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Common examples. Common examples of the use of F-tests include the study of the following cases . One-way ANOVA table with 3 random groups that each has 30 observations. F value is being calculated in the second to last column The hypothesis that the means of a given set of normally distributed populations, all having the same standard deviation, are equal.
One-way analysis of variance. In statistics, one-way analysis of variance (or one-way ANOVA) is a technique to compare whether two or more samples' means are significantly different (using the F distribution ). This analysis of variance technique requires a numeric response variable "Y" and a single explanatory variable "X", hence "one-way". [1]
The definitional equation of sample variance is = (¯), where the divisor is called the degrees of freedom (DF), the summation is called the sum of squares (SS), the result is called the mean square (MS) and the squared terms are deviations from the sample mean. ANOVA estimates 3 sample variances: a total variance based on all the observation ...
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 method 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 different sample sizes.
Tukey's range test. Tukey's range test, also known as Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD ( honestly significant difference) test, [1] is a single-step multiple comparison procedure and statistical test. It can be used to correctly interpret the statistical significance of the difference between means ...
Fisher's exact test is a statistical significance test used in the analysis of contingency tables. [1] [2] [3] Although in practice it is employed when sample sizes are small, it is valid for all sample sizes. It is named after its inventor, Ronald Fisher, and is one of a class of exact tests, so called because the significance of the deviation ...
Analyzing group differences across multiple outcome variables often provides more accurate information as a pure relationship between only X and only Y rarely exists in nature. In statistics, multivariate analysis of variance ( MANOVA) is a procedure for comparing multivariate sample means. As a multivariate procedure, it is used when there are ...
The Brown–Forsythe test is a statistical test for the equality of group variances based on performing an Analysis of Variance (ANOVA) on a transformation of the response variable. When a one-way ANOVA is performed, samples are assumed to have been drawn from distributions with equal variance. If this assumption is not valid, the resulting F ...