F-Test

(noun)

A statistical test using the F-distribution, 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.

Related Terms

(noun)

a statistical test using the $F$ distribution, 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

Related Terms

Examples of F-Test in the following topics:

  • Variance Estimates

    • The $F$-test can be used to test the hypothesis that the variances of two populations are equal.
    • This $F$-test is known to be extremely sensitive to non-normality.
    • $F$-tests are used for other statistical tests of hypotheses, such as testing for differences in means in three or more groups, or in factorial layouts.
    • However, for large alpha levels (e.g., at least 0.05) and balanced layouts, the $F$-test is relatively robust.
    • Discuss the $F$-test for equality of variances, its method, and its properties.

  • The F-Test

    • An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis.
    • An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis.
    • Exact F-tests mainly arise when the models have been fitted to the data using least squares.
    • The F-test is sensitive to non-normality.
    • This is perhaps the best-known F-test, and plays an important role in the analysis of variance (ANOVA).

  • The One-Way F-Test

    • The $F$-test as a one-way analysis of variance assesses whether the expected values of a quantitative variable within groups differ from each other.
    • The $F$ test as a one-way analysis of variance is used to assess whether the expected values of a quantitative variable within several pre-defined groups differ from each other.
    • If the $F$-test is performed at level $\alpha$ we cannot state that the treatment pair with the greatest mean difference is significantly different at level $\alpha$.
    • Note that when there are only two groups for the one-way ANOVA $F$-test, $F=t^2$ where $t$ is the Student's $t$-statistic.
    • Explain the purpose of the one-way ANOVA $F$-test and perform the necessary calculations.

  • Reading an ANOVA table from software

    • For these reasons, it is common to use statistical software to calculate the F statistic and p-value.
    • Table 5.30 shows an ANOVA summary to test whether the mean of on-base percentage varies by player positions in the MLB.
    • Many of these values should look familiar; in particular, the F test statistic and p-value can be retrieved from the last columns.
    • ANOVA summary for testing whether the average on-base percentage differs across player positions.

  • Analysis of variance (ANOVA) and the F test

    • We can use the F statistic to evaluate the hypotheses in what is called an F test.
    • An F distribution with 3 and 323 degrees of freedom, corresponding to the F statistic for the baseball hypothesis test, is shown in Figure 5.29.
    • The F statistic and the F test Analysis of variance (ANOVA) is used to test whether the mean outcome differs across 2 or more groups.
    • ANOVA uses a test statistic F, which represents a standardized ratio of variability in the sample means relative to the variability within the groups.
    • The test statistic for the baseball example is F = 1.994.

  • Summary

    • A One-Way ANOVA hypothesis test determines if several population means are equal.
    • The distribution for the test is the F distribution with 2 different degrees of freedom.
    • A Test of Two Variances hypothesis test determines if two variances are the same.
    • The distribution for the hypothesis test is the F distribution with 2 different degrees of freedom.

  • Test of Two Variances

    • Another of the uses of the F distribution is testing two variances.
    • In order to perform a F test of two variances, it is important that the following are true:
    • F has the distribution F∼F(n1−1,n2−1) where n1 −1 are the degrees of freedom for the numerator and n2 −1 are the degrees of freedom for the denominator.
    • A test of two variances may be left, right, or two-tailed.
    • Test the claim that the first instructor's variance is smaller.

  • Multivariate Testing

    • In this case a single multivariate test is preferable for hypothesis testing.
    • In particular, the distribution arises in multivariate statistics in undertaking tests of the differences between the (multivariate) means of different populations, where tests for univariate problems would make use of a $t$-test.
    • It is proportional to the $F$-distribution.
    • The test statistic is defined as follows:
    • The test statistic is defined as:

  • Randomization Tests: Two or More Conditions

    • Compute a randomization test for differences among more than two conditions.
    • The method of randomization for testing differences among more than two means is essentially very similar to the method when there are exactly two means.
    • The first step in a randomization test is to decide on a test statistic.
    • The F ratio is computed not to test for significance directly, but as a measure of how different the groups are.
    • Therefore, the proportion of arrangements with an F as large or larger than the F of 2.06 obtained with the data is

  • F Distribution and One-Way ANOVA: Purpose and Basic Assumptions of One-Way ANOVA

    • The purpose of a One-Way ANOVA test is to determine the existence of a statistically significant difference among several group means.
    • The test actually uses variances to help determine if the means are equal or not.
    • In order to perform a One-Way ANOVA test, there are five basic assumptions to be fulfilled: