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マスタ タイトルの書式設定
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------=_NextPart_01C83E3F.6D47C160 Content-Location: file:///C:/8ECB5C15/07dist_5.files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C83E3F.6D47C160 Content-Location: file:///C:/8ECB5C15/07dist_5.files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
データ分布= と予測
仮説検定
堀田敬介
2007/12/14,Fri.
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quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
Contents
•仮説検定とは？
–有意水準
–帰無仮説と対立仮説
–仮説検定における誤り=
–片側検定と両側検定
•母集団の母数に対する仮説検定
–母平均の検定（母分散= が既知の場合） = ;
–母平均の検定（母分散= が未知の場合） = ;
–母分散の検定<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 71%;display:none'>
–母比率の検定<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 71%;display:none'>
•2つの母集団<= /b>に対する仮説検定<= /span>
–既知の場合） <= /span>
–未知だが等しい場合） <= /span>
–未知で等しくない場合） <= /span>
–分散の比の検定
•適合度検定と独立性の検定
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仮説検定と= は？
仮説検定
hypo= thesis testing
推測統計=
stat= istical inference
標本データの平均値= ﾆ分散（標準偏差）から，= 齒W団の平均値と分散（標準= ﾎ差），母比率などの母数（= pラメータ）を推定する
標本データの平均値= ﾆ分散（標準偏差）などを= 烽ﾆに，母集団に対する= 「ある仮説」が間違いかどうか判定する
母集団 = ;
標本&#= 13;
標本から
母集団を
推定
母集団= ﾉ対する
仮説：<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";color:purple;mso-fareast-language: JA'>H0
標本から
仮説を
検定
母数
μ，σ2
無作為抽出
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仮説検定と= は？
•例：日本人成人女性の平均身長
= 211;　仮説　「日本人成人女性の平均身長は160cmである」
=
母集団
<= /span>成人女性 = ;
3D"環状矢印:
ランダ= サンプリング
（無作為抽出）
標本平均の値：157.5cm
仮説は間違っていた（正しかった）と言えるのか？&= #13;
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仮説検定と= は？
•例：日本人成人女性の平均身長
= 211;　仮説　「日本人成人女性の平均身長は160cmである」
= 標本平均の値：157.5cm
標本標準偏差の値：10.78cm
標本平均　　，標本分散　　とすると，= ﾈ下の確率変数 T が自由度 n-1 の t 分布に従う
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仮説検定と= は？
•例：日本人女性の平均身長
R= 11;　仮説　「日本人女性の平均身長は160cmである」
自= 由度9の
t分布に従う
　標本平均　　がこの分布の中心から= 大きく外れ= た位置にあるならば，仮説は間違って= いると判= 定できるのではないか？
注意<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:Verdana;mso-f= areast-font-family: "ＭＳ Ｐゴシック";font-size:111%;mso-fareast-hint:yes'>：仮説が間違いであ= 確率は0にはならない！&= #13;
仮説が間違いである= ﾍ囲を決める！&= #13;
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データ分布と予測　5．仮説検定
仮説検定と= は？
•採択域と棄却域
–例：自由度9のt分布における下側<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-hint:yes;mso-fareast-l= anguage: JA'>5%棄却域
棄却域= rejection region
（臨界= 域 critical region）
採択域 region of acceptance
95%
5%
T=3D-1.833
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仮説検定と= は？
•採択域と棄却域
–例：自由度9のt分布における= 下側5％棄却域
つまり，
棄却域：
= 採択域= ： となり，標本= 平均値が153.4cm以下であれば，仮説：「日本人成人女性の平均身長は160cmである」が棄却 (rejection of hypothesis)される
例題の場合は= ，標本平均値が157.5cmで棄却域にないため，棄却されない
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有意水準
<= span style=3D'mso-fareast-hint:yes'>•仮説検定の手順
&#= 8211;1．母集団に対する「仮説」を立てる
&#= 8211;2．「仮説」の棄却域を設定する
• 棄却域が5%とすれば95%信頼区間から外れて= いれば「仮説」を「棄却」することになる
棄却域：小
信頼区間：広=
棄却域：大
信頼区間：狭=
★ 棄却域が5%で「仮説」が「棄却」されるとき，5%はその「仮<= span style=3D'position:absolute;top:58.13%;left:0%;width:83.88%;height:44.18%'>= 説」が正しい可能性= ｪ残る！&= #13;
5%の間違いの危険性がある =
5%：有= 意水準(significance level)
     〔危険率(risk)〕
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帰無仮説と= 対立仮説
•検定における仮説は<= u>対立する2つ
= 211;〔仮説<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:86%;mso-fareast-hint:yes; mso-fareast-language:JA'>1〕日本人成人男性の平均体重は60kgである <= /span>
= 211;〔仮説<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:86%;mso-fareast-hint:yes; mso-fareast-language:JA'>2〕日本人成人男性の平均体重は60kgではない
