MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C8AC56.BF815BF0" このドキュメントは単一ファイル Web ページ (Web アーカイブ ファイル) です。お使いのブラウザ、またはエディタは Web アーカイブ ファイルをサポートしていません。Windows? Internet Explorer? など、Web アーカイブをサポートするブラウザをダウンロードしてください。 ------=_NextPart_01C8AC56.BF815BF0 Content-Location: file:///C:/CECB5C11/08dist_1.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ

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マスタ タイトルの書式設定
マスタ テキストの書式設定
第 2 レベル
第 3 レベル
第 4 レベル
第 5 レベル
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マスタ タイトルの書式設定
マスタ テキストの書式設定
第 2 レベル
第 3 レベル
第 4 レベル
第 5 レベル
<#>
------=_NextPart_01C8AC56.BF815BF0 Content-Location: file:///C:/CECB5C11/08dist_1.files/master107.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8AC56.BF815BF0 Content-Location: file:///C:/CECB5C11/08dist_1.files/master02.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis"
統計の分析と利用
2008/4/18
Confidential
<#>
------=_NextPart_01C8AC56.BF815BF0 Content-Location: file:///C:/CECB5C11/08dist_1.files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8AC56.BF815BF0 Content-Location: file:///C:/CECB5C11/08dist_1.files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ
= 統計の分析と利用
（旧カリ：データ分布と予測） =
<= span style=3D'font-size:93%'>n1次元のデータ
<= span style=3D'mso-special-format:bullet;color:#3B812F;mso-color-index:5;positio= n: absolute;left:-3.21%;top:.61em;font-family:Wingdings;font-size:60%'>q度数分布・ヒストグラム
<= span style=3D'mso-special-format:bullet;color:#3B812F;mso-color-index:5;positio= n: absolute;left:-3.21%;top:.61em;font-family:Wingdings;font-size:60%'>q代表値と散らばり
<= span style=3D'font-size:93%'>n2次元のデータ
<= span style=3D'layout-flow:horizontal'>q散布図，相関関係・共分散=
堀田　敬介
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20= 08/4/18, Fri.
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一次元のデータ
<= span style=3D'font-size:93%'>n度数分布
<= span style=3D'font-size:93%'>nヒストグラム
<= span style=3D'font-size:93%'>n幹葉プロット
<= span style=3D'font-size:93%'>n箱ひげ図
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度数分布
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nデータ [土日の来店客数の1年間のデータ]
データが多すぎて全体の傾向がよくわからない！
週末はどのぐらい= お客さんが来てくれたの？=
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file:///C:/CECB5C11/08dist_1.files/slide0003.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ
度数分布
=
=
n度数分布表[土日の来店客数の1年間のデータ]
階級値
各階級の上限・下限値の= 中間値
〔例〕344.5←330-359
〔例〕 345  ←330-360
3D"MCj02236400000[1]"
なるほど，週末の来店= = 客数はだいたいこのぐ= らいのことが多いんだ=
=
=
=
=
全体の傾向がよくわかる！
度数
(frequency)
階級
(class)
階級数:10
階級幅= :30
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file:///C:/CECB5C11/08dist_1.files/slide0004.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ
度数分布
=
=
n度数分布表[土日の来店客数の1年間のデータ]
階級数:6
階級幅:50
階級数:28
階級幅:10
階級数（階級幅）を
どうするかが問題
階級数:10
階級幅:30
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=
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=
=
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度数分布にすると全体の傾向がわかりやすくなるが，<= /span>= 生データと比べて情報量が少なくなるため，このよう<= /span>= なことがおこる．
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file:///C:/CECB5C11/08dist_1.files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ
度数分布
=
=
nスタージェスの公式 [階級数の目安]
（k：階級数，n：データ数）
例では
より，階級数は8ぐらいで十分
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ
度数分布
=
=
n階級数8= （階級幅38）で書く= ﾆ…
3D"MCj02236400000[1]"
なるほど，週末の来店= 客数の全体傾向はだいたいわかったぞ
でも，度数の多い階級= = は全体からみてどのぐ= らいの割合なの？
= 相対度数
(relative frequency)
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3D"MCj00791330000[1]" 3D"MCj02236400000[1]"
度数分布
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=
n度数分布表[相対度数]
データ数が異なる2つの
グループの比較ができる
