F-Distribution

Sunday, 18 August 2019

9:31 PM

Sampling distribution It can be shown that, if Ho is true, the ratio SSTr MSTr follows a particular distribution known as the Fisher's F-distribution with k — 1 and n — k degrees of freedom, which is usually denoted by

 

The Fisher's F-distribution A random variable, say X, is said to follow Fisher's F-distribution with dl and d2 degrees of freedom, i.e. x N Fd„d2

 

and for d2 > 2 E(X) = d2-2 2d2ä(d1 + ± — 2) for d2 dl(d2 — 4)

 

msTr reject Ho if msEr

 

ANOVA table The computations for this test are usually summarised in tabular form MSEr = Source Treatment Error Total Note I: dhot degrees Of freedom dfrr=k — I dfEr= n k dfTot = n 1 sum of squares SSTr ssrot mean square MSTr F-statistic dfTr + dfEr and SSTot = SSTr + SSEr Note 2: this table is the usual computer output when an ANOVA procedure is run

 

 

Created with Microsoft OneNote 2016.