帰無仮説 (null hypothesis)
　棄却されてはじめて意味を持つ=
★ 仮説1を統計的に検定したとき，その起こる確= ｦが棄却域= にあれば，この仮説= ｪ棄却される．
★ 仮説1が棄却されない場合，「仮説1が正しい= ﾆいう結論= は出せな= ｢」！
★ 仮説1は「棄却されてはじめて意味を持つ」
★ 仮説2は仮説1が棄却された場合に採択される&= #13;
対立仮説 (alternative hypothesis)
　本当に示したいこと
統計的検定の目的は「= 対立仮説の正しさを示す」こと！<= /div>
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仮説検定における誤りと検出力 <= /span>
•仮説検定における誤り = ;
–第１種の誤り error of the first kind
•帰無仮説H0= が正しいのにそれを棄却してしまう
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 90%;mso-fareast-hint:yes'>例：品質管理において「合格するはずの良製品を不合= 格判定」する
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 90%;mso-fareast-hint:yes'>例：刑事犯罪において「無罪の人を有罪」にする
–第２種の誤り error of the second kind
•帰無仮説H0= が誤っているのにそれを採択してしまう
–例：品質管理において「不合格のはずの不良品を合格= 判定」する
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 90%;mso-fareast-hint:yes'>例：刑事犯罪において「有罪の人を無罪」にする
正しい
（確率：1-β=3D検出力）
1
H1=
第2種の誤り
1-α）
H0=
= 検<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; font-size:71%;mso-fareast-hint:yes'>結 <= /div>
対立仮説 = H1
帰無仮説 = H0
= <= /div>
<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; font-size:71%;mso-special-format:lastCR;display:none'> <= /div>
= <= /div>
<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; font-size:71%;mso-special-format:lastCR;display:none'> <= /div>
α：大⇔β：小
α：小⇔β：大
となるので，共に小さくはできない
•帰無仮説が限定的なのでα（有意水準）は= 1つに定まる．<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:Verdana;mso-f= areast-font-family: "ＭＳ Ｐゴシック";font-size:89%;display:none'> •<= /span>サンプル数が大きけれ= ばβは小さくなる．&#= 13;
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Content-Location: file:///C:/8ECB5C15/07dist_5.files/slide0013.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
両側検定と= 片側検定
•両側検定 two tailed test%） <= /span>
R= 11;〔帰無仮説〕
= 211;　　日本人男性の平均体重は60kgである <= /span>
= 211; （μ＝60） <= /span>
R= 11;〔対立仮説〕
= 211;　　日本人男性の平均体重は60kgではない <= /span>
= 211; （μ≠60）
•片側（右側）検定 one tailed test（有意水準α%） <= /span>
R= 11;〔帰無仮説〕
= 211;　　日本人男性の平均身長は160cmである
= 211; （μ＝160） <= /span>
R= 11;〔対立仮説〕
= 211;　　日本人男性の平均身長は160cmより大きい
= 211; （μ＞160）
α%
α%
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•母平均に関する仮説検定（母分散　　既知）
•
•
•
•<= /span>母平均に関する仮説検定（母分散　　未知）
•
•
•
•<= /span>母分散に関する仮説検定
母数に関する仮説検定
= 搆v量　　　　　　　　　　　　　　が標準正規分布N<= /span>(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>0<= /span>,<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>1<= /span>)<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"'>に従うことを利用
= 搆v量　　　　　　　　　　　　　　　が自由度 n-1 の t 分布に従うことを利用
= 搆v量　　　　　　　　　　　　　が自由度 n-1 のχ2分布に従うことを利用
Z検定
t検定
χ2= 検定
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f/EBhxIhEWg88pLKHLNZe0Jlt+lQamVhszrusup1gsPRMZl6xm3TnzV74353zPIT5DC66/cHgP8P GEjXEVhoeIiYqCjIYbD4CBmJmBQgaXkpSeeIydl5OFbpKTrqh0B66lcAADs= ------=_NextPart_01C83E3F.6D47C160 Content-Location: file:///C:/8ECB5C15/07dist_5.files/slide0010.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
母数に関する仮説検定
•母平均の検定〔Z<= /span>検定〕 （母分散が既知の場合）
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>例：BMIによる肥満検査
= 226; BMI＝(体重)kg ÷ {()m}2
R= 26;　
= 226;　　ある会社の無作為抽出100
= 226;　　のBMI=3D22.35だった．
= 226;　　肥満の程度に問題があるといえるか？= 有意水準5
–〔帰無仮説〕 母平均μ＝22
–〔対立仮説〕 母平均μ≠22
–で両側検定．ただし，母標準偏差は過去の= 経験から2.5とする．
確率変数Zは
標準正規分布
N(0,1)に従う
〔出展：『図解雑学 統計解析』 p.192〕
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<= span style=3D'mso-fareast-hint:yes'>•母平均の検= 定〔Z<= /span>検定〕 （母分散が既知の場合）
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>例：BMIによる肥満検査 = ;
–　　有意5を表す不等式
母数に関する仮説検定
帰無仮説は= 棄却されない
–結論：肥満の程度に問題があるとはいえない
–　　　　ただし，「問題がない」とまでは= いえない
標準正規分布：両側5%<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:Verdana;mso-f= areast-font-family: "ＭＳ Ｐゴシック";mso-fareast-hint:yes'>棄却域
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母数に関する仮説検定
•母平均の検定〔t検定〕（母分散が未知の場合）
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>例：酒屋の不正疑惑 <= /span>
R= 26;　　ある酒屋では酒の量をごまかして売っ= ているという噂があったので実際に1(=3D180cc)のお酒を5
–〔帰無仮説〕 母平均μ＝180
–〔対立仮説〕 母平均μ＜180
–　　とし，有意水準5%で左片側検定．
確率変数T は
自由度n-1のt分布tα(n-1) に従う
標本平均値は172.0cc であり，180ccより8ccも少ないが，果たして= この店は不当表示で訴えられるか？
〔出展：『なるほど統計学』 p.125〕
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Content-Location: file:///C:/8ECB5C15/07dist_5.files/slide0026.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
母数に関する仮説検定
•母平均の検定〔t検定〕（母分散が未知の場合）
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>例：酒屋の不正疑惑 = ;
–　　　有意5を表す不等式
よって，
より，帰無仮説 H0= は棄却される．
= ｱの酒屋は酒量をご<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:Verdana;mso-f= areast-font-family: "ＭＳ Ｐゴシック"'>まかしているらしい…
t分布：片側= （下側）5%棄却域
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•母平均の検定〔t検定〕（母分散が未知の場合）
–演習1：空調システムの作動状況検査
&#= 8211;　　 設定温度を25℃とし，7日間室内温度測定し，このシステムが正しく動いているかどうか5%有意水準で両側検定
&#= 8211;
–　　〔帰無仮説〕μ＝25.0
–　　〔対立仮説〕μ≠25.0
有意水準5％で帰無仮説は棄却できない
母数に関する仮説検定
この空調システムは= ｳ常に動いてるらし= い．
〔出展：『統計学入門』 p.241〕
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S4ir2/vG6xtsxSpcvAdsXIycHLzM3Ov8nBstXUtdHXuN3aq9ndrtXQoePjpO/ml+vpmunsneXvkO Pyk//1hv34iffyvJb7vvn6GAAnf5K+iKIMJjBxd+a+hQHMSI5SZSRGfx4rqMNBrdcewY7yNIeiJH 3itpUh/KlP2IsdSk8GVMljNT1jR5c2ROkDs7BvoJNKjQoUSLGj0KqAAAOw== ------=_NextPart_01C83E3F.6D47C160 Content-Location: file:///C:/8ECB5C15/07dist_5.files/slide0018_image108.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBgATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAF ABEAgAAAAP9mAAIPhBGXetjrmDQQRvrm3bYAADs= ------=_NextPart_01C83E3F.6D47C160 Content-Location: file:///C:/8ECB5C15/07dist_5.files/slide0019.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
•母平均の検定〔t検定〕（母分散が未知の場合）
–演習2：補習授業の効果測定
= 211;　　　英語の補習を行った後の試験成績は上がったか？5%有意水準で効果を検定せよ．10名の対象学生に対する補習前後の得点差は下表
–
–　　　〔帰無仮説〕μ＝0
–　　　〔対立仮説〕μ>0
母数に関する仮説検定
有意水準5％で帰無仮説は棄却される
試験成績は上昇した= 轤ｵい（補習の効果= はあったらしい）
〔出展：『統計学入門』 p.241〕
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•母平均の検定〔t検定〕（母分散が未知の場合）
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; font-size:86%'>演習3 ：今年の生徒は出来= ｪよいか？
= 211;　　　数学の定期試験で10人の採点を終えた所= C平均が71点で昨年度（65.7点）より5.3= _も良い！今年の生徒は出来がよいのだろうか？ 5%有意水準で検定せよ．
= 211;
–　　　〔帰無仮説〕μ＝65.7
–　　　〔対立仮説〕μ>65.7
母数に関する仮説検定
有意水準5％で帰無仮説は棄却される
今年の生徒は昨年= xよりも出来が良い= らしい．
〔出展：『図解雑学 統計解析』 p.202〕
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Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
&#= 8226;母分散の検定〔χ2検定〕
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>例：製品のばらつき検査 = ;
–　　　目標重量25sの製品の重量のばらつきが大きいことがわかり修理した．修理後の製品を無作為抽出した結= 果が以下．修理前の分散が9s2のとき，この製品は性能が向上したといえ= るか？ <= /div>
母数に関する仮説検定
修理後は性能が向上したと考えられる
　　⇒　分散は小さくなったはず
　　⇒　片側（下側）検定
　〔帰無仮説〕 σ2= =3D9
　〔対立仮説〕 σ2= <9
確率変数χ2は =
自由度n-1の
χ2分布に従う
〔出展：『なるほど統計学』 p.132〕
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<= span class=3DBB style=3D'position:absolute;left:-4.57%'>•母分散の検定<= /span>〔χ2検定〕
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>例：製品のばらつき検査 = ;
–　　有意水準5%の棄却域を表す不等式
母数に関する仮説検定
有意水準5％で帰無仮説は棄却できない
この製造機械が修理後によくなったと= 結論できない．
χ<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:67%;position:relative; top:-.45em;mso-text-raise:30%;mso-fareast-language:JA'>2分布：片側（下側）5%<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:Verdana;mso-f= areast-font-family: "ＭＳ Ｐゴシック";mso-fareast-hint:yes'>棄却域