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Ｂさんのお店と比= べて，うちのお客さんの来店= 傾向はどうなのか比較= したいな… =
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度数分布
=
=
n累積度数分布表[累積度数，累積相対度数]
累積度数
(cumulati= ve frequency)
累積相対度数 =
(cumulati= ve relative frequency)
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度数分布
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n問題：以下の度数分布が与えられているとき，平均来店客数を求めなさい．
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ヒストグラム
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nヒストグラム(histogram)・柱状グラフ
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ヒストグラム
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=
nヒストグラム(histogram)・柱状グラフ
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度数分布
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n階級数8= で書くと…
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ヒストグラム
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nヒストグラムの形状
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単峰型 (unimodal)
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双峰型 (bimodal)
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右に歪んだ分布
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<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
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左に歪んだ分布
層= ﾊ（適当にグループ分けすること）を行うと単峰型分布が出現することが多い
峰が中央から左に寄っていて，右側に長く裾を引く分布
峰が中央から右に寄っていて，左側に長く裾を引く分布
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峰が２つ以上ある分布
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3DCG129<= ![endif]>
その他の手法１
n幹葉プロット，ステムプロット（stem-and-leaf diagram[plot]）
q野球選手の打率一覧
nAチーム
幹
葉
nBチーム
幹葉プロットがヒストグラムより優れているのはどんなところ？
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EKdA4YLppW1RKsQABUgg56p0pujqmq/K6OoFYjbUw0SkjprNMj146JAaAiQwgafEBoGBLAawd8yE BtxyAQDL5CotInUUuqE4S6Y+hEIByTZ7wLfghivuuOSWa+656Kar7rroplGErz/6KC8b9M5rb734 3qtvvvzu62+/AP/LWAgAOw== ------=_NextPart_01C8AC56.BF815BF0 Content-Location: file:///C:/CECB5C11/08dist_1.files/slide0046.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ
その他の手法２
n箱ひげ図，箱型図 （box plot）
q野球選手の打率一覧
nAチーム
nBチーム
〔Aチーム〕
max.0.392
Q3    0.338
med.0.288
Q1    0.265
min. 0.217
〔Bチーム〕
0.418 max.
0.332    Q3
0.309 med.
0.276    Q1
0.214 min.
=
=
0.214
0.276
0.309
0.332
0.418
0.217
0.265
0.288
0.338
0.392
注：ひげの上端・下端は，必ずmax，minを使うわけではない．
r:=3Dq3-q1 としたとき，上端= ﾍ区間(q3, q3+1.5r]内の最大値，
下端は区間[q1-1.5r, q1)内の最小値を用いる，など．
ひげ
箱
=
全体の
50%
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演習
=
n男女20人の身長のデータ= ｪある．
q男女それぞれのデータについて，10の位までを幹，1の位を葉として幹葉プロットを描け．
q男女それぞれのデータについて，箱ひげ図を描け．
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一次元のデータ
<= span style=3D'font-size:93%'>nデータ測定の尺度
x
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データの測定尺度による分類
n測定(measurement)と尺度(scale)&#= 13;
q名義（名目）尺度 nominal scale
n属性を表す基準（対象に区別がつけられる）
q例：性別（男，女，それ以外）<= /span>，パソコン保有（保有，非保有） =
q順序尺度 ordinal scale
n対象間に順序がつけられる基準
q例：成績（A＞B＞C＞D），居住性（住みやすい＞まあま= ＞すみにくい）
q間隔尺度 interval scale
n間隔のみが意味を持つ基準
q例：温度（摂氏℃，華氏゜F），時刻（午後3時から1時間後）
q比率尺度 ratio scale <= /div>
n比が意味を持つ基準
q例：身長（父は子の1.5倍の背），体重（5kg重い），絶対温度（゜K，絶対零度）
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質的（カテゴリ）データ
3D"ホームベース:
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3D"ホームベース:
量的（数値）データ
3D"ホームベース:
量的（数値）データ
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データの測定尺度による集計例
=
=
n質的データと量的データの集計例
質的データ
量的データ
性別
（男，女）
成績
（A，B，C，D）
3D"MCj04235670000[1]" 3D"MCj04235670000[1]"
（男，女）
（A，B，C，D）
3D"MCj04235670000[1]" 3D"MCj04235670000[1]"
（男，女）
（A，B，C，D）
3D"MCj04235670000[1]" 3D"MCj04235670000[1]"
（男，女）
（A，B，C，D）
3D"MCj04235670000[1]" 3D"MCj04235670000[1]"
（男，女）
（A，B，C，D）
3D"MCj04235670000[1]" 3D"MCj04235670000[1]"
（男，女）
（A，B，C，D）
3D"MCj04235670000[1]" 3D"MCj04235670000[1]"
（男，女）
（A，B，C，D）
3D"MCj04235670000[1]" 3D"MCj04235670000[1]"
（男，女）
（A，B，C，D）
3D"MCj04235670000[1]" 3D"MCj04235670000[1]"
（男，女）
（A，B，C，D）
3D"MCj04235670000[1]" 3D"MCj04235670000[1]"
（男，女）
（A，B，C，D）
3D"MCj04235670000[1]" 3D"MCj04235670000[1]"
（男，女）
（A，B，C，D）
3D"MCj04235670000[1]" 3D"MCj04235670000[1]"
データ例
集計例
A
B
C
D
計
男
3
2
1
0
6
女
1
0
2
2
5
計
4
2
3
2
11
女性身長
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一次元のデータ
<= span style=3D'font-size:93%;text-shadow:auto'>nデータの代表値
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3DCG125
データの代表値を考える
n例：16個のデータ
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=
=
このデータを代表する値って何だろう？
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代表値 averages
=
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n平均（算術平均，相加平均） arithmetic mean
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Content-Location: file:///C:/CECB5C11/08dist_1.files/slide0061_image200.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQAPAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAW AAsAgwAAADeZZjOVZjOaZzOZZjOXZDSZZjOVajOZZDWXaDWbZDORbkSZZgECAwECAwECAwQuEMhJ q7134E0LIRxnfCBlAGeKrif5TW4sx1IC2Pit2+4ZUoPXrzLyDSeKo1ISAQA7 ------=_NextPart_01C8AC56.BF815BF0 Content-Location: file:///C:/CECB5C11/08dist_1.files/slide0013.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ
Coffee Break
=
n記号の定義
q和を表す記号：Σ（しぐま） = ;
q
q
q
q
q積を表す記号：Π（ぱい）
x<= /span>i を i を <= 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>から n まで動かして足す
x<= /span>i を i を <= 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>から n まで動かして掛ける
使用例）
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代表値 averages
=
=
n幾何平均 geometric mean
☆どんなとき= ﾉ幾何平均が役に立つ？
　　例題：次の表から平均地価上昇率= 求めよ
= 補足：対数を利用すると計= 算が楽になる
年度
2002
2003
2004
2005
2006
地価上昇率=
1%
2%
3%
4%
5%
×
○
幾何平均
＝
n個の積のn乗根
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------=_NextPart_01C8AC56.BF815BF0 Content-Location: file:///C:/CECB5C11/08dist_1.files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ
代表値 averages
=
=
n調和平均 harmonic mean
調和平均
＝
逆数の算術平均
の
逆数
☆どんなとき= ﾉ調和平均が役に立つ？
　　例題：行きが時速25q，帰りが時速15qで走ったバスの= ｽ均時速を求めよ
×
○
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------=_NextPart_01C8AC56.BF815BF0 Content-Location: file:///C:/CECB5C11/08dist_1.files/slide0016.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ
代表値 averages
n中央値 median
qデータをソート して，ち= 蛯､ど真ん中にある値
n
n最頻値 mode <= /div>
qデータの中で最も頻繁に出てくる値
補足：データ数が偶数の場合は，中央値は真ん中2つの算術平均
補足：最も頻繁に出てくる値がない場合は最頻値はなし<= /div>
補足：ソート sort とは？
　データを値の小さい（大きい）順に並べること
ソート後
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=
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R0lGODlhDQAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAG ABoAgwAAAJVqM5VoM5NsNZVqMpFuM5RqMpRrMpNqMZlmRAECAwECAwECAwECAwECAwECAwQfEMg5 CQWW5nq39FgnaiNHnmb6lStqhIdkzBNNvVQgRQA7 ------=_NextPart_01C8AC56.BF815BF0 Content-Location: file:///C:/CECB5C11/08dist_1.files/slide0016_image257.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLAAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAr ABcAgAAAAP8AAAJEhI+pyxsNo3yy2ketbjTvf2DgaGQeOZ5odKqrowTuG3LAnN6szPN731v5YjSI CleslZKTJZPlfBqlFRl1d4VmGcjtqgAAOw== ------=_NextPart_01C8AC56.BF815BF0 Content-Location: file:///C:/CECB5C11/08dist_1.files/slide0017.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ
代表値 averages
=
n中央値や最頻値は何故必要なのか？
q例：年収（単位：万円）の代表値は？
q算術平均
n1130万円
q中央値
n(700+800) / 2 =3D 750万円
q最頻値 =
n700万円，800<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Ti= mes New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; font-size:122%;layout-flow:horizontal;mso-ansi-language:EN-US'>万円=
=
=
=
=
ここが平均?
