如何在Python中进行一样本T检验？

WBOY 转载: 2023-09-17 10:37:02 546浏览

如何在Python中进行一样本T检验？

介绍

One Sample T-Test是一种统计假设检验，用于确定总体均值是否与假设值显著不同。Python为我们提供了进行这个检验所需的资源。在本文中，我们将介绍如何使用SciPy库在Python中进行一样本T检验。

进行一样本T检验

在进行单样本T检验的第一步是陈述零假设和备择假设。零假设是假设总体均值等于假设值。备择假设是零假设的相反假设，即总体均值不等于假设值。

Assuming that we have a set of data and a hypothesized value for the population mean, we can perform a One Sample T-Test to determine whether the population mean is significantly different from the hypothesized value. Here are the steps to conduct a One Sample T-Test in Python using the SciPy library −

步骤1：导入所需的库

Importing the essential libraries will be the first step. To perform the One Sample T-Test in Python, we need to import the NumPy and SciPy libraries. While statistical operations are carried out using the SciPy library, mathematical operations are carried out using the NumPy library.

import numpy as np
from scipy.stats import ttest_1samp

Step 2: Load the Data

然后需要将数据加载到Python中。可以使用NumPy模块的loadtxt()方法来帮助我们。文件名作为参数传递给loadtxt()函数，该函数会生成一个包含内容的数组。

data = np.loadtxt('data.txt')

第三步：定义假设值

我们必须指定总体均值的假设值。这个数值将作为基准，用于评估总体均值是否与估计值显著偏离。

hypothesized_value = 50

Step 4: Perform the One Sample T-Test

We are now prepared to run the One Sample T-Test. The SciPy library's ttest_1samp() function can be used to run the One Sample T-Test. The data and the hypothesised value are the two arguments that the ttest_1samp() function requires.

t_statistic, p_value = ttest_1samp(data, hypothesized_value)

检验统计量和p值是ttest_1samp()函数的结果。t统计量计算了假设值下样本均值的方差的标准误差。在零假设下，p值是生成一个与观察到的统计量一样严重的t统计量的可能性。

Step 5: Interpret the Results

最后，我们必须解释一样本T检验的结果。通过对比p值和显著性水平，我们可以完成这个任务。显著性水平是拒绝原假设的临界值。如果p值小于0.05，也就是传统的显著性水平，那么原假设将被拒绝。

if p_value <r; 0.05:
   print('Reject Null Hypothesis')
else:
   print('Fail to Reject Null Hypothesis')

如果p值小于0.05，我们拒绝零假设，并得出结论，总体均值与假设值存在显著差异。如果p值大于或等于0.05，我们无法拒绝零假设，并得出结论，总体均值与假设值没有显著差异。

单样本T检验假设数据服从正态分布，这一点很重要。如果数据不服从正态分布，我们可能需要使用不同的统计检验方法，比如Wilcoxon符号秩检验。单样本T检验还假设数据是独立的，并且是随机从总体中抽取的。如果某些假设条件不满足，测试结果可能不准确。

带有代码和输出的示例

这是一个使用SciPy库在Python中进行单样本T检验的示例 -

Let's say we have a set of information that includes the weights of a sample of apples. We wish to determine if the population mean apple weight deviates significantly from 100 grammes. Using Python, we can perform a One Sample T-Test as follows −

import numpy as np
from scipy.stats import ttest_1samp

# Load the data
data = np.array([98, 102, 95, 105, 99, 101, 97, 103, 100, 98])

# Define the hypothesized value
hypothesized_value = 100

# Perform the One Sample T-Test
t_statistic, p_value = ttest_1samp(data, hypothesized_value)

# Interpret the results
if p_value < 0.05:
   print('Reject Null Hypothesis')
else:
   print('Fail to Reject Null Hypothesis')

输出

Fail to Reject Null Hypothesis

Because the p-value in this instance is higher than 0.05, we are unable to rule out the null hypothesis. We conclude that, at the 0.05 level of significance, there is no difference between the population mean weight of apples and 100 grams.