are independent random variables and not constant, then the expectation of the coefficient is zero. An explicit expression for Kendall's rank coefficient is τ = 2 n ( n − 1 ) ∑ i < j sgn ( x i − x j ) sgn ( y i − y j ) {\displaystyle \tau ={\frac {2}{n(n-1)}}\sum _{i<j}\operatorname {sgn}(x_{i}-x_{j})\operatorname ...
In other words, the two variables are not independent. If there is no contingency, it is said that the two variables are independent. The example above is the simplest kind of contingency table, a table in which each variable has only two levels; this is called a 2 × 2 contingency table. In principle, any number of rows and columns may be used.
SPSS 22 - 2013; SPSS 23 - 2015; SPSS 24 - 2016, March [15] SPSS 25 - 2017, July [16] SPSS 26 - 2018; SPSS 27 - 2019, June [17] (and 27.0.1 in November, 2020 [18]) SPSS 28 - 2021, May [19] SPSS 29 - 2022, Sept [20] SPSS 30 - 2024, Sept [21] SPSS was released in its first version in 1968 as the Statistical Package for the Social Sciences (SPSS ...
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.
SPSS Inc. was a software house headquartered in Chicago and incorporated in Delaware, most noted for the proprietary software of the same name SPSS. The company was started in 1968 when Norman Nie, Dale Bent, and Hadlai "Tex" Hull developed and started selling the SPSS software. The company was incorporated in 1975, and Nie was CEO from 1975 ...