![]() ![]() In order for the statistic to follow the F-distribution under the null hypothesis, the sums of squares should be statistically independent, and each should follow a scaled χ²-distribution. These sums of squares are constructed so that the statistic tends to be greater when the null hypothesis is not true. The test statistic in an F-test is the ratio of two scaled sums of squares reflecting different sources of variability. Most F-tests arise by considering a decomposition of the variability in a collection of data in terms of sums of squares. homogeneity of variance), as a preliminary step to testing for mean effects, there is an increase in the experiment-wise Type I error rate. However, when any of these tests are conducted to test the underlying assumption of homoscedasticity ( i.e. In the analysis of variance (ANOVA), alternative tests include Levene's test, Bartlett's test, and the Brown–Forsythe test. The F-test is sensitive to non-normality. Main article: F-test of equality of variances In addition, some statistical procedures, such as Scheffé's method for multiple comparisons adjustment in linear models, also use F-tests.į-test of the equality of two variances The hypothesis that a data set in a regression analysis follows the simpler of two proposed linear models that are nested within each other. ![]() The hypothesis that a proposed regression model fits the data well.This is perhaps the best-known F-test, and plays an important role in the analysis of variance (ANOVA). The hypothesis that the means of a given set of normally distributed populations, all having the same standard deviation, are equal.Common examples Ĭommon examples of the use of F-tests include the study of the following cases: Fisher initially developed the statistic as the variance ratio in the 1920s. Exact " F-tests" mainly arise when the models have been fitted to the data using least squares. It is most often used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled. Statistical hypothesis test, mostly using multiple restrictionsĪn F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. ![]()
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