{"id":272,"date":"2022-08-08T00:00:00","date_gmt":"2022-08-07T15:00:00","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/weighted-mean-integrated-standard-deviation-pooled-variance\/"},"modified":"2024-09-22T22:12:42","modified_gmt":"2024-09-22T13:12:42","slug":"weighted-mean-integrated-standard-deviation-pooled-variance","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/weighted-mean-integrated-standard-deviation-pooled-variance\/","title":{"rendered":"\u9023\u7d9a\u30c7\u30fc\u30bf\u306e\u5c64\u5225\u89e3\u6790\u7d50\u679c\u3092\u7d71\u5408\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

\u9023\u7d9a\u30c7\u30fc\u30bf\u306e\u4ee3\u8868\u7684\u306a\u8981\u7d04\u5024\u3001\u5e73\u5747\u5024\u3068\u6a19\u6e96\u504f\u5dee\u3092\u7d71\u5408\u3059\u308b\u306b\u306f\u3069\u3046\u3084\u3063\u305f\u3089\u3088\u3044\u304b\uff1f<\/p>\n\n\n\n

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\u9023\u7d9a\u30c7\u30fc\u30bf\u306e\u5c64\u5225\u89e3\u6790\u306e\u7d71\u5408\u3068\u306f\uff1f<\/h2>\n\n\n\n

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\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\tR \u3067\u5e73\u5747\u5024\u306e\u5dee\u306e\u30e1\u30bf\u89e3\u6790\u3092\u884c\u3046\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t\u5e73\u5747\u5024\u306e\u5dee\u306e\u30e1\u30bf\u89e3\u6790\u306e\u3084\u308a\u65b9\u3092\u89e3\u8aac\u3002 \u30e1\u30bf\u89e3\u6790\u306e\u3084\u308a\u65b9\u89e3\u8aac\u306e\u305f\u3081\u306e\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf \u30e1\u30bf\u89e3\u6790\u306e\u3084\u308a\u65b9\u3092\u89e3\u8aac\u3059\u308b\u305f\u3081\u306e\u30c7\u30fc\u30bf\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002 m\u304c\u5e73\u5747\u3001s\u304c\u6a19\u6e96\u504f\u5dee\u3001n…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n

\u9023\u7d9a\u30c7\u30fc\u30bf\u306e\u5c64\u5225\u89e3\u6790\u306e\u7d71\u5408\u306f\u3069\u306e\u3088\u3046\u306a\u8a08\u7b97\u3092\u3059\u308b\u306e\u304b\uff1f<\/h2>\n\n\n\n

\u5e73\u5747\u306e\u7d71\u5408\uff08\u91cd\u307f\u4ed8\u3051\u5e73\u5747\uff09<\/h3>\n\n\n\n

\u5e73\u5747\u5024\u306e\u7d71\u5408\u306f\u4ee5\u4e0b\u306e\u5f0f\u306e\u3088\u3046\u306b\u3001\u5404\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u91cd\u307f\u3068\u3057\u305f\u3001\u91cd\u307f\u4ed8\u3051\u5e73\u5747 $ \\bar{X_t} $ \u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n

$$ \\bar{X_t} = \\frac{\\sum{n \\bar{X}}}{n_t} $$<\/p>\n\n\n\n\n\n\n\n

\u3053\u3053\u3067\u3001n \u306f\u5404\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3001$ \\bar{X} $ \u306f\u5404\u7fa4\u306e\u5e73\u5747\u5024\u3001$ n_t $ \u306f\u5168\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306e\u5408\u8a08\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u6a19\u6e96\u504f\u5dee\u306e\u7d71\u5408<\/h3>\n\n\n\n

\u6a19\u6e96\u504f\u5dee\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n

U \u306f\u5404\u7fa4\u306e\u6a19\u6e96\u504f\u5dee\u30922\u4e57\u3057\u3066\u8a08\u7b97\u3057\u305f\u4e0d\u504f\u5206\u6563\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

$$ \\sqrt{\\frac{\\sum{(n – 1) U} + \\sum{n(\\bar{X} – \\bar{X_t})^2}}{n_t – 1}} $$<\/p>\n\n\n\n\n\n\n\n

\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n\"\"<\/a>\r\n

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\u3053\u3061\u3089\u306e\u30ea\u30f3\u30af\u5148\u306b\u3042\u308b\u4f8b\u984c\u3092\u4f7f\u3063\u3066\u5b9f\u969b\u306b\u3084\u3063\u3066\u307f\u308b\u3002<\/p>\n\n\n\n

\u7fa4\u3054\u3068\u306e\u5e73\u5747\u5024\u30fb\u4e0d\u504f\u5206\u6563\u3092\u7d71\u5408\u3059\u308b\u65b9\u6cd5\u3068\u306f\u4f55\uff1f \u308f\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac Weblio\u8f9e\u66f8<\/a><\/p>\n\n\n\n

