assumptions

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--- assumptions [2023/03/15 14:08] – yunyuqu
+++ assumptions [2024/03/19 04:04] (当前版本) – 2104龚文滕
@@ 行 1: / 行 1: @@
-=====Z检验的前提（Assumptions）=====
+=====Z检验的前提（The Premise of Z-test）=====
 **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 。
 **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。
 **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。
 **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。
@@ 行 14: / 行 17: @@
 **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**
+  *Reason: If the sampled samples cannot be approximated as a normal distribution, they cannot be standardized to obtain the corresponding Z value.
+  *There are two cases of relative normality: ① the original population distribution is a normal distribution; ② Due to the fact that the central limit law can be approximated as a normal distribution.
+  *An example of relative normality: binomial distribution
+**Consequences of violating any premise:**
+Seriously endangers the validity of inferring the population based on the sample.

assumptions.1678889329.txt.gz · 最后更改: 2023/03/15 14:08 由 yunyuqu