ここが平均
300
500
700
800
1000
5000
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代表値 averages
=
=
n算術平均，中央値，最頻値の= 関係
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<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
=
=
=
=
<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
=
右に歪んだ分布
=
=
=
=
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=
<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
=
=
単峰型
<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
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=
=
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=
=
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左に歪んだ分布
=
平均
中央値
最頻値
=
=
=
=
中央値
最頻値
平均
中央値
最頻値
平均
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n四分位点 quartile
qデータをソートし，4等分したときの3つの分割点の値
nQ<= /span>1：第1四分位点= CQ<= /span>3：第3四分位点 =
n
q注意：四分位数の定義は= 複数ある
nk<= /span>1 :=3D 0.25= ×(n-1), k<= /span>3 :=3D 0.75= ×(n-1) とし，
q
q
n  など
代表値 averages
MS Excel <= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Ti= mes New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; font-size:89%;mso-ansi-language:EN-US'>の 関数QUARTILE() では，Q1 =3D5.75, Q3 =3D9.25
Mathematica の関数quantile[]では，Q1 =3D5, Q3 =3D9
Rの関数quantile() では，Q1 =3D5.75, Q3 =3D9.25
※quartile：四分位数
 quantile：分位数
Q1
Q2
Q3
補足：Q2：第2四分位点は中央値 xmed である
x<= /span>med
=
=
=
=
=
=
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Content-Location: file:///C:/CECB5C11/08dist_1.files/slide0047.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ
代表値 averages
=
nミッド= ・レンジ mid-range
qデータの最大値と最小値の算術平均
=
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演習２
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n統計データを使って代表値を計算する&= #13;
q総務省統計局（= http://www.stat.go.jp）から世帯収入，世帯貯蓄などのデ<= /span>ータを取得し，グラフ= ｻせよ．グラフの形状はどのようになるか？
qこのデータの「算術平均」「中央= l」「最頻値」を計算し，分布の代表値として最も適切だと思わ= 黷驍ﾌはどれか考察せよ．
q「第1四分位数」「第3四分位数」「ミッドレンジ」を求めよ．
q
n簡単なデータを使って代表値を計算す=
q以下の10個のデータがある
q
q
q「算術平均」「中央値」「最頻値」を求めよ．
q「第1四分位数」「第3四分位数」「ミッドレンジ」を求めよ．
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一次元のデータ
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<= span style=3D'mso-special-format:bullet;color:#3B812F;mso-color-index:5;positio= n: absolute;left:-3.21%;top:.61em;font-family:Wingdings;font-size:60%'>q平均偏差
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x
11
9
-3
14
5
23
=
n個
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n例：16個のデータ
3DCG125
データの値らばりを考える
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このデータの散らばり具合はどのように測るの？
散らばりの度合いを一つの数値で示し= ，利用したい
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散らばり dispersion
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q最大値と最小値の差
ソート後
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散らばり dispersion
=
n四分位偏差 quartile deviation
q第3四分位点 Q3 <= /span>と第1四分位点 Q1 <= /span>の差の半分
ソート後
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散らばり dispersion
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n偏差 deviation
q各データと平均との差
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散らばり具合の度合い
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平均値からの平= 均的な差
= ﾎ差の和は必ず0になる（意味がない・使えな= い）
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3
5    6    7
9   10
50
算術平均
偏差
偏差
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散らばり dispersion
=
n平均偏差 mean deviation
q偏差の絶対値の合計を平均化した値
3D"AG00013_"
散らばり具合の度合い
＝
平均値からの平= 均的な差
=
それぞれの偏差の= 竭ﾎ値をとり，平均する
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=
=
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=
=
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=
<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
=
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=
=
3
5    6    7
9   10
50
算術平均
|偏差|
|偏差|
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散らばり dispersion
=
n分散 variance
q偏差の2乗の合計を平均化した値
= 補足：分散は，データの2乗の平均から平均の2乗を引いても計算できる
それぞれの偏差を2= し，平均する
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<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
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=
=
3
5    6    7
9   10
50
算術平均
偏差<= b>2
偏差<= b>2
