La prueba t (también llamada prueba t de Student) compara dos promedios (medias) y dice si son diferentes entre sí. La prueba t también indica cuán significativas son las diferencias. En otras palabras, le permite saber si esas diferencias podrían haber ocurrido por casualidad. La prueba t se puede calcular usando la fórmula:
donde,
x̄ 1 es la media del primer conjunto de datos
x̄ 2 es la media del segundo conjunto de datos
S 1 2 es la desviación estándar del primer conjunto de datos
S 2 2 es la desviación estándar del segundo conjunto de datos
N 1 es el número de elementos en el primer conjunto de datos
N 2 es el número de elementos en el segundo conjunto de datos
Ejemplos:
Input : arr1[] = {10, 20, 30, 40, 50}
arr2[] = {1, 29, 46, 78, 99}
Output : -1.09789
Input : arr1[] = {5, 20, 40, 80, 100, 120}
arr2[] = {1, 29, 46, 78, 99}
Output : 0.399518
Explicación:
en el ejemplo 1, x̄ 1 = 30, x̄ 2 = 50.6, S 1 2 = 15.8114, S 1 2 = 38.8626
usando la fórmula, prueba t = -1.09789
A continuación se muestra la implementación de la prueba t.
C++
// CPP Program to implement t-test.
#include <bits/stdc++.h>
using namespace std;
// Function to find mean.
float Mean(float arr[], int n)
{
float sum = 0;
for (int i = 0; i < n; i++)
sum = sum + arr[i];
return sum / n;
}
// Function to find standard
// deviation of given array.
float standardDeviation(float arr[], int n)
{
float sum = 0;
for (int i = 0; i < n; i++)
sum = sum + (arr[i] - Mean(arr, n)) *
(arr[i] - Mean(arr, n));
return sqrt(sum / (n - 1));
}
// Function to find t-test of
// two set of statistical data.
float tTest(float arr1[], int n,
float arr2[], int m)
{
float mean1 = Mean(arr1, n);
float mean2 = Mean(arr2, m);
float sd1 = standardDeviation(arr1, n);
float sd2 = standardDeviation(arr2, m);
// Formula to find t-test
// of two set of data.
float t_test = (mean1 - mean2) / sqrt((sd1 * sd1)
/ n + (sd2 * sd2) / m);
return t_test;
}
// Driver function.
int main()
{
float arr1[] = { 10, 20, 30, 40, 50 };
// Calculate size of first array.
int n = sizeof(arr1) / sizeof(arr1[0]);
float arr2[] = { 1, 29, 46, 78, 99 };
// Calculate size of second array.
int m = sizeof(arr2) / sizeof(arr2[0]);
// Function call.
cout << tTest(arr1, n, arr2, m);
return 0;
}
Java
// Java Program to implement t-test.
import java.util.*;
import java.io.*;
class GFG
{
// Function to find mean.
static float Mean(float arr[], int n)
{
float sum = 0;
for (int i = 0; i < n; i++)
sum = sum + arr[i];
return sum / n;
}
// Function to find standard
// deviation of given array.
static float standardDeviation(float arr[], int n)
{
float sum = 0;
for (int i = 0; i < n; i++)
sum = sum + (arr[i] - Mean(arr, n))
* (arr[i] - Mean(arr, n));
return (float)Math.sqrt(sum / (n - 1));
}
// Function to find t-test of
// two set of statistical data.
static float tTest(float arr1[], int n,
float arr2[], int m)
{
float mean1 = Mean(arr1, n);
float mean2 = Mean(arr2, m);
float sd1 = standardDeviation(arr1, n);
float sd2 = standardDeviation(arr2, m);
// Formula to find t-test
// of two set of data.
float t_test = (mean1 - mean2) /
(float)Math.sqrt((sd1 * sd1) /
n + (sd2 * sd2) / m);
return t_test;
}
// Driver code
public static void main(String args[])
{
float arr1[] = { 10, 20, 30, 40, 50 };
// Calculate size of first array.
int n = arr1.length;
float arr2[] = { 1, 29, 46, 78, 99 };
// Calculate size of second array.
int m = arr2.length;
// Function call.
System.out.print(tTest(arr1, n, arr2, m));
}
}
// This code is contributed by Sahil_Bansall
Python3
# Python 3 Program to implement t-test.
from math import sqrt
# Function to find mean.
def Mean(arr, n):
sum = 0
for i in range(0, n, 1):
sum = sum + arr[i]
return sum / n
# Function to find standard
# deviation of given array.
def standardDeviation(arr, n):
sum = 0
for i in range(0, n, 1):
sum = (sum + (arr[i] - Mean(arr, n)) *
(arr[i] - Mean(arr, n)))
return sqrt(sum / (n - 1))
# Function to find t-test of
# two set of statistical data.
def tTest(arr1, n, arr2, m):
mean1 = Mean(arr1, n)
mean2 = Mean(arr2, m)
sd1 = standardDeviation(arr1, n)
sd2 = standardDeviation(arr2, m)
# Formula to find t-test
# of two set of data.
t_test = (mean1 - mean2) / sqrt((sd1 * sd1) / n +
(sd2 * sd2) / m)
return t_test
# Driver Code
if __name__ == '__main__':
arr1 = [10, 20, 30, 40, 50]
# Calculate size of first array.
n = len(arr1)
arr2 = [1, 29, 46, 78, 99]
# Calculate size of second array.
m = len(arr2)
# Function call.
print('{0:.6}'.format(tTest(arr1, n, arr2, m)))
# This code is contributed by
# Surendra_Gangwar
C#
// C# Program to implement t-test.
