January 2015
Beginner to intermediate
628 pages
13h 33m
Japanese
Content preview from 統計クイックリファレンス 第2版
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161
161
6.2 一標本 t 検定
t
この関数は
3
章の
Z
統計量によく似ている。ただし、
t
統計量では標準偏差として母集団
の標準偏差ではなく標本の標準偏差を用いるが、
Z
統計量では母集団の標準偏差を用いるこ
とだけが異なる。
付録
D
には異なる自由度の
t
分布の上方棄却値の表を掲載している（図
D-7
）。
t
分布は対
称的であるから、低い方の棄却値は必要ないので「上方棄却値」と言う（低い方はそれをマ
イナスにすればよい）。正の値だけがその表に掲載されているから、両側
t
検定の棄却値を求
めるためには、欲しい値の半分の値である
α
値の列を使う。
α
＝
0.05
の両側検定であれば、
0.025
の列を使う。当然のことながら、標本が大きくなるにつれ、
t
検定の棄却値は標準正規
分布の棄却値に近づく。例えば、付録
D
の図
D-7
と
3
章の議論より、
α
＝
0.05
の両側検定
の標準正規分布中の上方棄却値は
1.96
であることがわかる。
t
分布を使った
α
＝
0.05
の両側
検定では、上方棄却値は自由度（
df
）に依存する。
1 df
では上方棄却値は
12.706
、
10 df
では
上方棄却値は
2.228
、
30 df
では
2.042
、
50 df
では
2.009
、
100 df
では
1.987
、自由度無限大で
は
1.96
となる。
ウィリアム・シーリー・ゴセット
ゴセットは、近代初の産業統計家と言われることが多い。彼の功績の動機は勤務先（アー
サー・ギネス Son&Co 醸造所）の実用目的によるものだったが、彼が発見した
t
分布に基
づいて一連の主要な推測統計検定ができたのは、彼の功績だ ...
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