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<= span class=3DBB style=3D'position:absolute;left:-4.57%'>•母分散の検定<= /span>〔χ2検定〕
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>演習：小学校の知能テスト = ;
= 211;　　　ある小学校の入学時知能テストの結果は平均50，分散36だった．本年度入学児25名を無作為抽出したところ平均53，分散48だった．本年度入学児の揃い方は例年と違うか？
= 211;
–　　〔帰無仮説〕 σ2＝36
–　　〔対立仮説〕 σ2≠36
= 211;
–有意水準10%棄却域
母数に関する仮説検定
有意水準10％で= = 帰無仮説は棄却= できない
今年度入学児童が例年と違うとはいえ= ない．
〔出展：『統計学入門』 p.242〕
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•両側検定と片= ､検定の使い分け <= /div>
<= span style=3D'font-family:"Times New Roman";font-size:86%;mso-fareast-hint:yes'= >–例：母平均の両側検定
–　　〔帰無仮説〕 μ＝μ0&= #13;
–　　〔対立仮説〕 μ≠μ0
Coffee Break!
《μ0は既知の値》
＜片側検定を実施する理由
　１．μ<μ<= i>0が起こり得ない
　２．μ>μ0を積極的に見いだせればそれでよい
　３．母数の大きさが理論的・経験的に予測される
–例：母平均の（右）片側検定<= /span>
　　〔帰無仮説〕 μ=3Dμ0= 3;
　　〔対立仮説〕 μ>μ0
例：補習後の成績は上がった？（上がったと積極的に知りたい）
例：今年の夏は寒い気がする．本当か？ =
　（「寒い」という経験から平均気温が低い= ｱとを予測）
＜両側検定を実施する理由
　母数の値がある目標値と等しいかどうかを調べたい
例：生産ラインの機械が正しく動いているか？
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<= span style=3D'color:#003399;text-shadow:auto;mso-fareast-hint:yes'>•母平均の差の検定
&= #8211;2つの正規母集= cについて母平均の差の検定
•母分散が既知の場合
•
•母分散が未知だが等しい場合
•
•母分散が未知で等しくない場合
•
•母分散の比の検定
–2つの正規母= 集団について母分散の比の検定
2標本検定 two-sample test
Z <= /span>検定
ウェルチの検定
t 検定
3D"ホームベース:
F 検定
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•母平均の差の検定
&= #8211;2つの正規母集= cについて母平均の差の検定
〔帰無仮説〕
〔対立仮説〕
2標本検定 two-sample test
m<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes'>個 無作為抽出
n<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes'>個 無作為抽出
←2つの正規母集団の母平均に差がない
←2つの正規母集団の母平均に差がある
両側検定の場合
片側検定の場合
〔帰無仮説〕
〔対立仮説〕
←2つの正規母集団の母平均に差がない
←2つの正規母集団の母平均に差がある
標本平均：
標本平均：
２= つの母平均に
「= 差がある」か「ない」か
の= 検定
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•母平均の差の検定
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>２標本の標本平均の差の標本分布 = ;
–
–
–
–
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>この検定の例：医薬の効果の検証 = ;
•患者を新薬を使った治療を行うグループ（処理群）とそれ以外（対照群）に分け，グループで結果に差があるかどうか（新薬の効果があるかどうか）を検定する．
2標本検定 two-sample test
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charset="shift_jis" データ分布と予測　5．仮説検定
•母平均の差の検定（母分散が既知のとき）
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>標本平均の差の標本分布
2標本検定 two-sample test
Z検定
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•母平均の差の検定（母分散が未知だが等しい　　　　　　 ）
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>標本平均の差の標本分布 = ;
•
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>合併分散 pooled varian= ce
–
–
–
•
•
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes;color:black;mso-color-index:3'>補足：『合併分散は不偏推定量である』
2標本検定 two-sample test
ただし，　　　　　 は不偏推定量
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•母平均の差の検定（母分散が未知だが等しい　　　　　　 ）
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";mso-fareast-hint: yes;mso-special-format:lastCR;display:none'>
2標本検定 two-sample test
t検定
= （ただし，Zとχ2は独立）
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Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
=
–5%有意水準で両側検定 = ;
–  （〔帰無仮説〕　　　　  〔対立仮説〕　　　    ）
•母平均の差の検定（母分散が未知だが等しい　　　　　　 ）
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>例：苗木の生長における2社の肥料の違い = ;
= 211;　　ある苗木の生長について2社の肥料に違いがあるか？
2標本検定 two-sample test
t検定
より，仮説を棄却
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•母平均の差の検定（母分散が未知で等しくない　　　　 ）
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>標本平均の差の標本分布 = ;
•<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 83%;mso-fareast-hint:yes'>どのように工夫しても，2つの母分散に拠らない統計量を作れない