\u7fa4<\/th>\u90fd\u9053\u5e9c\u770c\u6570<\/th>\u5e73\u5747\u5024<\/th>\u6a19\u6e96\u504f\u5dee<\/th><\/tr><\/thead>
\u7b2c1\u7fa4<\/td>8<\/td>135.83<\/td>19.59<\/td><\/tr>
\u7b2c2\u7fa4<\/td>11<\/td>160.49<\/td>12.28<\/td><\/tr>
\u7b2c3\u7fa4<\/td>22<\/td>178.35<\/td>15.01<\/td><\/tr>
\u7b2c4\u7fa4<\/td>6<\/td>188.06<\/td>9.81<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

R \u3067\u3084\u3063\u3066\u307f\u308b<\/h3>\n\n\n\n
><\/span> n <-<\/span> c<\/span>(<\/span>8<\/span>,<\/span>11<\/span>,<\/span>22<\/span>,<\/span>6<\/span>)<\/span>\n><\/span> m <-<\/span> c<\/span>(<\/span>135.83<\/span>,<\/span>160.49<\/span>,<\/span>178.35<\/span>,<\/span>188.06<\/span>)<\/span>\n><\/span> s <-<\/span> c<\/span>(<\/span>19.59<\/span>,<\/span>12.28<\/span>,<\/span>15.01<\/span>,<\/span>9.81<\/span>)<\/span>\n><\/span> sum<\/span>(<\/span>n*<\/span>m)<\/span>\/<\/span>sum<\/span>(<\/span>n)<\/span>\n[<\/span>1<\/span>]<\/span> 168.1721<\/span>\n<\/code><\/pre>\n\n\n\n
\u91cd\u307f\u4ed8\u3051\u5e73\u5747\u306f168.1721\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002<\/p>\n\n\n\n
><\/span> U <-<\/span> s^<\/span>2<\/span>\n><\/span> sqrt<\/span>((<\/span>sum<\/span>((<\/span>n-<\/span>1<\/span>)<\/span>*<\/span>U)<\/span>+<\/span>sum<\/span>(<\/span>n*<\/span>(<\/span>m-<\/span>sum<\/span>(<\/span>n*<\/span>m)<\/span>\/<\/span>sum<\/span>(<\/span>n))<\/span>^<\/span>2<\/span>))<\/span>\/<\/span>(<\/span>sum<\/span>(<\/span>n)<\/span>-<\/span>1<\/span>))<\/span>\n[<\/span>1<\/span>]<\/span> 22.39771<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d71\u5408\u3057\u305f\u6a19\u6e96\u504f\u5dee\u306f\u300122.39771\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002<\/p>\n\n\n\n
StatsToDo\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u3084\u3063\u3066\u307f\u308b<\/h3>\n\n\n\n
\u30aa\u30f3\u30e9\u30a4\u30f3\u3067\u7121\u6599\u3067\u63d0\u4f9b\u3055\u308c\u3066\u3044\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u4e0b\u8a18\u306e\u30ea\u30f3\u30af\u5148\u306b\u3042\u308b\u3002<\/p>\n\n\n\n
CombineMeanSD<\/a><\/p>\n\n\n\n
\u3053\u308c\u3092\u4f7f\u3063\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
Javascript Program\u306b\u4e0a\u8a18\u306e\u30c7\u30fc\u30bf\u3092\u5165\u529b\u3059\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u5165\u529b\u3057\u7d42\u308f\u3063\u305f\u3089\u3001\u8d64\u77e2\u5370\u306e\u30dc\u30bf\u30f3\u3092\u30af\u30ea\u30c3\u30af\u3059\u308b\u3002<\/p>\n\n\n\n
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\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
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\u30d7\u30fc\u30eb\u3057\u305f\u5206\u6563\u306e\u5e73\u65b9\u6839<\/h3>\n\n\n\n
\u30d7\u30fc\u30eb\u3057\u305f\u5206\u6563\u3092\u7528\u3044\u308b\u65b9\u6cd5\u3082\u3042\u308b\u3068\u601d\u3046\u3002<\/p>\n\n\n\n
\u30d7\u30fc\u30eb\u3057\u305f\u5206\u6563 | \u7d71\u8a08\u7528\u8a9e\u96c6 | \u7d71\u8a08WEB<\/a><\/p>\n\n\n\n
\u6570\u5f0f\u3067\u8868\u3059\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
$$ \\frac{(n_1 – 1) U_1 + (n_2 – 1) U_2}{n_1 – 1 + n_2 – 1} $$<\/p>\n\n\n\n\n\n\n\n
n, U \u306f\u5404\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3068\u4e0d\u504f\u5206\u6563\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\u3053\u308c\u306f\uff54\u691c\u5b9a\u306e\u6642\u306b\u7528\u3044\u3089\u308c\u308b\u5206\u6563\u306e\u7d71\u5408\u65b9\u6cd5\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