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散らばり dispersion
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n標準偏差 standard deviation
q分散の平方根
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統計の分析と利用　1．一次元と二次元のデータ
演習３
= n以下の10個のデータについて散らばりを計= Zせよ．（式だけでもよい）
q
q
qこのデータの「範囲」を計算せよ．
n例） data[ 1, 5, 7, 9, 3 ] → 範囲：9 – 1=3D 8
qこのデータの「四分位偏差」を計算せよ．
qこのデータの「偏差」をだし，合計が０になることを確かめよ．
qこのデータの「平均偏差」を計算せよ．
qこのデータの「分散」を計算せよ．
qこのデータの「標準偏差」を計算せよ．
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一次元のデータ
<= span style=3D'font-size:93%'>nデータの変換
<= span style=3D'mso-special-format:bullet;color:#3B812F;mso-color-index:5;positio= n: absolute;left:-3.21%;top:.61em;font-family:Wingdings;font-size:60%'>q標準化（正規化）
Cf. 偏差値&= #13;
<= span style=3D'visibility:hidden'>q
x
11
9
-3
14
5
23
=
n個
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データの一次変換
=
n標準化 standardi= zation
q各データについて，平均を引き標準偏差で割る=
標= 準得点 standard score，= Z得= 点
変換後のデータは
　　平均0，
　　<= /span>標準偏差1
となる．
=
=
=
60=
80=
70=
90=
=
=
=
=
=
100
=
=
=
-20
0<= /div>
-10
10=
=
=
=
=
<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
20=
「平均を引く」ということは，
全体の位置を移動し，
真ん中（平均）を0にすること．
=
=
=
-2=
0<= /div>
-1=
1<= /div>
=
=
=
=
=
2<= /div>
=
「標準偏差で割る」ということは<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; font-size:89%;mso-ansi-language:EN-US'>，
全体を左右から圧縮して，
標準偏差を1にすること．
どんな1次元データも
標準化しちゃえば
同じ土俵で比= rできるね！
3D"MCj02934660000[1]" 3D"MCj02331420000[1]" 3D"MCj02331420000[1]"
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3D"MCj03325100000[1]"
データの一次変換
偏= 差値得点，T得= 点
=
n偏差値 <= /div>
q標準得点に以下の一次変換を= 施す
=
=
=
60=
80=
70=
90=
=
=
=
=
=
100
=
=
=
-20
0<= /div>
-10
10=
=
=
=
=
<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
20=
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0<= /div>
-1=
1<= /div>
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=
=
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=
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<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
-20
0<= /div>
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10=
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=
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<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
20=
=
=
=
-30
50=
-40
60=
=
=
=
=
=
70=
=
=
変換後のデータは
　平均50，
　標準偏差10
となる．
=
標準化
元の点数
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統計の分析と利用　1．一次元と二次元のデータ
データの一次変換
n例：10人の中間・期末試験の得点，z得点と偏差値
平均88,= 標準偏差9.8
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平均33,= 標準偏差16
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=
中間試験
期末試験
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演習４
=
n偏差値を計算しよう
q以下のデータはある試験の16人の学生の結果である．
q英語の結果について，各学生の得点を標準化し，z得点を出せ． =
q国語の結果について，各学生の偏差値を計算せよ．
q３教科合計点について，各学生の偏差値を計算せよ．
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= 統計の分析と利用
（旧カリ：データ分布と予測）
<= span style=3D'font-size:93%'>n一次元のデータ
<= span style=3D'mso-special-format:bullet;color:#3B812F;mso-color-index:5;positio= n: absolute;left:-2.92%;top:.61em;font-family:Wingdings;font-size:60%'>q度数分布・ヒストグラム
<= span style=3D'mso-special-format:bullet;color:#3B812F;mso-color-index:5;positio= n: absolute;left:-2.92%;top:.61em;font-family:Wingdings;font-size:60%'>q代表値と散らばり
<= span style=3D'font-size:93%'>n二次元のデータ
<= span style=3D'layout-flow:horizontal'>q散布図，相関関係・共分散=
堀田　敬介
x
11
9
-3
14
5
23
x
11
9
-3
14
5
23
y
3
0
5
-2
7
-4
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二次元のデータ
<= span style=3D'font-size:93%'>n相関と回帰
<= span style=3D'font-size:93%'>n共分散
<= span style=3D'font-size:93%'>n相関係数
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n2次元デ= [タ x , y の比較
q相関 correlation <= /span>
nx<= /span> <= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Ti= mes New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-ansi-language:EN-US'>と y との間に区別をつけず対等に見る見方・方法
q例：身長と体重，数学の成績と英語の成績
n
n
q回帰 regression
nx から y を見る見= 方・方法
nある一方が他方を左右する場合
q例：年齢と血圧，所得と消費，
q　　　　= 人口と商業，気候と住環境
二次元のデータ
身長
165
175
184
172
169
170
172
168
178
体重
59
68
75
72
69
65
60
68
74
=
年齢
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散布図 scattergram