= 226; ↓ = ;
•<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 83%;mso-fareast-hint:yes'>標本平均の差の正確な分布を求められない
= 226; ↓ = ;
•<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 83%;mso-fareast-hint:yes'>近似的に分布を求める〔ウェルチの近似法〕
2標本検定 two-sample test
ウェルチの検定
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Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
=
–5%有意水準で両側検定 = ;
–  （〔帰無仮説〕　　　　  〔対立仮説〕　　　    ）
•母平均の差の検定（母分散が未知で等しくない　　　　 ）
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>例：2つの鉱山から採れる鉱石に含まれる物質の含有量 = ;
= 211; 各鉱山から採れる鉱石の物質含有量に差があるか？
2標本検定 two-sample test
ウェルチの検定=
より，自由度17のt分布を考える
より，仮説を棄却
〔出展：『パソコンによるデータマイニ= 塔O』 p.132〕
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Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAAeAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAgAa ABoAhAAAAACAANH/0dT/1Nn/2d//39r/2s7/zuX/5ez/7PL/8vb/9vr/+v3//f7//vf/9+b/5uD/ 4AECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwWPICCOpBiUaJoGrOqi gSCcbx0MOF2rAeETul0pUCgWgyOWcrlEOJ9IQCBBrVqvVmRAwe16v99gYEEum89oXYDBbrvfcAYt 0Kjb7/h8/RRw+P+AgYJ/LIOGhyx6iop8cY5xcw+Sk5SVlmpgmZliWJ1YWkyhARCkpVE7ARGqqqeo Bq8Grag4A7KoMraoB7movCEAOy== ------=_NextPart_01C83E3F.6D47C160 Content-Location: file:///C:/8ECB5C15/07dist_5.files/slide0035.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
•母分散の比の検定〔F検定〕
&= #8211;2つの正規母集= cについて母分散の比<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック"'>の検定
2標本検定 two-sample test
m<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes'>個 無作為抽出
n<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes'>個 無作為抽出
〔帰無仮説〕
〔対立仮説〕
←2つの正規母集団の母分散に差がない
←2つの正規母集団の母分散に差がある
両側検定の場合
片側検定の場合
〔帰無仮説〕
〔対立仮説〕
←2つの正規母集団の母分散に差がない
←2つの正規母集団の母分散に差がある
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file:///C:/8ECB5C15/07dist_5.files/slide0050.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
•母分散の比の検定〔F検定〕
–F分布とフィッシャーの分散比<= span style=3D'font-family: "ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-special-fo= rmat:lastCR; display:none'>
2標本検定 two-sample test
フィッシャー
の分散比
自由度(m-1, n-1)<= /span>のF分布に従う
F分布：両側= 5%棄却域
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–5%有意水準で両側検定 = ;
–  （〔帰無仮説〕　　　　  ，〔対立仮説〕　　　    ）
•母分散の比の検定〔F検定〕
–例題：2つの工作機械の製品バラツキ検査
2標本検定 two-sample test 3D"テキスト
＞
より，仮説は=
棄却される&= #13;
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•母分散の比の検定〔F検定〕
–F分布表からのF値の求め方
= 226;F分布表はαが通常｢0.1,0.05,0.25,0.01,0.005｣のときの表のみ表示されていて，下側(左側)パーセント点は表示されていない．そこで…
= 226;
= 226;
= 226;
= 226;であることを利用して求める．
–例：自由度(10,13)のF<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes'>分布の下側(左側)5%点
2標本検定 two-sample test
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•適合度のχ2検定 〔Chi-square goodness-of-fit test<= /span>〕
= 211;　　　仮定された理論上の確率分布に対し，標本から求められた度数が適合するか否かを検証する．
–例：さいころ投げ = ;
–　　さいころを300回投げると理論上は1〜6の目が50回ずつ出る (さいころの目は一様分布と= なる） ．実際に300回投げると…
= 211;
= 211;
= 211;
–　〔帰無仮説〕　さいころの目の出方に偏りがない(一様分布に従う)
–　〔対立仮説〕　さいころの目の出方に偏りがある(一様分布に従わない)
適合度検定 goodness-of-fit t= est
適合度検定：
　　母集団分布の従う確率分布につい= て= 立てた帰無仮説を検証する
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•適合度の測定
R= 11;例：さいころ投げ
= 211;　〔帰無仮説〕　さいころの目の出方に偏りがない(一様分布に従う)
= 211;　〔対立仮説〕　さいころの目の出方に偏りがある(一様分布に従わない)
適合度検定 goodness-of-fit t= est
K.Pearsonの適合度基準
（nが十分大きければ= j
自由度k-1の
χ2分布に従う
　　　　　　　　　= @はk個の確率変数だが，
より，自由度は1つ減る&= #13;
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•適合度の測定
R= 11;例：さいころ投げ
= 211;　有意水準5%棄却域を表す不等式
適合度検定 goodness-of-fit t= est
このさいころは、目の出方に= 偏りがない（一様分布に従う）といえるようだ
より，棄却域にない= ﾌで，帰無仮説は棄却できない&= #13;
χ<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:67%;position:relative; top:-.45em;mso-text-raise:30%;mso-fareast-language:JA'>2分布：上側5%棄却域
〔p値：0.92>0.05：有意水= 準〕
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<= span style=3D'color:#0099CC;text-shadow:auto;mso-fareast-hint:yes'>•適合度のχ2検定
&#= 8211;　例：メンデルの法則〔えんどう豆の形質遺伝〕
= 211;
&#= 8211;
&#= 8211;
= 211;
–　〔帰無仮説〕　えんどう豆の表現型はメンデルの法= 則に適合している
–　〔対立仮説〕　えんどう豆の表現型はメンデルの法= 則に適合していない
適合度検定 goodness-of-fit t= est
より，5%有意水準の棄却域にないので，帰無仮説は棄却でき= ﾈい&= #13;
えんどう豆の表現型= ﾍメンデル= の法則に適合してい= 驍謔､だ&= #13;
〔出展：『統計学入門』 p.245〕
〔p値：0.93>0.05：有意水= 準〕
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<= span style=3D'color:#FF3399;text-shadow:auto;mso-fareast-hint:yes'>•独立性のχ2検定 〔Chi-squar= e test of independence〕 =
•　　　　2つの属性の間に関係があるかどうかを検証する = ;
•　　　例：支持政党に男女差があるか？
独立性の検定 test of indep= endence
支持政= 党に男女差= があるか？=
〔出展：『図解雑学 統計解析』 p.224〕
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------=_NextPart_01C83E3F.6D47C160 Content-Location: file:///C:/8ECB5C15/07dist_5.files/slide0039.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
= <= span style=3D'color:#FF3399;text-shadow:auto;mso-fareast-hint:yes'>•独立性の測定
•　　　例：支持政党に男女差があるか？
•　　　　〔帰無仮説〕= 支持政党に男女差がない ⇒ <= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 63%;mso-fareast-hint:yes'>ともに全体比率に等しい = ;
•　　　　〔対立仮説〕= 支持政党に男女差がある
独立性の検定 test of indep= endence
観測
度数&= #13;
理論
度数
独立性の基準
（nが十分大きければ）
自由度(r-1)(c-1)の
χ2分布に従う
この差を適合度検定&#= 13;
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<= span style=3D'color:#FF3399;text-shadow:auto;mso-fareast-hint:yes'>•独立性の測定
•　　　例：支持政党に男女差があるか？
•　　　　　有意水準5%棄却域を表す不等式
独立性の検定 test of indep= endence
χ<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:67%;position:relative; top:-.45em;mso-text-raise:30%;mso-fareast-language:JA'>2分布：上側5%棄却域
支持政党に男女間で= ｷ= があるとはいえない<= /span>&= #13;
より，棄却域にない= ﾌで，帰無仮説は棄却できない&= #13;
〔p値：0.13>0.05：有意水= 準〕
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•独立性のχ2= 検定
= 211;　演習：某工学部の期末試験成績：代数と解析の成績に関係があるか？
R= 11;
= 211;
= 211;
R= 11;
R= 11;　〔帰無仮説〕　代数と解析の成績に関係がない
R= 11;　〔対立仮説〕　代数と解析の成績に関係がある
独立性の検定 test of indep= endence
より，5%有意水準の棄却域にないので，帰無仮説は棄却でき= ﾈい&= #13;
代数と解析の成績に= ﾍ関係があ= るとはいえない&= #13;
〔出展：『統計学入門』 p.248= 〕
〔p値：0.996>0.05：有意水= 準〕
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　5．仮説検定
•独立性のχ= 2検定
–<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 71%;mso-fareast-hint:yes'>例題：男性・女性各看護師に対する恋愛についてのア= ンケート
= 211; 　　　（結果に男女差があるか？）
独立性の検定 test of indep= endence
〔= 出展：『マンガでわかるナ= ースの統計学』= p.111〕
210
155
55
計
156
121
35
女性看護師
54
34
20
男性看護師
計
否定
肯定
好きな異性を前にす= ると緊張する？
210
76
134
計
156
47
109
女性看護師
54
29
25
男性看護師
計
否定
肯定
異性に対しては自分= から話しかける方？
210
155
55
計
156
115.14
40.86
女性看護師
54
39.86
14.14
男性看護師
計
否定&#= 13;
肯定&#= 13;
好きな異性を前にすると緊張する？
観測度数
観測度数
理論度数=
210
76
134
計
156
56.46
99.54
女性看護師
54
19.54
34.46
男性看護師
計
否定&#= 13;
肯定&#= 13;
異性に対しては自分から話しかける方？
=
χ2乗値が棄= 却域にあるので，帰無仮説は棄却される
（男女間= に差がある→女性の方がより緊張する）
χ2乗値が棄= 却域にあるので，帰無仮説は棄却される
（男女間= に差がある→女性の方が異性に話し掛けない）
p値:0.035
<
0.05
有意水準
p値:0.002
<
0.05
有意水準
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•演習1：サイコロの目の出方に偏りがあるか？　= 有意水準5%で検定せよ．
適合度検定・独立性の検定
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賽の目
•演習2：コーヒーの嗜好に違いがあるか？　有意= 水準5％で検定せよ．
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27
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参考文献
<= span style=3D'font-size:63%'>•東大教養学部統計学教室編　「統計学入門」<= /span> 東大出版会（1991）
<= span style=3D'font-size:63%'>•東大教養学部統計学教室編　「自然科学の統= v学」 東大出版会（1992）
