Noncentral *F* inverse cumulative distribution
function

`X = ncfinv(P,NU1,NU2,DELTA)`

`X = ncfinv(P,NU1,NU2,DELTA)`

returns
the inverse of the noncentral *F* cdf with numerator
degrees of freedom `NU1`

, denominator degrees of
freedom `NU2`

, and positive noncentrality parameter `DELTA`

for
the corresponding probabilities in `P`

. `P`

, `NU1`

, `NU2`

,
and `DELTA`

can be vectors, matrices, or multidimensional
arrays that all have the same size, which is also the size of `X`

.
A scalar input for `P`

, `NU1`

, `NU2`

,
or `DELTA`

is expanded to a constant array with the
same dimensions as the other inputs.

One hypothesis test for comparing two sample variances is to
take their ratio and compare it to an *F* distribution.
If the numerator and denominator degrees of freedom are 5 and 20 respectively,
then you reject the hypothesis that the first variance is equal to
the second variance if their ratio is less than that computed below.

critical = finv(0.95,5,20) critical = 2.7109

Suppose the truth is that the first variance is twice as big as the second variance. How likely is it that you would detect this difference?

prob = 1 - ncfcdf(critical,5,20,2) prob = 0.1297

If the true ratio of variances is 2, what is the typical (median)
value you would expect for the *F* statistic?

ncfinv(0.5,5,20,2) ans = 1.2786

[1] Evans, M., N. Hastings, and B. Peacock. *Statistical
Distributions*. Hoboken, NJ: Wiley-Interscience, 2000.

[2] Johnson, N., and S. Kotz. *Distributions
in Statistics: Continuous Univariate Distributions-2.* Hoboken,
NJ: John Wiley & Sons, Inc., 1970, pp. 189–200.

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