using System;
class GFG {
// Function to find mean.
static float Mean(float[] arr, int n)
{
float sum = 0;
for (int i = 0; i < n; i++)
sum = sum + arr[i];
return sum / n;
}
// Function to find standard
// deviation of given array.
static float standardDeviation(float[] arr, int n)
{
float sum = 0;
for (int i = 0; i < n; i++)
sum = sum + (arr[i] - Mean(arr, n)) *
(arr[i] - Mean(arr, n));
return (float)Math.Sqrt(sum / (n - 1));
}
// Function to find t-test of
// two set of statistical data.
static float tTest(float[] arr1, int n,
float[] arr2, int m)
{
float mean1 = Mean(arr1, n);
float mean2 = Mean(arr2, m);
float sd1 = standardDeviation(arr1, n);
float sd2 = standardDeviation(arr2, m);
// Formula to find t-test
// of two set of data.
float t_test = (mean1 - mean2) /
(float)Math.Sqrt((sd1 * sd1) /
n + (sd2 * sd2) / m);
return t_test;
}
// Driver code
static public void Main ()
{
float[] arr1 = {10, 20, 30, 40, 50};
// Calculate size of first array
int n = arr1.Length;
float[] arr2 = { 1, 29, 46, 78, 99 };
// Calculate size of second array
int m = arr2.Length;
// Function calling
Console.Write(tTest(arr1, n, arr2, m));
}
}
// This code is contributed by Ajit.
PHP
<?php
// PHP Program to implement t-test.
// Function to find mean.
function Mean($arr, $n)
{
$sum = 0;
for ($i = 0; $i < $n; $i++)
$sum = $sum + $arr[$i];
return $sum / $n;
}
// Function to find standard
// deviation of given array.
function standardDeviation($arr,$n)
{
$sum = 0;
for ($i = 0; $i < $n; $i++)
$sum = $sum + ($arr[$i] - Mean($arr, $n)) *
($arr[$i] - Mean($arr, $n));
return sqrt($sum / ($n - 1));
}
// Function to find t-test of
// two set of statistical data.
function tTest($arr1, $n,
$arr2, $m)
{
$mean1 = Mean($arr1, $n);
$mean2 = Mean($arr2, $m);
$sd1 = standardDeviation($arr1, $n);
$sd2 = standardDeviation($arr2, $m);
// Formula to find t-test
// of two set of data.
$t_test = ($mean1 - $mean2) /
sqrt(($sd1 * $sd1) /
$n + ($sd2 * $sd2) / $m);
return $t_test;
}
// Driver Code
{
$arr1 = array(10, 20, 30, 40, 50);
// Calculate size of first array.
$n = sizeof($arr1) / sizeof($arr1[0]);
$arr2 = array( 1, 29, 46, 78, 99 );
// Calculate size of second array.
$m = sizeof($arr2) / sizeof($arr2[0]);
// Function call.
echo tTest($arr1, $n, $arr2, $m);
return 0;
}
// This code is contributed by nitin mittal.
?>
Javascript
<script>
// Javascript program to implement t-test.
// Function to find mean.
function Mean(arr, n)
{
let sum = 0;
for(let i = 0; i < n; i++)
sum = sum + arr[i];
return sum / n;
}
// Function to find standard
// deviation of given array.
function standardDeviation(arr, n)
{
let sum = 0;
for(let i = 0; i < n; i++)
sum = sum + (arr[i] - Mean(arr, n)) *
(arr[i] - Mean(arr, n));
return Math.sqrt(sum / (n - 1));
}
// Function to find t-test of
// two set of statistical data.
function tTest(arr1, n, arr2, m)
{
let mean1 = Mean(arr1, n);
let mean2 = Mean(arr2, m);
let sd1 = standardDeviation(arr1, n);
let sd2 = standardDeviation(arr2, m);
// Formula to find t-test
// of two set of data.
let t_test = (mean1 - mean2) /
Math.sqrt((sd1 * sd1) /
n + (sd2 * sd2) / m);
return t_test.toFixed(5);
}
// Driver code
let arr1 = [ 10, 20, 30, 40, 50 ];
// Calculate size of first array
let n = arr1.length;
let arr2 = [ 1, 29, 46, 78, 99 ];
// Calculate size of second array
let m = arr2.length;
// Function calling
document.write(tTest(arr1, n, arr2, m));
// This code is contributed by decode2207
</script>
Producción:
-1.09789
Publicación traducida automáticamente
Artículo escrito por Dharmendra_Kumar y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA