{"id":4827,"date":"2026-09-23T08:09:18","date_gmt":"2026-09-22T23:09:18","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4827"},"modified":"2026-09-23T08:09:18","modified_gmt":"2026-09-22T23:09:18","slug":"how-to-test-whether-a-time-series-is-increasing-in-r-mann-kendall-test-and-sens-slope","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-test-whether-a-time-series-is-increasing-in-r-mann-kendall-test-and-sens-slope\/","title":{"rendered":"\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u306e\u300c\u5897\u3048\u3066\u3044\u308b\u300d\u3092R\u3067\u5224\u5b9a\u3059\u308b\u65b9\u6cd5\uff5cMann-Kendall\u691c\u5b9a\u3068Sen&#8217;s slope"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u5f8c\u8f29<\/strong>\uff1a\u300c\u5148\u8f29\u3001\u77e5\u308a\u5408\u3044\u306e\u55ab\u8336\u5e97\u306e\u30de\u30b9\u30bf\u30fc\u306b\u76f8\u8ac7\u3055\u308c\u305f\u3093\u3067\u3059\u3002\u30a2\u30a4\u30b9\u30b3\u30fc\u30d2\u30fc\u306e\u58f2\u4e0a\u304c10\u5e74\u3067\u3058\u308f\u3058\u308f\u4f38\u3073\u3066\u3044\u308b\u6c17\u304c\u3059\u308b\u304b\u3089\u3001\u305d\u308c\u3092\u6570\u5b57\u3067\u78ba\u304b\u3081\u305f\u3044\u3063\u3066\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5148\u8f29<\/strong>\uff1a\u300c\u6708\u3054\u3068\u306e\u58f2\u4e0a\u30c7\u30fc\u30bf\u304c\u3042\u308b\u306e\u304b\u3044\uff1f\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5f8c\u8f29<\/strong>\uff1a\u300c\u306f\u3044\u300110\u5e74\u5206\u3067120\u304b\u6708\u3042\u308a\u307e\u3059\u3002\u6a2a\u8ef8\u306b\u6642\u9593\u3001\u7e26\u8ef8\u306b\u58f2\u4e0a\u3092\u53d6\u3063\u3066\u56de\u5e30\u76f4\u7dda\u3092\u5f15\u304d\u3001\u50be\u304d\u306eP\u5024\u3092\u898b\u308c\u3070\u3044\u3044\u3067\u3059\u3088\u306d\uff1f\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5148\u8f29<\/strong>\uff1a\u300c\u305d\u306e\u524d\u306b\u30b0\u30e9\u30d5\u3092\u898b\u3066\u3054\u3089\u3093\u3002\u590f\u306b\u8df3\u306d\u4e0a\u304c\u3063\u3066\u51ac\u306b\u843d\u3061\u8fbc\u3080\u6ce2\u304c\u3042\u308b\u3060\u308d\u3046\u3002\u305d\u308c\u306b\u3001\u3088\u304f\u58f2\u308c\u305f\u6708\u306e\u7fcc\u6708\u3082\u3088\u304f\u58f2\u308c\u308b\u3001\u3068\u3044\u3046\u30af\u30bb\u3082\u3042\u308a\u305d\u3046\u3060\u3002\u56de\u5e30\u76f4\u7dda\u306eP\u5024\u304c\u524d\u63d0\u306b\u3057\u3066\u3044\u308b\u300e\u8aa4\u5dee\u306f\u4e92\u3044\u306b\u72ec\u7acb\u3067\u3070\u3089\u3064\u304d\u65b9\u3082\u540c\u3058\u300f\u3068\u3044\u3046\u6761\u4ef6\u306f\u3001\u305f\u3076\u3093\u6e80\u305f\u3055\u308c\u3066\u3044\u306a\u3044\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5f8c\u8f29<\/strong>\uff1a\u300c\u3058\u3083\u3042\u3001\u3069\u3046\u3059\u308c\u3070\u2026\u2026\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5148\u8f29<\/strong>\uff1a\u300c\u3053\u3046\u3044\u3046\u3068\u304d\u306b\u983c\u308a\u306b\u306a\u308b\u306e\u304c <strong>Mann-Kendall\u691c\u5b9a<\/strong> \u3060\u3002\u4ee5\u524d\u306b\u7d39\u4ecb\u3057\u305f\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u3092\u899a\u3048\u3066\u3044\u308b\u304b\u3044\uff1f \u3042\u308c\u3092&#8221;\u6642\u9593&#8221;\u306b\u4f7f\u3046\u691c\u5b9a\u306a\u3093\u3060\u3088\u300d<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u306e\u30c8\u30ec\u30f3\u30c9\uff08\u50be\u5411\uff09\u3092\u8abf\u3079\u308b\u65b9\u6cd5\u3068\u3057\u3066\u3001Mann-Kendall\u691c\u5b9a\uff08\u4ee5\u4e0b\u3001MK\u691c\u5b9a\uff09\u306f\u6c17\u8c61\u5b66\u30fb\u6c34\u6587\u5b66\u30fb\u74b0\u5883\u79d1\u5b66\u3067\u6700\u3082\u3088\u304f\u4f7f\u308f\u308c\u308b\u624b\u6cd5\u306e\u4e00\u3064\u3067\u3042\u308b\u3002\u6b63\u898f\u5206\u5e03\u3092\u4eee\u5b9a\u3057\u306a\u3044\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u306a\u624b\u6cd5\u3067\u3001\u4ed5\u7d44\u307f\u3082\u9a5a\u304f\u307b\u3069\u5358\u7d14\u3060\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u8a18\u4e8b\u3067\u306f\u3001\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u306e\u8003\u3048\u65b9\u3092\u305d\u306e\u307e\u307e\u6642\u7cfb\u5217\u306b\u5f53\u3066\u306f\u3081\u308b\u3068\u3053\u308d\u304b\u3089\u59cb\u3081\u308b\u3002\u305d\u306e\u3046\u3048\u3067\u3001\u521d\u5b66\u8005\u304c\u30cf\u30de\u308a\u3084\u3059\u30443\u3064\u306e\u7f60\uff08\u81ea\u5df1\u76f8\u95a2\u30fb\u5b63\u7bc0\u6027\u30fb\u9014\u4e2d\u3067\u306e\u65b9\u5411\u8ee2\u63db\uff09\u3068\u3001\u305d\u306e\u5bfe\u51e6\u6cd5\u307e\u3067\u3092R\u3067\u4e00\u6c17\u306b\u78ba\u8a8d\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u305d\u306e\u3082\u306e\u306b\u3064\u3044\u3066\u306f\u3001\u4ee5\u524d\u306e\u8a18\u4e8b\u3067\u89e3\u8aac\u3057\u3066\u3044\u308b\u3002\u307e\u3060\u8aad\u3093\u3067\u3044\u306a\u3044\u65b9\u306f\u3001\u5148\u306b\u76ee\u3092\u901a\u3057\u3066\u304a\u304f\u3068\u7406\u89e3\u304c\u30b9\u30e0\u30fc\u30ba\u3060\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#x1f449; <a href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/kendall-rank-correlation-coefficient\/\">R\u3067\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">1. Mann-Kendall\u691c\u5b9a\u3068\u306f\uff1f\u300c\u5168\u54e1\u3068\u63e1\u624b\u3057\u3066\u80cc\u6bd4\u3079\u300d<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u4ed5\u7d44\u307f\u306f\u305f\u3063\u305f\u3053\u308c\u3060\u3051<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">MK\u691c\u5b9a\u306e\u4e2d\u8eab\u306f\u3001\u6b21\u306e\u3088\u3046\u306a\u80cc\u6bd4\u3079\u5927\u4f1a\u3060\u3068\u30a4\u30e1\u30fc\u30b8\u3059\u308b\u3068\u3088\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">120\u304b\u6708\u5206\u306e\u58f2\u4e0a\u30c7\u30fc\u30bf\u3092\u3001\u53e4\u3044\u9806\u306b\u4e00\u5217\u306b\u4e26\u3079\u308b\u3002\u305d\u3057\u3066\u5404\u6708\u304c\u3001<strong>\u81ea\u5206\u3088\u308a\u5f8c\u308d\u306b\u3044\u308b\u3059\u3079\u3066\u306e\u6708\u3068\u4e00\u4eba\u305a\u3064\u63e1\u624b\u3092\u3057\u3066<\/strong>\u3001\u3053\u3046\u5c0b\u306d\u308b\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u300c\u3042\u306a\u305f\u306f\u79c1\u3088\u308a\u5927\u304d\u3044\u3067\u3059\u304b\uff1f\u300d<\/p>\n<\/blockquote>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u76f8\u624b\u306e\u65b9\u304c\u5927\u304d\u3051\u308c\u3070 <strong>+1<\/strong><\/li>\n\n\n\n<li>\u76f8\u624b\u306e\u65b9\u304c\u5c0f\u3055\u3051\u308c\u3070 <strong>\u22121<\/strong><\/li>\n\n\n\n<li>\u540c\u3058\u306a\u3089 <strong>0<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u308c\u3092\u5168\u30da\u30a2\uff08120\u304b\u6708\u306a\u3089 120\u00d7119\u00f72 = 7,140\u7d44\uff09\u3067\u884c\u3044\u3001\u5408\u8a08\u3057\u305f\u70b9\u6570\u304c\u691c\u5b9a\u7d71\u8a08\u91cf <strong>S<\/strong> \u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6642\u9593\u3068\u3068\u3082\u306b\u58f2\u4e0a\u304c\u5897\u3048\u3066\u3044\u308c\u3070\u300c\u5f8c\u308d\u306e\u65b9\u304c\u5927\u304d\u3044\u300d\u30da\u30a2\u304c\u591a\u304f\u306a\u308a\u3001S\u306f\u5927\u304d\u306a\u30d7\u30e9\u30b9\u306b\u306a\u308b<\/li>\n\n\n\n<li>\u6e1b\u3063\u3066\u3044\u308c\u3070S\u306f\u5927\u304d\u306a\u30de\u30a4\u30ca\u30b9\u306b\u306a\u308b<\/li>\n\n\n\n<li>\u50be\u5411\u304c\u306a\u3051\u308c\u3070+1\u3068\u22121\u304c\u6253\u3061\u6d88\u3057\u5408\u3044\u3001S\u306f0\u306e\u8fd1\u304f\u306b\u843d\u3061\u7740\u304f<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">S\u304c0\u304b\u3089\u3069\u308c\u3060\u3051\u96e2\u308c\u3066\u3044\u308b\u304b\u3092\u3001\u300c\u50be\u5411\u304c\u306a\u3044\u300d\u3068\u4eee\u5b9a\u3057\u305f\u3068\u304d\u306e\u6563\u3089\u3070\u308a\uff08\u5206\u6563\uff09\u3068\u6bd4\u3079\u3066\u5224\u5b9a\u3059\u308b\u3002\u3053\u308c\u304cMK\u691c\u5b9a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u300c\u5927\u304d\u3055\u300d\u3067\u306f\u306a\u304f\u300c\u52dd\u3061\u8ca0\u3051\u300d\u3060\u3051\u3092\u898b\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u63e1\u624b\u306e\u5834\u9762\u3067\u805e\u3044\u3066\u3044\u308b\u306e\u306f\u300c\u3069\u3061\u3089\u304c\u5927\u304d\u3044\u304b\u300d\u3060\u3051\u3067\u3001\u300c\u3069\u308c\u304f\u3089\u3044\u5927\u304d\u3044\u304b\u300d\u306f\u554f\u308f\u306a\u3044\u3002\u305d\u306e\u305f\u3081\u3001<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u3042\u308b\u6708\u3060\u3051\u56e3\u4f53\u5ba2\u304c\u6765\u3066\u58f2\u4e0a\u304c\u7570\u5e38\u306b\u8df3\u306d\u305f\uff08\u5916\u308c\u5024\uff09<\/li>\n\n\n\n<li>\u30c7\u30fc\u30bf\u306e\u5206\u5e03\u304c\u5de6\u53f3\u975e\u5bfe\u79f0\u3067\u3042\u308b<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3068\u3044\u3063\u305f\u72b6\u6cc1\u3067\u3082\u3001\u7d50\u679c\u304c\u5927\u304d\u304f\u632f\u308a\u56de\u3055\u308c\u306a\u3044\u3002\u6b63\u898f\u5206\u5e03\u3092\u4eee\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u306a\u3044\u306e\u306f\u3001\u3053\u306e\u300c\u52dd\u3061\u8ca0\u3051\u3060\u3051\u3092\u898b\u308b\u300d\u8a2d\u8a08\u306e\u304a\u304b\u3052\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b9f\u306f\u300c\u6642\u9593\u300d\u3068\u306e\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u305d\u306e\u3082\u306e<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\uff08\u03c4\uff09\u306e\u8a18\u4e8b\u3067\u306f\u30012\u3064\u306e\u5909\u6570x\u3068y\u306b\u3064\u3044\u3066\u300c\u30da\u30a2\u306e\u5927\u5c0f\u95a2\u4fc2\u304c\u305d\u308d\u3063\u3066\u3044\u308b\u304b\uff08\u4e00\u81f4\uff09\u3001\u9006\u306b\u306a\u3063\u3066\u3044\u308b\u304b\uff08\u4e0d\u4e00\u81f4\uff09\u300d\u3092\u6570\u3048\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">MK\u691c\u5b9a\u306f\u3001\u3053\u306ex\u306b <strong>\u6642\u9593\uff081, 2, 3, \u2026, 120\u304b\u6708\u76ee\uff09<\/strong> \u3092\u5165\u308c\u305f\u3082\u306e\u306b\u307b\u304b\u306a\u3089\u306a\u3044\u3002\u6642\u9593\u306f\u5fc5\u305a\u300c\u5f8c\u308d\u306e\u65b9\u304c\u5927\u304d\u3044\u300d\u306e\u3067\u3001y\u304c\u300c\u5f8c\u308d\u306e\u65b9\u304c\u5927\u304d\u3044\u300d\u306a\u3089\u4e00\u81f4(+1)\u3001\u300c\u5f8c\u308d\u306e\u65b9\u304c\u5c0f\u3055\u3044\u300d\u306a\u3089\u4e0d\u4e00\u81f4(\u22121)\u306b\u306a\u308b\u3002\u63e1\u624b\u306e\u80cc\u6bd4\u3079\u3068\u307e\u3063\u305f\u304f\u540c\u3058\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3057\u305f\u304c\u3063\u3066\u3001MK\u691c\u5b9a\u306e\u7d50\u679c\u306b\u306fKendall\u306e\u03c4\u304c\u4e00\u7dd2\u306b\u51fa\u3066\u304f\u308b\u3002\u03c4\u306f \u22121\u301c+1 \u306e\u5024\u3092\u53d6\u308a\u3001<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>+1\uff1a\u6bce\u6708\u5fc5\u305a\u524d\u306e\u6708\u3092\u3059\u3079\u3066\u4e0a\u56de\u308b\uff08\u5b8c\u5168\u306a\u53f3\u80a9\u4e0a\u304c\u308a\uff09<\/li>\n\n\n\n<li>0\uff1a\u4e0a\u4e0b\u306e\u50be\u5411\u306a\u3057<\/li>\n\n\n\n<li>\u22121\uff1a\u5b8c\u5168\u306a\u53f3\u80a9\u4e0b\u304c\u308a<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3092\u610f\u5473\u3059\u308b\u3002\u03c4\u306f\u300c\u50be\u5411\u306e\u4e00\u8cab\u6027\u300d\u3092\u8868\u3059\u52b9\u679c\u91cf\u3068\u3057\u3066\u8aad\u3080\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1a\u300c\u5358\u8abf\u306a\u50be\u5411\u300d\u3063\u3066\u3069\u3046\u3044\u3046\u610f\u5473\uff1f<\/strong><br>MK\u691c\u5b9a\u304c\u898b