test_variance_ratio

test-variance-ratio

Function: test_variance_ratio (x1, x2)

Function: test_variance_ratio (x1, x2, options ...)

This is the variance ratio F-test for two normal populations. Arguments x1 and x2 are lists or column matrices containing two independent samples.

Example 1:

load("stats")$
x: [20.4,62.5,61.3,44.2,11.1,23.7]$
y: [1.2,6.9,38.7,20.4,17.2]$
test_variance_ratio(x,y,'alternative='greater);

Example 2:

load("stats")$
x: [16.0,16.1,23.5,20.0,16.5,12.2,19.9,18.2,19.2,24.7]$
y: [20.9,20.4,21.5,20.6,22.1,21.6,23.3,18.9,19.2]$
test_variance_ratio(x,y,alternative=twosided);

Function: quantile_f (q, m, n)

Returns the q-quantile of a F random variable F(m,n), with m,n>0; in other words, this is the inverse of cdf_f. Argument q must be an element of [0,1].

This function has no closed form and it is numerically computed if the global variable numer equals true, otherwise it returns a nominal expression.

Example 1:

load (distrib)$
quantile_f(2/5,sqrt(3),5);

Example 2:

load (distrib)$
quantile_f(0.975,9,8);

See Also ...

R :: var.test

母集団が2つの場合の母分散の推定と検定

$$A:16.0,16.1,23.5,20.0,16.5,12.2,19.9,18.2,19.2,24.7$$

$$B:20.9,20.4,21.5,20.6,22.1,21.6,23.3,18.9,19.2$$

$$\mathrm{点}\mathrm{推}\mathrm{定}：7.21$$

$$\mathrm{区}\mathrm{間}\mathrm{推}\mathrm{定}：(1.6532,48.2207)$$

$$F_0=\frac{V_A}{V_B}=7.21$$

$$>F({\phi }_A,{\phi }_B,\alpha /2)=F(n_A-1,n_B-1,\alpha /2)=F(9,8,0.025)=4.36$$

AとBではばらつきが異なると判定される。

test-variance-ratio

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