•鈴木達三・高橋宏一 「標本抽出の計画と方法」 = 放送大学 （1991）
<= span style=3D'font-size:75%'>•永田靖 「統計的方法のしくみ」 日科技連 （1996）
<= span style=3D'font-size:75%'>•永田靖 「サンプルサイズの決め方」 朝倉書店 （2003）
<= span style=3D'font-size:75%'>•村上雅人 「なるほど統計学」 海鳴社 （2002）
<= span style=3D'font-size:75%'>•丹慶勝市 「図解雑学 統計解析」 ナツメ社 （2003）
<= span style=3D'font-size:63%'>•高橋信[著]・トレンドプロ[マンガ]「マンガでわかる統計学」オーム社（= 2004）
<= span style=3D'font-size:63%;mso-fareast-hint:yes'>•田久浩志ほか「マンガでわかる<= /span>ナースの統計学」オーム社（2006）<= /div>
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マスタ テキストの書式設定
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if( !g_supportsPPTHTML ) { =09 sld.style.visibility=3D"visible" return } if( MakeNotesVis() ) return runAnimations =3D _InitAnimations(); =09 if( IsWin("PPTSld") ) parent.SldUpdated(GetSldId()) g_origSz=3DparseInt(SlideObj.style.fontSize) g_origH=3Dsld.style.posHeight g_origW=3Dsld.style.posWidth g_scaleHyperlinks=3D(document.all.tags("AREA").length>0) if( g_scaleHyperlinks ) InitHLinkArray() if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) ) document.body.scroll=3D"no" _RSW() if( IsWin("PPTSld") && parent.IsFullScrMode() ) FullScrInit(); =09 MakeSldVis(); ChkAutoAdv() if( runAnimations ) { if( document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis()=20 { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans )=09 { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply()=09 } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis()=20 { if( !IsNts() ) return false=20 SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) {=20 nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) setTimeout("parent.GoToNextSld()",sld.mAdvDelay) } function GetObj(id) { if(g_supportsPPTHTML) return document.all(id); else return document.getElementById(id); } function SldHasTrans() { return SlideObj.style.filter !=3D ""; } function GetSldId()=20 { var regExp =3D /file:\/\/\//i var pos =3D location.href.search(regExp) if (MHTMLPrefix !=3D "" && pos !=3D -1) sId =3D location.href.substring(pos) else { sId =3D RemoveFilePrefixFromHref(location.href); var regExp =3D /\// var fixedHref =3D sId var pos =3D -1 =09 pos =3D fixedHref.search(regExp) while (pos !=3D -1) { fixedHref =3D fixedHref.replace(regExp, "\\") pos =3D fixedHref.search(regExp) } =09 if (g_fBaseHyperlink =3D=3D true) sId =3D "file:///" + fixedHref; else sId =3D fixedHref.substring(fixedHref.lastIndexOf('\\') + 1) } =09 return sId } function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx= tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl= e.display=3D'none'; return true } return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } }function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { =09 if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex= t ) return; parent.GoToNextSld(); } } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"スライド ショーの最後です。 クリックすると終了します。"= , SCREEN_MODE=3D"Frames", gIsEndShow=3D0, NUM_VIS_SLDS=3D48, SCRIPT_HREF=3D= "script.js", FULLSCR_HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var g_fBaseHyperlink =3D false; var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0002.htm",1,-1,1),new hrefList("slide0003.htm",1,-1,1),new hrefList("= slide0005.htm",1,-1,1),new hrefList("slide0006.htm",1,-1,1),new hrefList("s= lide0007.htm",1,-1,1),new hrefList("slide0008.htm",1,-1,1),new hrefList("sl= ide0009.htm",1,-1,1),new hrefList("slide0011.htm",1,-1,1),new hrefList("sli= de0012.htm",1,-1,1),new hrefList("slide0024.htm",1,-1,1),new hrefList("slid= e0013.htm",1,-1,1),new hrefList("slide0028.htm",1,-1,1),new hrefList("slide= 0010.htm",1,-1,1),new hrefList("slide0014.htm",1,-1,1),new hrefList("slide0= 015.htm",1,-1,1),new hrefList("slide0026.htm",1,-1,1),new hrefList("slide00= 18.htm",1,-1,1),new hrefList("slide0019.htm",1,-1,1),new hrefList("slide002= 7.htm",1,-1,1),new hrefList("slide0020.htm",1,-1,1),new hrefList("slide0029= .htm",1,-1,1),new hrefList("slide0030.htm",1,-1,1),new hrefList("slide0056.