Psychology Wiki

F test

Revision as of 09:11, November 15, 2008 by Dr Joe Kiff (Talk | contribs)

34,190pages on
this wiki

Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |

Statistics: Scientific method · Research methods · Experimental design · Undergraduate statistics courses · Statistical tests · Game theory · Decision theory

An F-test is any statistical test in which the test statistic has an F-distribution if the null hypothesis is true. A great variety of hypotheses in applied statistics are tested by F-tests. Among these are given below:

  • The hypothesis that the means of multiple normally distributed populations, all having the same standard deviation, are equal. This is perhaps the most well-known of hypotheses tested by means of an F-test, and the simplest problem in the analysis of variance.
  • The hypothesis that the standard deviations of two normally distributed populations are equal, and thus that they are of comparable origin.

In many cases, the F-test statistic can be calculated through a straightforward process. Two regression models are required, one of which constrains one or more of the regression coefficients according to the null hypothesis. The test statistic is then based on a modified ratio of the sum of squares of residuals of the two models as follows:

Given n observations, where model 1 has k unrestricted coefficients, and model 0 restricts m of the coefficients (typically to zero), the F-test statistic can be calculated as

\frac{\left(\frac{RSS_0 - RSS_1 }{m}\right)}{\left(\frac{RSS_1}{n - k}\right)}.

The resulting test statistic value would then be compared to the corresponding entry on a table of F-test critical values, which is included in most statistical texts.

de:F-Test es:Test F nl:F-toetssu:Uji-F

This page uses Creative Commons Licensed content from Wikipedia (view authors).

Around Wikia's network

Random Wiki