24-3. 2\u6a19\u672ct\u691c\u5b9a\u3068\u306f | \u7d71\u8a08\u5b66\u306e\u6642\u9593 | \u7d71\u8a08WEB<\/a><\/p>\n\n\n\n
\u3053\u306e\u30d7\u30fc\u30eb\u3057\u305f\u5206\u6563\u306e\u5e73\u65b9\u6839\u3092\u53d6\u308b\u3053\u3068\u3067\u3082\u30d7\u30fc\u30eb\u3057\u305f\u6a19\u6e96\u504f\u5dee\u306b\u306a\u308b\u3068\u601d\u3046\u3002<\/p>\n\n\n\n
\u3053\u3061\u3089\u306f\u3001\u81ea\u7531\u5ea6\u3092\u91cd\u307f\u306b\u3057\u305f\u91cd\u307f\u4ed8\u3051\u4e0d\u504f\u5206\u6563\u304b\u3089\u8a08\u7b97\u3055\u308c\u305f\u5024\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n
\uff12\u7fa4\u304b\u3089\uff14\u7fa4\u306b\u62e1\u5f35\u3057\u3066\u8003\u3048\u3001\u7d71\u8a08\u30bd\u30d5\u30c8R\u3067\u8a08\u7b97\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
><\/span> sqrt<\/span>(<\/span>sum<\/span>((<\/span>n-<\/span>1<\/span>)<\/span>*<\/span>U)<\/span>\/<\/span>sum<\/span>(<\/span>n-<\/span>1<\/span>))<\/span>\n[<\/span>1<\/span>]<\/span> 14.79067<\/span>\n<\/code><\/pre>\n\n\n\n
\uff14\u7fa4\u306e\u3061\u3087\u3046\u3069\u771f\u3093\u4e2d\u3042\u305f\u308a\u306e\u5024\u306b\u306a\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
\u3055\u304d\u307b\u3069\u306e\u8a08\u7b97\u7d50\u679c\u3068\u306f\u82e5\u5e72\u7570\u306a\u308b\u7d50\u679c\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
\u3044\u305a\u308c\u306b\u3057\u3066\u3082\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3092\u3057\u305f\u304b\u3092\u660e\u8a18\u3059\u308c\u3070\u3001\u3069\u3061\u3089\u306e\u65b9\u6cd5\u3067\u3082\u554f\u984c\u306a\u3044\u3068\u601d\u3046\u3002<\/p>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
\u9023\u7d9a\u30c7\u30fc\u30bf\u306e\u5c64\u5225\u89e3\u6790\u8981\u7d04\u5024\u3092\u7d71\u5408\u3057\u305f\u3044\u3068\u304d\u306b\u3069\u3046\u3059\u308c\u3070\u3088\u3044\u304b\u3001\u8aac\u660e\u3057\u305f\u3002<\/p>\n\n\n\n
\u7d71\u5408\u3057\u305f\u5e73\u5747\u3068\u6a19\u6e96\u504f\u5dee\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u63d0\u793a\u3057\u3001\u7121\u6599\u3067\u4f7f\u3048\u308bOnline\u30b5\u30fc\u30d3\u30b9\u3082\u7d39\u4ecb\u3057\u305f\u3002<\/p>\n\n\n\n
\u6a19\u6e96\u504f\u5dee\u306e\u7d71\u5408\u306b\u306f\u3001\uff12\u3064\u306e\u65b9\u6cd5\u304c\u8003\u3048\u3089\u308c\u308b\u304c\u3001\u3069\u3061\u3089\u306e\u65b9\u6cd5\u3092\u4f7f\u3063\u305f\u306e\u304b\u3092\u660e\u8a18\u3059\u308c\u3070\u3001\u3069\u3061\u3089\u3067\u3082\u3088\u3044\u3060\u308d\u3046\u3002<\/p>\n\n\n\n
\u53c2\u8003\u30b5\u30a4\u30c8<\/h2>\n\n\n\n
\u91cd\u307f\u4ed8\u3051\u5e73\u5747<\/p>\n\n\n\n
https:\/\/staff.aist.go.jp\/t.ihara\/weight.html<\/a><\/p>\n\n\n\n
\u7fa4\u3054\u3068\u306e\u5e73\u5747\u5024\u30fb\u4e0d\u504f\u5206\u6563\u3092\u7d71\u5408\u3059\u308b\u65b9\u6cd5<\/p>\n\n\n\n
\u7fa4\u3054\u3068\u306e\u5e73\u5747\u5024\u30fb\u4e0d\u504f\u5206\u6563\u3092\u7d71\u5408\u3059\u308b\u65b9\u6cd5\u3068\u306f\u4f55\uff1f \u308f\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac Weblio\u8f9e\u66f8<\/a><\/p>\n\n\n\n
\u30d7\u30fc\u30eb\u3057\u305f\u5206\u6563<\/p>\n\n\n\n
\u30d7\u30fc\u30eb\u3057\u305f\u5206\u6563 | \u7d71\u8a08\u7528\u8a9e\u96c6 | \u7d71\u8a08WEB<\/a><\/p>\n\n\n\n
\uff54\u691c\u5b9a<\/p>\n\n\n\n
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