= htm",1,-1,1),new hrefList("slide0048.htm",1,-1,1),new hrefList("slide0021.h= tm",1,-1,1),new hrefList("slide0044.htm",1,-1,1),new hrefList("slide0031.ht= m",1,-1,1),new hrefList("slide0042.htm",1,-1,1),new hrefList("slide0046.htm= ",1,-1,1),new hrefList("slide0049.htm",1,-1,1),new hrefList("slide0043.htm"= ,1,-1,1),new hrefList("slide0047.htm",1,-1,1),new hrefList("slide0035.htm",= 1,-1,1),new hrefList("slide0050.htm",1,-1,1),new hrefList("slide0051.htm",1= ,-1,1),new hrefList("slide0052.htm",1,-1,1),new hrefList("slide0033.htm",1,= -1,1),new hrefList("slide0036.htm",1,-1,1),new hrefList("slide0037.htm",1,-= 1,1),new hrefList("slide0038.htm",1,-1,1),new hrefList("slide0034.htm",1,-1= ,1),new hrefList("slide0039.htm",1,-1,1),new hrefList("slide0040.htm",1,-1,= 1),new hrefList("slide0041.htm",1,-1,1),new hrefList("slide0055.htm",1,-1,1= ),new hrefList("slide0054.htm",1,-1,1),new hrefList("slide0053.htm",1,-1,1)= ); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function RemoveFilePrefixFromHref(href) { var regExp =3D /^file:\/\/\//i; return href.replace(regExp, "") } function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if (MHTMLPrefix !=3D "") href =3D RemoveFilePrefixFromHref(href) if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; =09 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref= )) else PPTSld.location.replace(obj.mSldHref) =09 if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href)) else PPTSld.location.replace(href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('


' + ENDSHOW_MESG + '

') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice= ","nb_voiceBorder",18,parent.ToggleVNarration ) gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT= xt","nb_otlTxtBorder",23,parent.ToggleOtlText ) gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts" gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState /********************************************* Context menu implementation _CM() is the function that's hooked up to the oncontextmenu event. Once we're asked to show the menu, we first build it by creating DIVs on-the-fly. Then we position it=20 within the screen area so it doesn't get clipped. Creating the DIVs using createElement() means we don't have to write out any extra HTML into the slide HTML files. **********************************************/ var sNext=3D"次へ",sPrev=3D"前へ",sEnd=3D"スライド ショーの終了",sFont=3D"= lＳ 明朝",sArrow=3D"矢印",sFreeform=3D"フリーフォーム",sRect=3D"四角形",sOv= al=3D"楕円" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) =09 CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();= PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; 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charset="shift_jis" データ分布と予測　5．仮説検定 ------=_NextPart_01C83E3F.6D47C160 Content-Location: file:///C:/8ECB5C15/07dist_5.files/outline.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis"
 ノ= ート
スラ= Cド ショー
アウトライン
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