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Introduction. Calculating Fisher’s F-ratio is a key step in a number of statistical procedures involving null hypothesis significance testing. This is particularly so in the case of ANOVA (analysis of variance) in its several forms, but even multiple regression includes a test of significance of the overall model which employs an F-ratio.
A random variable has an F distribution if it can be written as a ratio between a Chi-square random variable with degrees of freedom and a Chi-square random variable , independent of , with degrees of freedom (where each variable is divided by its degrees of freedom).
The F - ratio is widely used in quality life research in the psychosocial, behavioral, and health sciences. It broadly refers to a statistic obtained from dividing two sample variances assumed to come from normally distributed populations in order to compare two or more groups.
The F statistic is a ratio (a fraction). There are two sets of degrees of freedom; one for the numerator and one for the denominator. For example, if F follows an F distribution and the number of degrees of freedom for the numerator is four, and the number of degrees of freedom for the denominator is ten, then F ~ F 4,10.
F statistic from an F distribution with (number of groups – 1) as the numerator degrees of freedom and (number of observations – number of groups) as the denominator degrees of freedom. These statistics are summarized in the ANOVA table.
Contexts where ratio estimation is useful Motivating context: as an alternative to the vanilla estimator when there is population information about the auxilliary variable. Another context: when what you are trying to estimate really is a ratio e.g. want to estimate number of children per bedroom amongst families (with kids) in a particular city: x
DEFINITION. Statistics is a branch of mathematics used to summarize, analyze, and interpret a group of numbers or observations. We begin by introducing two general types of statistics: • Descriptive statistics: statistics that summarize observations. • Inferential statistics: statistics used to interpret the meaning of descriptive statistics.
