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assumptions

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assumptions [2024/03/19 04:03] – 2104龚文滕assumptions [2024/03/19 04:04] (当前版本) – 2104龚文滕
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 **1.随机样本** **1.随机样本**
   * 原因：样本必须对总体有代表性，而随机取样有助于确保取样的代表性 。   * 原因：样本必须对总体有代表性，而随机取样有助于确保取样的代表性 。
-**1.Random sample** +
-  * Reason: The sample must be representative of the population, and random sampling helps ensure the representativeness of the sample+
 **2.独立观察** **2.独立观察**
   * 原因：与样本代表性有关, 每个观察应该与所有其它观察是独立的。一个特定的观察的概率应当保持恒定。    * 原因：与样本代表性有关, 每个观察应该与所有其它观察是独立的。一个特定的观察的概率应当保持恒定。 
-**2.Independent observation** +
-  * Reason: It is related to the representativeness of the sample, and each observation should be independent of all other observations. The probability of a specific observation should remain constant.+
 **3.σ保持恒定** **3.σ保持恒定**
   * 原因：在Z检验的处理中，对总体中的每一个个体都加上(或减去) 一个常数，总体的均值可能因处理而导致变化，但标准差不变。   * 原因：在Z检验的处理中，对总体中的每一个个体都加上(或减去) 一个常数，总体的均值可能因处理而导致变化，但标准差不变。
-**3.σ maintain constant** +
-  * Reason: In the processing of Z-test, a constant is added (or subtracted) for each individual in the population, and the mean of the population may change due to processing, but the standard deviation remains unchanged.+
 **4.取样样本是相对正态的** **4.取样样本是相对正态的**
   * 原因：如果取样样本不能近似为正态分布，就无法将它们标准化得到对应的Z值。   * 原因：如果取样样本不能近似为正态分布，就无法将它们标准化得到对应的Z值。
   * 相对正态的两种情况：①原总体分布就是正态分布；②由于中心极限定律可以近似为正态分布。   * 相对正态的两种情况：①原总体分布就是正态分布；②由于中心极限定律可以近似为正态分布。
   * 相对正态的例子：二项分布   * 相对正态的例子：二项分布
 +
 +**违反任一前提的后果：**
 +严重地危及依据样本对总体作出推论的有效性。
 +
 +**1.Random sample**
 +  * Reason: The sample must be representative of the population, and random sampling helps ensure the representativeness of the sample
 +
 +**2.Independent observation**
 +  * Reason: It is related to the representativeness of the sample, and each observation should be independent of all other observations. The probability of a specific observation should remain constant.
 +
 +**3.σ maintain constant**
 +  * Reason: In the processing of Z-test, a constant is added (or subtracted) for each individual in the population, and the mean of the population may change due to processing, but the standard deviation remains unchanged.
 +
 **4.The sample is sampled relatively normal** **4.The sample is sampled relatively normal**
   *Reason: If the sampled samples cannot be approximated as a normal distribution, they cannot be standardized to obtain the corresponding Z value.   *Reason: If the sampled samples cannot be approximated as a normal distribution, they cannot be standardized to obtain the corresponding Z value.
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   *An example of relative normality: binomial distribution   *An example of relative normality: binomial distribution
-**违反任一前提的后果：** 
-严重地危及依据样本对总体作出推论的有效性。 
  
 **Consequences of violating any premise:** **Consequences of violating any premise:**
 Seriously endangers the validity of inferring the population based on the sample. Seriously endangers the validity of inferring the population based on the sample.
assumptions.1710821037.txt.gz · 最后更改: 2024/03/19 04:03 由 2104龚文滕