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q例：身長と体重
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相関の度合いを
数値化することで，
比較・分析できないか？
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相関関係
=
=
n共分散 covariance
ある i 番目のデータについて，　　と平均　　　との差= と，　　と平均　　との差が共に大きいとき，共分散の値は大きくなり，そうではないとき共分散の値は小さくなる．すなわち，2種類のデータの関係の強さを表している．
<= span style=3D'font-family:"Times New Roman";font-size:111%'>q例：文教太郎君と湘南花子さんの昼食= に掛けた費用
=
= ﾎ
=
= ﾘ
=
= 太郎
\400
\300
\100
\200
\200
= 花子
\100
\200
\300
\400
\200
太郎君がリッチな食= 事をとるとき，花子= さんは貧乏な食事= で我慢してるの？
（2次元データ{x1,…,xn},{y1,…,yn}について<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; font-size:111%;mso-ansi-language:EN-US'>）
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<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
相関関係
=
=
n共分散 covariance
<= span style=3D'font-family:"Times New Roman";font-size:111%'>q例：文教太郎君と湘南花子さんの昼食= に掛けた費用
=
= ﾎ
=
= ﾘ
=
= 太郎
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\300
\100
\200
\200
= 花子
\100
\200
\300
\400
\200
太郎君がリッチな食事をとるとき，花子さんは貧乏な食事で我慢してるの？
=
平均
共分散
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相関関係
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相関関係
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正の相関
無相関
負の相関
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じゃぁ，
「相関の強さ」
を
「共分散の大きさ」
で表せる？
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相関関係
=
n共分散と関係の強さ
q例：文教太郎君と湘南花子さんの昼食=
=
= ﾎ
=
= ﾘ
=
= 太郎
\400
\300
\100
\200
\200
= 花子
\100
\200
\300
\400
\200
太郎君がリッチな食事をとるとき，花子さんは貧乏な食事で我慢してるの？
=
= ﾎ
=
= ﾘ
=
次郎
\40万
\30万
\10万
\20万
\20万
= 花子
\100
\200
\300
\400
\200
q例：文教次郎君と湘南花子さんの昼食= 費
超リ= bチな食事をとる次郎君と比べたら，花子さんの食事ってどうなの？
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相関関係
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08dist1_資料<= /span>.xls<= /span>
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相関関係
=
=
n相関係数 correlation coefficient
（2次元データ{x1,…,xn},{y1,…,yn}について<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; font-size:111%;mso-ansi-language:EN-US'>）
共分散をそれぞれのデータ xi, yi の標準偏差で割ることにより，測定単位を気にせずに，2種類のデータの関係の強さを表せる．
（ピアソンの）積率相関係数
(Peason’= s) productmoment correlation coefficient
n注意
q相関係数は，2つの変数の直線的関= 係を見るため= ﾌもの．曲線関係が認められる= 鼾等には向かない
q相関係数は，因果関係を保証するものではない．
=
正の相関
無相関
負の相関
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★順位相関係数を使うとき= とは？
= 　相関関係
n参考：その他の相関係数
q（スピアマンの= j順= 位相関= 係数= rank correlation coefficient <= /span>
q&#= 13;
n
n
n
q（ケンドールの= j順= 位相関= 係数= rank correlation coefficient <= /span>
n
n
n
q
q偏相関係数 partial correlation coefficient = ;
q（時系列データに対する）自己相関係数
q auto-correlation coefficient
A
R1, R<= i>2, …, R<= i>n
B
Q1, Q<= i>2, …, Q<= i>n
（Ri ： A が i を好きな順番）
順位が完全に一致しているとき rK =3D +1
順位が完全に逆のとき rK =3D ｰ1
順位が完全に一致しているとき= rS =3D +1
順位が完全に逆のとき rS =3D ｰ1
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統計の分析と利用　1．一次元と二次元のデータ
相関関係
=
n参考：その他の相関係数
q例題：男= 翌ｻれぞれが好きな花の順番
桜=
菊=
薔薇
梅=
百合
鬱= 熏
カーネーション<= /div>
椿=
男
1<= /span>
2<= /span>
3<= /span>
4<= /span>
5<= /span>
6<= /span>
7<= /span>
8<= /span>
女
3<= /span>
1<= /span>
2<= /span>
5<= /span>
4<= /span>
7<= /span>
6<= /span>
8<= /span>
出= W：
（『統計学入門』p.55）<= /span>
☆（スピ= Aマンの）順位相関係数
☆（ケン= hールの）順位相関係数
菊
薔
梅
百
鬱
カ
椿
桜
×
×
○
○
○
○
○
菊
○
○
○
○
○
○
薔
○
○
○
○
○
梅
×
○
○
○
百
○
○
○
鬱
×
○
カ
○
桜 v.s. 椿1<8
3<8
<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"= ＭＳ Ｐゴシック"; mso-ansi-language:EN-US;mso-special-format:lastCR;display:none'>
正順<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Ti= mes New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; font-size:89%;layout-flow:horizontal;color:#663300;mso-ansi-language:EN-US; mso-special-format:lastCR;display:none'>
鬱 v.s. カ6<7
7>6
=
逆順<= span lang=3DJA style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Ti= mes New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; font-size:89%;layout-flow:horizontal;color:#663300;mso-ansi-language:EN-US; mso-special-format:lastCR;display:none'>
G：正順の数=3D24
H：逆順の数=3D4<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; font-size:89%;layout-flow:horizontal;color:#663300;mso-fareast-language:JA; mso-special-format:lastCR;display:none'>
ピアソンの積率相関係数を順序= 尺度に素直にあてはめたもの
