Welch's t-test: Difference between revisions

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=== Integration using Simpson's Rule ===

Perhaps "inspired by C example" may be more accurate. Gamma subroutine from [[Gamma_function#Perl_6 |Gamma function task]].

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<lang perl6>sub Γ(\z) {

constant g = 9;

z < .5 ?? π / sin(π * z) / Γ(1 - z) !!

z < .5 ?? π / sin(π × z) / Γ(1 - z) !!

τ.sqrt * (z + g - 1/2)**(z - 1/2) *

τ.sqrt × (z + g - 1/2)**(z - 1/2) ×

exp(-(z + g - 1/2)) *

exp(-(z + g - 1/2)) ×

[+] <

1.000000000000000174663

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0.5384136432509564062961e-7

-0.4023533141268236372067e-8

> Z* 1, |map 1/(z + *), 0..*

> Z× 1, |map 1/(z + *), 0..*

}

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return 1 unless $a-variance && $b-variance;

my \~~Welsh~~-𝒕-statistic = ($a-mean - $b-mean)/($a-variance/@A + $b-variance/@B).sqrt;

my \Welchs-𝒕-statistic = ($a-mean - $b-mean)/($a-variance/@A + $b-variance/@B).sqrt;

my $DoF = ($a-variance / @A + $b-variance / @B)² /

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my $sa = $DoF / 2 - 1;

my $x = $DoF / (~~Welsh~~-𝒕-statistic² + $DoF);

my $x = $DoF / (Welchs-𝒕-statistic² + $DoF);

my $N = 65355;

my $h = $x / $N;

my ( $sum1, $sum2 );

for ^$N »*» $h -> $i {

for ^$N »×» $h -> $i {

$sum1 += (($i + $h / 2) ** $sa) / (1 - ($i + $h / 2)).sqrt;

$sum2 += $i ** $sa / (1 - $i).sqrt;

}

(($h / 6) * ( $x ** $sa / (1 - $x).sqrt + 4 * $sum1 + 2 * $sum2)) /

(($h / 6) × ( $x ** $sa / (1 - $x).sqrt + 4 × $sum1 + 2 × $sum2)) /

( Γ($sa + 1) * π.sqrt / Γ($sa + 1.5) );

( Γ($sa + 1) × π.sqrt / Γ($sa + 1.5) );

}