F distribution or variance ratio distribution, Mathematics

Assignment Help:

Frequency Distribution or Variance Ratio Distribution

This was developed by R. A Fisher in 1924 and is normally defined in terms of the ratio of the variances of two usually distributed populations. This is utilized to test the hypothesis that the two generally distributed populations have two equal variances. F distribution ratio of the variances between two generally distributed population may be expressed like:  (s12/d12)/(s22/d22)

Along with Ω-11 = n1-1 and Ω-12 = n2-1 degrees of freedom

Whereas general population means are unknown

n1 - sample size of independent random 1

n2 - sample size of independent random 2

s12 - Sample variance of 1

s22 - sample variance of 2

d12 - Population variance of 1? 

d22 - Population variance of 2

s12 and s22 are described by

s12 = (Σ(x1 - x¯1)2)/(n1 - 1) as the unbiased estimator of d12

s22 = (Σ(x2 - x¯2)2)/(n1 - 1) as the unbiased estimator of d22

if  d12  =  d22 then the statistic F = s12/s22

= larger estimate of variance/smaller estimate of variance

F - Distribution along with n1-1 and n2-1 degrees of freedom. F distribution depends on the degrees of freedom Ω-11 for the numerator and Ω-12 for the denominator. This has parameters Ω-11 and Ω-12 such that for various values of Ω-11 and Ω-12 will have various distributions.


Related Discussions:- F distribution or variance ratio distribution

Determine the derivative f ( x ) = 2 x2 -16x + 35, Determine the derivative...

Determine the derivative of the following function by using the definition of the derivative. f ( x ) = 2 x 2 -16x + 35 Solution Thus, all we actually have to do is to pl

Homotopy, prove same homotopy type is an equivalent relation

prove same homotopy type is an equivalent relation

..percentage, how to express 15/4 into percentage

how to express 15/4 into percentage

Utilize the chain rule to differentiate, Chain Rule : Assume that we have ...

Chain Rule : Assume that we have two functions f(x) & g(x) and they both are differentiable. 1.   If we define F ( x ) = ( f o g ) ( x ) then the derivative of F(x) is,

Elps in maths, 25 cookies have to be divided equally among 4 children.hw ca...

25 cookies have to be divided equally among 4 children.hw can we use elps to answer this question?

X and y -intercept, X-intercept  If an intercept crosses the x-axis we ...

X-intercept  If an intercept crosses the x-axis we will call it as x-intercept .  Y-intercept Similar, if an intercept crosses the y-axis we will call it as a y-inter

Polar coordinates - parametric equations & polar coordinates, Polar Coordin...

Polar Coordinates Till this point we've dealt completely with the Cartesian (or Rectangular, or x-y) coordinate system.  Though, as we will see, this is not all time the easie

Prove that 7cot - 3cosec = 3, If 7 cosec?-3cot? = 7, prove that 7cot? - 3co...

If 7 cosec?-3cot? = 7, prove that 7cot? - 3cosec? = 3. Ans:    7 Cosec?-2Cot?=7 P.T 7Cot? - 3 Cosec?=3 7 Cosec?-3Cot?=7 ⇒7Cosec?-7=3Cot? ⇒7(Cosec?-1)=3Cot? ⇒7(C

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd