{"id":773,"date":"2023-07-28T19:28:17","date_gmt":"2023-07-28T19:28:17","guid":{"rendered":"https:\/\/statorials.org\/ja\/anova-%e3%81%af%e6%89%8b%e5%8b%95%e3%81%a6%e3%82%99%e6%b8%ac%e5%ae%9a%e3%82%92%e7%b9%b0%e3%82%8a%e8%bf%94%e3%81%97%e3%81%be%e3%81%97%e3%81%9f\/"},"modified":"2023-07-28T19:28:17","modified_gmt":"2023-07-28T19:28:17","slug":"anova-%e3%81%af%e6%89%8b%e5%8b%95%e3%81%a6%e3%82%99%e6%b8%ac%e5%ae%9a%e3%82%92%e7%b9%b0%e3%82%8a%e8%bf%94%e3%81%97%e3%81%be%e3%81%97%e3%81%9f","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/anova-%e3%81%af%e6%89%8b%e5%8b%95%e3%81%a6%e3%82%99%e6%b8%ac%e5%ae%9a%e3%82%92%e7%b9%b0%e3%82%8a%e8%bf%94%e3%81%97%e3%81%be%e3%81%97%e3%81%9f\/","title":{"rendered":"\u53cd\u5fa9\u6e2c\u5b9a anova \u3092\u624b\u52d5\u3067\u5b9f\u884c\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/ja\/\u5206\u6563\u5206\u6790\u306b\u3088\u308b\u7e70\u308a\u8fd4\u3057\u6e2c\u5b9a\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>\u53cd\u5fa9\u6e2c\u5b9a ANOVA \u306f\u3001<\/strong><\/a>\u5404\u30b0\u30eb\u30fc\u30d7\u306b\u540c\u3058\u88ab\u9a13\u8005\u304c\u542b\u307e\u308c\u308b 3 \u3064\u4ee5\u4e0a\u306e\u30b0\u30eb\u30fc\u30d7\u306e\u5e73\u5747\u9593\u306b\u7d71\u8a08\u7684\u306b\u6709\u610f\u306a\u5dee\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u3067\u306f\u3001\u4e00\u5143\u914d\u7f6e\u53cd\u5fa9\u6e2c\u5b9a\u5206\u6563\u5206\u6790\u3092\u624b\u52d5\u3067\u5b9f\u884c\u3059\u308b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u4f8b: \u624b\u52d5\u306b\u3088\u308b\u4e00\u5143\u914d\u7f6e\u53cd\u5fa9\u6e2c\u5b9a\u5206\u6563\u5206\u6790<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u7814\u7a76\u8005\u306f\u30013 \u3064\u306e\u7570\u306a\u308b\u85ac\u5264\u304c\u7570\u306a\u308b\u53cd\u5fdc\u6642\u9593\u3092\u5f15\u304d\u8d77\u3053\u3059\u304b\u3069\u3046\u304b\u3092\u77e5\u308a\u305f\u3044\u3068\u8003\u3048\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3092\u30c6\u30b9\u30c8\u3059\u308b\u305f\u3081\u306b\u3001\u5404\u85ac\u5264\u306b\u5bfe\u3059\u308b 5 \u4eba\u306e\u60a3\u8005\u306e\u53cd\u5fdc\u6642\u9593 (\u79d2\u5358\u4f4d) \u3092\u6e2c\u5b9a\u3057\u307e\u3057\u305f\u3002\u7d50\u679c\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8449 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/repanovahand1.png\" alt=\"\" width=\"315\" height=\"145\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u5404\u60a3\u8005\u306f 3 \u3064\u306e\u85ac\u5264\u306e\u305d\u308c\u305e\u308c\u306b\u3064\u3044\u3066\u6e2c\u5b9a\u3055\u308c\u308b\u305f\u3081\u3001\u4e00\u5143\u914d\u7f6e\u53cd\u5fa9\u6e2c\u5b9a\u5206\u6563\u5206\u6790\u3092\u4f7f\u7528\u3057\u3066\u3001\u5e73\u5747\u53cd\u5fdc\u6642\u9593\u304c\u85ac\u5264\u9593\u3067\u7570\u306a\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3057\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u53cd\u5fa9\u6e2c\u5b9a ANOVA \u3092\u624b\u52d5\u3067\u5b9f\u884c\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u624b\u9806\u306b\u5f93\u3044\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 1: SST \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u307e\u305a\u3001\u7dcf\u5e73\u65b9\u548c (SST) \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">SST = s <sup>2<\/sup><sub>\u5408\u8a08<\/sub>(n<sub>\u5408\u8a08<\/sub>-1)<\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>s <sup>2<\/sup> <sub>total<\/sub><\/strong> : \u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u5206\u6563<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>n <sub>total<\/sub><\/strong> : \u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u5185\u306e\u89b3\u6e2c\u5024\u306e\u5408\u8a08\u6570<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u3053\u306e\u4f8b\u3067\u306f\u3001SST \u3092\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059: (64.2667)(15-1) = <strong>899.7<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 2: SSB \u3092\u8a08\u7b97\u3059\u308b<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306b\u3001\u4e8c\u4e57\u548c (SSB) \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">SSB = \u03a3n <sub>j<\/sub> ( <span style=\"text-decoration: overline;\">x<\/span> <sub>j<\/sub> \u2013 <span style=\"text-decoration: overline;\">x<\/span><sub>\u5408\u8a08<\/sub>) <sup>2<\/sup><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : \u300c\u548c\u300d\u3092\u610f\u5473\u3059\u308b\u30ae\u30ea\u30b7\u30e3\u8a9e\u306e\u8a18\u53f7<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>n <sub>j<\/sub><\/strong> : j<sup>\u756a\u76ee\u306e<\/sup>\u30b0\u30eb\u30fc\u30d7\u306e\u89b3\u6e2c\u5024\u306e\u7dcf\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> <sub>j<\/sub><\/strong> : <sup>j \u756a\u76ee<\/sup>\u306e\u30b0\u30eb\u30fc\u30d7\u306e\u5e73\u5747<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> <sub>total<\/sub><\/strong> : \u3059\u3079\u3066\u306e\u30c7\u30fc\u30bf\u306e\u5e73\u5747<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u3053\u306e\u4f8b\u3067\u306f\u3001SSB \u3092\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059: (5)(26.4-22.533) <sup>2<\/sup> +(5)(25.6-22.533) <sup>2<\/sup> + (5)(15.6-22.533) <sup>2<\/sup> = <strong>362.1<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 3: SSS \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306b\u3001\u88ab\u9a13\u8005\u306e\u4e8c\u4e57\u548c (SSS) \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">SSS =(\u03a3r <sup>2<\/sup> <sub>k<\/sub> \/c) \u2013 (N <sup>2<\/sup> \/rc)<\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : \u300c\u548c\u300d\u3092\u610f\u5473\u3059\u308b\u30ae\u30ea\u30b7\u30e3\u8a9e\u306e\u8a18\u53f7<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>r <sup>2<\/sup><\/strong> <sub>k<\/sub> : <sup>k \u756a\u76ee<\/sup>\u306e\u60a3\u8005\u306e\u4e8c\u4e57\u548c<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>N:<\/strong>\u3059\u3079\u3066\u306e\u30c7\u30fc\u30bf\u306e\u7dcf\u8a08<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>r:<\/strong>\u60a3\u8005\u306e\u7dcf\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>c:<\/strong>\u30b0\u30eb\u30fc\u30d7\u306e\u7dcf\u6570<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u3053\u306e\u4f8b\u3067\u306f\u3001SSS \u3092\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059: ((74 <sup>2<\/sup> + 42 <sup>2<\/sup> + 62 <sup>2<\/sup> + 92 <sup>2<\/sup> + 68 <sup>2<\/sup> )\/3) \u2013 (338 <sup>2<\/sup> \/(5)(3)) = <strong>441.1<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 4: SES \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306b\u3001\u4e8c\u4e57\u8aa4\u5dee\u548c (SSE) \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">SSE = SST \u2013 SSB \u2013 SSS<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u306e\u4f8b\u3067\u306f\u3001SES \u3092\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059: 899.7 \u2013 362.1 \u2013 441.1 = <strong>96.5<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 5: \u53cd\u5fa9\u6e2c\u5b9a ANOVA \u8868\u3092\u5b8c\u6210\u3055\u305b\u307e\u3059\u3002<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">SSB\u3001SSS\u3001SSE \u304c\u5f97\u3089\u308c\u305f\u306e\u3067\u3001\u53cd\u5fa9\u6e2c\u5b9a ANOVA \u30c6\u30fc\u30d6\u30eb\u306b\u5024\u3092\u5165\u529b\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>\u30bd\u30fc\u30b9<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>\u4e8c\u4e57\u548c (SS)<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>DF<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>\u5e73\u5747\u4e8c\u4e57 (MS)<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>F<\/strong><\/span><\/th>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000;\"><strong>\u9593<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">362.1<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">181.1<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">15.006<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000;\"><strong>\u4e3b\u984c<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">441.1<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">4<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">110.3<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000;\"><strong>\u30a8\u30e9\u30fc<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">96.5<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">12.1<\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"color: #000000;\">\u8868\u5185\u306e\u3055\u307e\u3056\u307e\u306a\u6570\u5024\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>df between:<\/strong> #groups \u2013 1 = 3 \u2013 1 = 2<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>DF \u4ef6\u540d:<\/strong> #\u53c2\u52a0\u8005 \u2013 1 = 5 \u2013 1 = 4<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u30a8\u30e9\u30fc df:<\/strong> df between * df subject = 2*4 = 8<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>MS \u304c\u5165\u308b:<\/strong> SSB \/ df \u304c\u5165\u308b = 362.1 \/ 2 = 181.1<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>MS \u30b5\u30d6\u30b8\u30a7\u30af\u30c8:<\/strong> SSS \u30b5\u30d6\u30b8\u30a7\u30af\u30c8 \/ df = 441.1 \/ 4 = 110.3<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>MS \u30a8\u30e9\u30fc:<\/strong> SSE \u30a8\u30e9\u30fc \/ df = 96.5 \/ 8 = 12.1<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>F:<\/strong> MS \u5165\u529b \/ MS \u30a8\u30e9\u30fc = 181.1 \/ 12.1 = 15.006<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 6: \u7d50\u679c\u3092\u89e3\u91c8\u3057\u307e\u3059\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u306e\u4e00\u5143\u914d\u7f6e\u53cd\u5fa9\u6e2c\u5b9a ANOVA \u306e F \u691c\u5b9a\u7d71\u8a08\u91cf\u306f<strong>15.006<\/strong>\u3067\u3059\u3002<\/span>\u3053\u308c\u304c\u7d71\u8a08\u7684\u306b\u6709\u610f\u306a\u7d50\u679c\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u306b\u306f\u3001<span style=\"color: #000000;\">\u6b21\u306e\u5024\u3092<\/span>\u6301\u3064<a href=\"https:\/\/statorials.org\/ja\/f\u5206\u5e03\u8868\/\" target=\"_blank\" rel=\"noopener noreferrer\">F \u5206\u5e03\u8868<\/a><span style=\"color: #000000;\">\u306b\u3042\u308b\u81e8\u754c F \u5024\u3068\u6bd4\u8f03\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059<\/span>\u3002<\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u03b1 (\u6709\u610f\u6c34\u6e96) = 0.05<\/span><\/li>\n<li> <span style=\"color: #000000;\">DF1 (\u5206\u5b50\u306e\u81ea\u7531\u5ea6) = df between = 2<\/span><\/li>\n<li> <span style=\"color: #000000;\">DF2 (\u5206\u6bcd\u306e\u81ea\u7531\u5ea6) = \u8aa4\u5dee df = 8<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">F \u306e\u81e8\u754c\u5024\u306f<strong>4.459<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">ANOVA \u8868\u306e F \u691c\u5b9a\u7d71\u8a08\u91cf\u306f F \u5206\u5e03\u8868\u306e\u81e8\u754c\u5024 F \u3088\u308a\u5927\u304d\u3044\u305f\u3081\u3001\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u85ac\u5264\u306e\u5e73\u5747\u5fdc\u7b54\u6642\u9593\u306e\u9593\u306b\u7d71\u8a08\u7684\u306b\u6709\u610f\u306a\u5dee\u304c\u3042\u308b\u3068\u8a00\u3048\u308b\u5341\u5206\u306a\u8a3c\u62e0\u304c\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u53cd\u5fa9\u6e2c\u5b9a ANOVA \u306f\u3001\u5404\u30b0\u30eb\u30fc\u30d7\u306b\u540c\u3058\u88ab\u9a13\u8005\u304c\u542b\u307e\u308c\u308b 3 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