统计第8回

Jun 4, 20122 likes637 views

Chiaki Yamaguchi

統計学　第8回
推計学のすすめ　決定と計画の科学
（佐藤信著、講談社）より

第3章　バラついた数を読む
2.　バラツキはばらせという話

２０１２/０６/０４
　担当：山口
1

睡眠薬の効果をためす実験
●
睡眠薬の効果を検証したい！
● ↑「薬を飲んだ」という安心感だけでよく
眠れるという心理効果が無視できない

睡眠薬服用時の睡眠時間と　
実験方法偽薬服用時の睡眠時間を比較

睡眠薬利用偽薬利用

睡眠時間を記録 2

睡眠薬の効果をためす実験
睡眠薬偽薬
結果 11 5
効果はありそうだが
11 8
8 5
ばらついている
平均 10 6
総平均 8

睡眠薬偽薬睡眠薬偽薬睡眠薬偽薬
8 8 2 -2 1 -1
8 8 2 -2 1 2
8 8 2 -2 -2 -1
総平均薬効差による誤差（個人差?偶然誤差）
バラツキによるバラツキ

バラツキ度が同じ程度なら、 3
薬効差はないと判断

バラツキの大きさをはかるには
バラツキの大きさは不偏分散で推定

偏差平方和
不偏分散= 自由度

分散分析表（下図）でまとめるとわかりやすい
偏差平方和自由度不偏分散
薬効差 22+22+22+(-2)2+(-2)2+(-2)2 2-1 24/1
= 24 =1 = 24
誤差 12+12+(-2)2+(-1)2+22+(-1)2 6-2 12/4
= 12 = 4 =3

4

薬効差分散と誤差分散の比較
２つの分散の差を比べるには、比をとる
　　→薬効差分散/誤差分散
=24/3 = 8
この差が大きいかどうかは
F分布を利用して判断できる

※注意！
第２章とは違い、5%の表を使う
↑薬効差があるかは
　　薬効差分散＞誤差分散
　　で判断するから

5

結果
● 薬効差分散/誤差分散＞５%の危険率
↓
● もし薬効差がないとすれば、この差がでる確率は
5%以下
↓
● 薬効差はある！　

6

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统计第8回

1. 統計学　第8回推計学のすすめ　決定と計画の科学（佐藤信著、講談社）より第3章　バラついた数を読む 2.　バラツキはばらせという話２０１２/０６/０４　担当：山口 1

2. 睡眠薬の効果をためす実験 ● 睡眠薬の効果を検証したい！ ● ↑「薬を飲んだ」という安心感だけでよく眠れるという心理効果が無視できない睡眠薬服用時の睡眠時間と　実験方法偽薬服用時の睡眠時間を比較睡眠薬利用偽薬利用睡眠時間を記録 2

3. 睡眠薬の効果をためす実験睡眠薬偽薬結果 11 5 効果はありそうだが 11 8 8 5 ばらついている平均 10 6 総平均 8 睡眠薬偽薬睡眠薬偽薬睡眠薬偽薬 8 8 2 -2 1 -1 8 8 2 -2 1 2 8 8 2 -2 -2 -1 総平均薬効差による誤差（個人差?偶然誤差）バラツキによるバラツキバラツキ度が同じ程度なら、 3 薬効差はないと判断

4. バラツキの大きさをはかるにはバラツキの大きさは不偏分散で推定偏差平方和不偏分散= 自由度分散分析表（下図）でまとめるとわかりやすい偏差平方和自由度不偏分散薬効差 22+22+22+(-2)2+(-2)2+(-2)2 2-1 24/1 = 24 =1 = 24 誤差 12+12+(-2)2+(-1)2+22+(-1)2 6-2 12/4 = 12 = 4 =3 4

5. 薬効差分散と誤差分散の比較２つの分散の差を比べるには、比をとる　　→薬効差分散/誤差分散 =24/3 = 8 この差が大きいかどうかは F分布を利用して判断できる ※注意！第２章とは違い、5%の表を使う ↑薬効差があるかは　　薬効差分散＞誤差分散　　で判断するから 5

6. 結果 ● 薬効差分散/誤差分散＞５%の危険率 ↓ ● もし薬効差がないとすれば、この差がでる確率は 5%以下 ↓ ● 薬効差はある！　 6

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统计第8回

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统计第8回