实施 t 检验的程序

t 检验（也称为学生 T 检验）比较两个平均值（均值）并判断它们是否彼此不同。 t 检验还说明了差异的显着性。换句话说，它让您知道这些差异是否可能是偶然发生的。 t检验可以使用公式计算：

在哪里，
x̄ ₁是第一个数据集的平均值
x̄ ₂是第二个数据集的平均值
S ₁ ²是第一个数据集的标准差
S ₂ ²是第二个数据集的标准差
N ₁是第一个数据集中的元素个数
N ₂是第二个数据集中的元素个数

例子 ：

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

解释 ：
在示例 1 中，x̄ ₁ = 30, x̄ ₂ = 50.6, S ₁ ² = 15.8114, S ₁ ² = 38.8626
使用公式，t 检验 = -1.09789

下面是t检验的实现。

C++

// CPP Program to implement t-test.
#include 
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.

Javascript

 
// 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
 

输出：

-1.09789