The post Application Of F Distribution appeared first on StepUp Analytics.
]]>In the estimation theory, we draw samples from the population and then estimate the population parameters on the basis of these sample values. In the testing procedure, we test whether these estimates are of required precision or not. Here in this article, we will discuss the application of F Distribution.
So many of the times, we come across the situations when we are supposed to check the two or more samples drawn from the same or different population having the same or different variability. F Distribution thus has application.
Now the solution for this is:
We want to test H_{0}: σ^{2}_{x }= σ^{2}_{y}
Against H_{1}: σ^{2}_{x }≠ σ^{2}_{y }
Here n1= 11 n2 =9 s_{x}=0.8 s_{y} = 0.6
Under H_{0, } F= S_{x}^{2}/ S_{y}^{2 }follows F(n1,n2)
S_{x}^{2 }= (n1/n1+n2) s_{x}^{2} =0.704
S_{y}^{2}= (n1/n1+n2) s_{y}^{2} =0.28125
F_{cal}= 0.704/0.28125 = 2.5
F_{tab }(0.05) = 3.35 at (10,8) d.f
So F_{cal} < F_{tab }at 5% level of significance.
H_{0 }may not be rejected, hence we can say that true variance is not equal. Or the samples of the pumpkins have come from the population having different variability with 95% confidence.
R program
> Sxs=0.704 > Sys=0.28125 > fcal=Sxs/Sys > fcal [1] 2.503111 > qf(0.95,df1=10,df2=8) [1] 3.347163
Clearly, fcal < qf , H_{0} is not rejected, i.e. the samples have come from populations having different variability.
A general program using the F-test functions in R:
> x=c(2.3,1,4.5,4,7,8,6.8,2,9,3.7) > y=c(1.2,4.5,5,6.7,8.2,5,3,2.2,0.6,1,2) > var.test(x,y,alternative="two.sided") F test to compare two variances data: x and y F = 1.206, num df = 9, denom df = 10, p-value = 0.7699 alternative hypothesis: true ratio of variances is not equal to 1 95 percent confidence interval: 0.319129 4.780328 sample estimates: ratio of variances 1.205976
_{ }
F_{tab} = 2.28 at 95% confidence interval and (9,25) d.f.
clearly, F_{cal} > F_{tab, }H_{0 }is rejected. i.e. any of the regression of coefficient is non zero, or the study variable is has dependence on at least one of the independent variable.
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The post Application Of F Distribution appeared first on StepUp Analytics.
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