= 全対（n(n-1)/2個）について，正順と逆順の個数の差を比較したもの<= /div>
★順位相関係数を使うとき= とは？
= 　
A
R1, R<= i>2, …, R<= i>n
B
Q1, Q<= i>2, …, Q<= i>n
（Ri ： A が i を好きな順番）
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演習５
n相関係数を計算しよう
q右のデータ x, y について，
nそれぞれの分散 S<= i>x<= i>2, S<= i>y<= i>2 を計算せよ．
n共分散 covxy を計算せよ．
n（ピアソンの積率)相関係数 r<= i>xy を計算せよ．
q
q
q右のA君, Bさんの色の好みに関す= 髑I好順位データについて，
n（スピアマンの）順位相関係数 r<= i>S を計算せよ．
n（ケンドールの）順位相関係数 r<= i>K を計算せよ．
x
1
3
5
7
9
y
4
6
2
0
3
赤
青
橙=
緑
紫=
A
1
2
3
4
5
B
4
5
2
1
3
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参考：散らばりの比較
=
n変動係数 coefficie= nt of variation
q分布の中心が著しく異なる場合，分散で単純に散らばりを比較できない　⇒　相対比を指標として用いる
（n個の観測値　　　= 　　　　　に対して）
1965年：7.5/26.6 =3D 0.28 (28%)
1975年：23.8/117.5 =3D 0.20 (20%)
q例：県民所得（単位：万円）の比較
単純には所得格差は3倍に =
広がっているように見える
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最後に…
=
=
n統計解析・予測手法
記述統計学
descriptive statistics
推測統= 計学
inferential statistics
多変量= 析
multivariate analysis
度数分布，代表値，
散らばり，相関関係，
etc.
確率分布，
母集団・標本，
推定，検定，etc.
重回帰分析，主成分分析，
判別分析，数量化理論，
etc.
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参考文献
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q東大教養統計= 教室編 「統計学入門」 東大出版会(1991)
q東大教養統計= 教室編 「自然科学の統計学」 東大出版会(1992)
q村上雅人 「なるほど統計学」 海鳴社(2002)
q大村平 「改訂版 統計解析の= ﾍなし」 日科技連(2006,1980)<= /span>q大村平 「ＱＣ数学のはなし」 日科技連(2003)
q丹慶勝市 「図解雑学 統計解析」<= /span> ナツメ社(2003)q高橋信 「マンガでわかる統計学」 オーム社(2004)
q田栗正章ほか「やさしい統計入門」　講談社(2007)
q桑田秀夫 「経営・経済系のための統計学」 日科技連(1992)
qJ.アルバート&J.ベネット「メジャーリ= ーグの数理科学」シュプリンガ= ー(2004)
q間瀬茂他「工= 学のためのデータサイエンス入門」数理工学社(2004)
q荒木勉他 「Excelで学ぶ統計= 析」 実教出版(2000)
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統計の分析と利用
2008/4/18
マスタ テキストの書式設定
第 2 レベル
第 3 レベル
第 4 レベル
第 5 レベル
Confidential
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統計の分析と利用
2008= /4/18
Confidential
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統計の分析と利用
2008= /4/18
Confidential
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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() { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans ) { 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() } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis() { if( !IsNts() ) return false SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) { 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() { return sId=3Dlocation.href.substring(location.href.la= stIndexOf('/')+1) } 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(); } } var g_HLinkArray =3D new Array(); function IMapAreaObj( areaObj, coords ) { this.areaObj =3D areaObj; this.coords =3D coords; } function InitHLinkArray() { var appVer =3D navigator.appVersion; var msie =3D appVer.indexOf ( "MSIE " ) var ver =3D 0; if ( msie >=3D 0 ) ver =3D parseInt ( appVer.substring( msie+5 ) ); linkNum =3D 0; for (i=3D0; i 4 ) ) g_HLinkArray[linkNum++] =3D new IMapAreaObj( areaObj, ParseCoords( ar= eaObj.coords ) ); } } function ScaleHyperlinks( factor ) { for( ii=3D0; ii< g_HLinkArray.length; ii++) { coordsStr=3D""; imaObj =3D g_HLinkArray[ii]; for ( jj=3D0; jj < imaObj.coords.length-1; jj++ ) coordsStr +=3D (imaObj.coords[jj]*factor) + ","; coordsStr +=3D (imaObj.coords[jj]*factor); imaObj.areaObj.coords =3D coordsStr; } } function ParseCoords( coordsStr ) { var numArray =3D new Array(); var i =3D curPos =3D commaPos =3D 0; while ( ( commaPos =3D coordsStr.indexOf(",", curPos) ) !=3D -1 ) { numArray[i++] =3D parseInt( coordsStr.substr( curPos, commaPos ) ); curPos =3D commaPos + 1; } numArray[i] =3D parseInt( coordsStr.substr( curPos ) ); return numArray; } function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { 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=3D64, 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 gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0052.htm",1,-1,1),new hrefList("slide0002.htm",1,-1,1),new hrefList("= slide0003.htm",1,-1,1),new hrefList("slide0004.htm",1,-1,1),new hrefList("s= lide0005.htm",1,-1,1),new hrefList("slide0033.htm",1,-1,1),new hrefList("sl= ide0006.htm",1,-1,1),new hrefList("slide0007.htm",1,-1,1),new hrefList("sli= de0050.htm",1,-1,1),new hrefList("slide0008.htm",1,-1,1),new hrefList("slid= e0009.htm",1,-1,1),new hrefList("slide0034.htm",1,-1,1),new hrefList("slide= 0011.htm",1,-1,1),new hrefList("slide0045.htm",1,-1,1),new hrefList("slide0= 046.htm",1,-1,1),new hrefList("slide0051.htm",1,-1,1),new hrefList("slide00= 53.htm",1,-1,1),new hrefList("slide0010.htm",1,-1,1),new hrefList("slide006= 2.htm",1,-1,1),new hrefList("slide0059.htm",1,-1,1),new hrefList("slide0035= .htm",1,-1,1),new hrefList("slide0061.htm",1,-1,1),new hrefList("slide0013.