独立样本的t统计量
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| 独立样本的t统计量 [2023/03/19 15:20] – yunyuqu | 独立样本的t统计量 [2024/03/22 04:29] (当前版本) – 2104龚文滕 | ||
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| **5.t统计量的计算** | **5.t统计量的计算** | ||
| * {{ : | * {{ : | ||
| + | |||
| + | ---- | ||
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| + | **与单样本T检验有三点不同之处** | ||
| + | - 比较的分布是均值差异的分布（X1-X2） | ||
| + | - 确定t的临界值是基于两个样本的自由度（df1+df2） | ||
| + | - 比较分布的样本分数是基于两个分数之差 | ||
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| + | **1.Hypothesis of independent sample t-test** | ||
| + | *The null hypothesis (H0: μ1- μ2=0): There is no significant difference between the means of the two populations from which the independent samples come, indicating that the two samples are from the same population. | ||
| + | *Alternative hypothesis (H1: μ1- μ2≠0): There is a significant difference between the means of two populations from which independent samples come. | ||
| + | |||
| + | **2.Estimation of population variance** | ||
| + | The combined estimated value of the overall variance is {{ : | ||
| + | *Estimation approach: Perform a __weighted average__ of two samples, with the weight being the __ degrees of freedom of the samples__. | ||
| + | *Assumption for estimation: The variance of the two samples is roughly equal (i.e. __satisfies the homogeneity of variance__) | ||
| + | |||
| + | **3.Calculation of variance of mean distribution** | ||
| + | * {{ :s1.png?80 |}} | ||
| + | * {{ :s2.png?80 |}} | ||
| + | *Calculation approach: Due to differences in sample size n, the distribution of the mean values between the two samples may not be the same. Therefore, the variability of the mean distribution needs to consider the __sample size__. | ||
| + | |||
| + | **4.Calculation of standard error** | ||
| + | * {{ : | ||
| + | * {{ : | ||
| + | *Calculation idea: The variance of the mean difference sample is the sum of the variances of the mean distributions of population 1 and population 2. | ||
| + | |||
| + | **5.Calculation of t-statistic** | ||
| + | * {{ : | ||
| + | |||
| + | ---- | ||
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| + | **There are three differences from single sample T-test** | ||
| + | |||
| + | - The distribution of comparison is the distribution of mean difference (X1-X2) | ||
| + | - The determination of the critical value of t is based on the degrees of freedom of two samples (df1+df2) | ||
| + | - The sample scores for comparing distributions are based on the difference between two scores | ||
独立样本的t统计量.1679239220.txt.gz · 最后更改: 2023/03/19 15:20 由 yunyuqu