→ daniel1982:謝啦小美 你真是好男人... 推 61.230.7.232 12/12
這是取自於
Freedman, Pisani, Purves, and Adhikari (1991),
Statistics, 2nd ed., Norton. (茂昌代理進口)
第 494 頁的內容:
Where do th 5% and 1% lines come from? To find out,
we have to look at the way statistical tables are laid out.
The t-table is a good example. Part of it is reproduced below:
degrees of freedom 10% 5% 1%
1 3.08 6.31 31.82
2 1.89 2.92 6.96
3 1.64 2.35 4.54
...
How is this table used in testing? Suppose investigators are
making a t-test with 2 degrees of freedom. They are using the
5% line, and want to know how big the t-statistic has to be in
order to achieve "statistical significance" --- a P-value below
5%. The table is laid out to make this easy.
... (omitted)
So the result is "statistical significance" as soon as t is more
than 2.35. In other words, the table gives the cutoff for
"statistical significance." Similarly, it gives the cutoff for
the 1% line, or for any other significance level listed across
the top.
R. A. Fisher was one of the first to publish such tables, and
it seems to have been his idea to lay them out that way. There
is a limited amount of room on a page. Once the number of levels
was limited, 5% and 1% stood out as nice round numbers, and they
soon acquired a magical life of their own. With computers
everywhere, this kind of table is almost obsolete. So are the
5% and 1% levels.
This history is on the authority of G. A. Barnard, formely
professor of statistics, Imperial College of Science and Technology,
London; now retired.
(Page A-27)
意思大概是:
因列印空間有限, 只能選少數分位數, 10%, 5%, 1% 是幾個較簡單的數字。
由於這個緣故, 使 10%, 5% 及 1% 成為常用的「顯著水準」。
今日電腦普及, 這些數值表無大用處, 5%, 1% 等水準也可休矣!
這段歷史是根據倫敦Imperial College of Science and Technology
大學的統計系教授 G. A. Barnard的說法。
我不知 Fisher 原先發表時有無加用法註解﹖
後來許多教科書偷懶, 沒告訴學生如何正確使用這些數值表...
雖然我們都知道顯著水準訂 5%, 1% 沒有道理; 但常見的說法是
「5% 和 1% 是『常用的水準』...」
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老師要的答案不是這個方向，OK？
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