= htm",1,-1,1),new hrefList("slide0014.htm",1,-1,1),new hrefList("slide0015.h= tm",1,-1,1),new hrefList("slide0016.htm",1,-1,1),new hrefList("slide0017.ht= m",1,-1,1),new hrefList("slide0018.htm",1,-1,1),new hrefList("slide0019.htm= ",1,-1,1),new hrefList("slide0047.htm",1,-1,1),new hrefList("slide0040.htm"= ,1,-1,1),new hrefList("slide0054.htm",1,-1,1),new hrefList("slide0036.htm",= 1,-1,1),new hrefList("slide0066.htm",1,-1,1),new hrefList("slide0067.htm",1= ,-1,1),new hrefList("slide0068.htm",1,-1,1),new hrefList("slide0069.htm",1,= -1,1),new hrefList("slide0070.htm",1,-1,1),new hrefList("slide0022.htm",1,-= 1,1),new hrefList("slide0041.htm",1,-1,1),new hrefList("slide0055.htm",1,-1= ,1),new hrefList("slide0024.htm",1,-1,1),new hrefList("slide0060.htm",1,-1,= 1),new hrefList("slide0039.htm",1,-1,1),new hrefList("slide0042.htm",1,-1,1= ),new hrefList("slide0026.htm",1,-1,1),new hrefList("slide0056.htm",1,-1,1)= ,new hrefList("slide0025.htm",1,-1,1),new hrefList("slide0027.htm",1,-1,1),= new hrefList("slide0028.htm",1,-1,1),new hrefList("slide0071.htm",1,-1,1),n= ew hrefList("slide0030.htm",1,-1,1),new hrefList("slide0058.htm",1,-1,1),ne= w hrefList("slide0057.htm",1,-1,1),new hrefList("slide0072.htm",1,-1,1),new= hrefList("slide0029.htm",1,-1,1),new hrefList("slide0073.htm",1,-1,1),new = hrefList("slide0063.htm",1,-1,1),new hrefList("slide0064.htm",1,-1,1),new h= refList("slide0043.htm",1,-1,1),new hrefList("slide0048.htm",1,-1,1),new hr= efList("slide0031.htm",1,-1,1),new hrefList("slide0032.htm",1,-1,1)); 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 ) { 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(); function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') { href=3Dnew String(document.location.href) Start=3Dhref.indexOf('!')+1 End=3Dhref.lastIndexOf('/')+1 if (End < Start) return href.substring(0, Start) else return href.substring(0, End) } 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() { if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() { 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(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() { obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else return gCurSld } function GetNumSlds() { 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; PPTSld.location.replace(MHTMLPrefix+obj.mSldHref) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 PPTSld.location.replace(MHTMLPrefix+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; 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(); 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 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0 } 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() } } 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() { 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 ) { if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } } 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 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() { b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() { 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 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 ) 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(); 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charset="shift_jis" 統計の分析と利用　1．一次元と二次元のデータ ------=_NextPart_01C8AC56.BF815BF0 Content-Location: file:///C:/CECB5C11/08dist_1.files/outline.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis"
 ノ= ート
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アウトライン
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