Chapter 7 Sampling Distribution Samples and sampling error
Chapter 7 Sampling Distribution 抽樣分配
• Samples and sampling error – Sample vs. population – z-score 來描述sample 分佈 – Sampling error: 樣本統計量 (sample statistics) 與母體 參數值 (population parameters)的差異 • Fact 1: 利用樣本去推知母體 • Fact 2: different samples 產生different results • Question: 如何知道樣本的結果可以正確的描述母 體的特徵?
The distribution of samples means • The distribution of samples means (樣本平 均數的抽樣分配) – Sampling distribution of • Sampling distribution 抽樣分配 – 在母體中重複抽取固定大小的隨機樣本，所有隨 機樣本的統計值的機率分配稱為抽樣分配
= 100 etc. for all possible samples of a given N from the population
When n=2 sample 91, 92 Sample mean 91. 5 92, 94 Sample mean 93 91, 94 91, 95 92, 93 92 92. 5 93 92. 5 92, 95 93, 94 93, 95 94, 95 93. 5 94 94. 5
When n=3 sample Sample mean 91, 92, 93 92 91, 94, 95 93. 33 91, 92, 94 92. 33 92, 93, 94 93 91, 92, 95 92. 67 92, 93, 95 93. 33 91, 93, 94 92. 67 92, 94, 95 93. 67 91, 93, 95 93 93, 94, 95 94
Central Limit Theorem 中央極限定理 • 無論母體分配是否為normal distribution, 當我 們隨機重複抽取固定大小的樣本時, 只要樣本 的N夠大，則此一抽樣分配也會趨近normal distribution with a mean of and a standard deviation of • If n is sufficiently large ~ N( , 2/n) • How large? Variance
• Sampling distribution of sample mean – Mean of the sampling distribution = – St. D. of the sampling distribution (Standard Error, ) = – Standard error (樣本平均數的標準誤)告訴我們樣本平 均數對母體平均數的估計有多準確 – N, Standard Error
• Difference b/w standard deviation and standard error – When n=1 = =
• Sampling error – Distance b/w a single and • Standard error – Averaged distance b/w any given and – 小standard error 代表樣本與母體無太大差異 – 可以幫助我們了解樣本的結果是happened by chance or greater than chance
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