最近選舉民調滿天飛，
很多人都在問一個統計名詞
「信心水準95%，抽樣誤差3%」是何意思？
我的統計學得很差，重新複習了一下
https://web.ntnu.edu.tw/~494402345/CI/CI.pdf選股就是統計學的抽樣，
選對股機率p 70%
可是抽樣得到的結果不會每次剛好70%，
而是有偏差，很可能落在正負2個標準差之內。
Stock selection is akin to statistical sampling.
Probability of accurately selecting the right stock, denoted as p, is 70%.
Nonetheless, the results of the sampling will not consistently align with the precise 70%.
Instead, they tend to show a bias, highly likely falling within a range of plus or minus two standard deviations.
以上換成統計術語為：
信心水準95%之信賴區間為正負2個標準差s
[p - 2s, p + 2s] = [70% - 2s, 70% + 2s]
信心水準95%即白話文的「很可能」
The above can be translated into statistical terminology as follows:
The confidence interval at a 95% confidence level is ±2 standard deviations (s).
[p - 2s, p + 2s] = [70% - 2s, 70% + 2s]
A 95% confidence level is colloquially referred to as "highly likely."
標準差指資料之間的平均距離
＝[px(1-p)/n]^0.5 = [70%x30%/n]^0.5
樣本數n
The standard deviation refers to the average distance between data points.
= [px(1-p)/n]^0.5 = [70%x30%/n]^0.5
Sample size n
n=1, [-22%, 162%]
n=5, [29%, 111%]
n=10, [41%, 98%]
n=30, [53%, 87%]
n=50, [57%, 83%]
n=100, [61%, 79%]
n=200, [64%, 76%]
n=300, [65%, 75%]
n=500, [66%, 74%]
n=1,000, [67%, 73%]
n=1, [-22%, 162%]
n=5, [29%, 111%]
機率在0到100%之間，故上式應改為
n=1, [0, 100%]，單押1支選對股機率很可能為0或100%
n=5, [29%, 100%]，僅押5支選對股機率很可能落於29%到100%之間
n=10, [41%, 98%]，買10檔選對股機率很可能落於41%到98%之間，表示績效大好大壞
For different sample sizes:
n=1, [-22%, 162%].
n=5, [29%, 111%].
Since the probability ranges from 0% to 100%, the formula above requires adjustment.
n=1, [0, 100%]: When selecting only 1 stock, the probability of selecting the correct stock is likely to be either 0% or 100%.
n=5, [29%, 100%]: By selecting only 5 stocks, the probability of correctly identifying the stocks is very likely to fall between 29% and 100%.
n=10, [41%, 98%]: Buying 10 stocks, the probability of selecting the correct stocks is highly likely to fall within the range of 41% to 98%, indicating a wide range of performance outcomes.
n=100, [61%, 79%]，買100支選對股機率很可能落於61%到79%之間，至少61%這是我們建議至少買100支持股的原因
n=100, [61%, 79%]: When purchasing 100 stocks, the probability of selecting the correct stocks is very likely to fall within the range of 61% to 79%. With a minimum threshold of 61%, this is the rationale behind our recommendation to acquire a minimum of 100 stocks.
上述至少買100檔持股的統計證明相當重要，
分散或集中持股不再是見仁見智沒有結論的議題，
而是必須遵守的準則。
也給足大家信心，
持股100支以上績效大壞的可能性很低，
不必每天緊張兮兮關注股市，
有更多時間去吃喝玩樂
The above statistical evidence underscores the significance of holding a minimum of 100 stocks in your portfolio. Whether to diversify or concentrate one's holdings is no longer a debatable issue, but a guideline that must be followed. This also gives everyone confidence that the likelihood of poor performance with holding more than 100 stocks is very low. There is no need to be nervous and pay close attention to the stock market every day, instead, we can spend more time enjoying life.
http://mikeon88.blogspot.com/2018/08/1221.html