\u3064\u3051\u3089\u308c\u308b\u306e\u306f\u300c\u5358\u8abf\u306a\uff08monotonic\uff09\u300d\u50be\u5411\u3067\u3042\u308b\u3002\u5358\u8abf\u3068\u306f\u300c\u9014\u4e2d\u3067\u5411\u304d\u304c\u5909\u308f\u3089\u306a\u3044\u300d\u3068\u3044\u3046\u610f\u5473\u3067\u3001\u76f4\u7dda\u3067\u3042\u308b\u5fc5\u8981\u306f\u306a\u3044\u3002\u3086\u308b\u3084\u304b\u306a\u5742\u3067\u3082\u3001\u9014\u4e2d\u304b\u3089\u6025\u306b\u306a\u308b\u5742\u3067\u3082\u3001\u305a\u3063\u3068\u4e0a\u308a\u7d9a\u3051\u3066\u3044\u308c\u3070\u300c\u5358\u8abf\u5897\u52a0\u300d\u3060\u3002\u9006\u306b\u30015\u5e74\u9593\u4e0a\u304c\u3063\u30665\u5e74\u9593\u4e0b\u304c\u308b\u300c\u5c71\u578b\u300d\u306e\u30c7\u30fc\u30bf\u3067\u306f\u3001\u524d\u534a\u306e+1\u3068\u5f8c\u534a\u306e\u22121\u304c\u6253\u3061\u6d88\u3057\u5408\u3044\u3001S\u304c0\u306b\u8fd1\u3065\u3044\u3066\u3057\u307e\u3046\u3002MK\u691c\u5b9a\u306f\u300c\u5c71\u767b\u308a\u306e\u9014\u4e2d\u3067\u5f15\u304d\u8fd4\u3057\u305f\u304b\u3069\u3046\u304b\u300d\u306f\u6559\u3048\u3066\u304f\u308c\u306a\u3044\u3002<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2. \u50be\u304d\u306e\u300c\u5927\u304d\u3055\u300d\u306fSen&#8217;s slope\u3067\u8a9e\u308b<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">MK\u691c\u5b9a\u304c\u7b54\u3048\u3066\u304f\u308c\u306a\u3044\u3053\u3068<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">MK\u691c\u5b9a\u304c\u7b54\u3048\u308b\u306e\u306f\u300c\u4e00\u8cab\u3057\u3066\u4e0a\u304c\u3063\u3066\u3044\u308b\uff08\u4e0b\u304c\u3063\u3066\u3044\u308b\uff09\u3068\u8a00\u3048\u308b\u304b\u300d\u3068\u3044\u3046 <strong>\u5411\u304d<\/strong> \u306e\u554f\u3044\u3060\u3051\u3067\u3042\u308b\u3002\u300c1\u304b\u6708\u3042\u305f\u308a\u4f55\u676f\u5897\u3048\u3066\u3044\u308b\u306e\u304b\u300d\u3068\u3044\u3046 <strong>\u5927\u304d\u3055<\/strong> \u306b\u306f\u7b54\u3048\u306a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u3067\u5927\u4e8b\u306a\u6ce8\u610f\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>P\u5024\u304c\u5c0f\u3055\u3044\u3053\u3068\u306f\u3001\u300c\u6025\u6fc0\u306b\u5897\u3048\u3066\u3044\u308b\u300d\u3053\u3068\u3092\u610f\u5473\u3057\u306a\u3044\u3002<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">MK\u691c\u5b9a\u306eP\u5024\u306f\u3001\u30c7\u30fc\u30bf\u306e\u6570\uff08\u671f\u9593\u306e\u9577\u3055\uff09\u304c\u5897\u3048\u308b\u307b\u3069\u5c0f\u3055\u304f\u306a\u308a\u3084\u3059\u3044\u3002100\u5e74\u5206\u306e\u6c17\u6e29\u30c7\u30fc\u30bf\u306a\u3089\u3001\u5e740.01\u2103\u3068\u3044\u3046\u3054\u304f\u308f\u305a\u304b\u306a\u4e0a\u6607\u3067\u3082 P &lt; 0.001 \u306b\u306a\u308a\u5f97\u308b\u3002P\u5024\u306f\u3042\u304f\u307e\u3067\u300c\u5076\u7136\u3068\u306f\u8003\u3048\u306b\u304f\u3044\u304b\u300d\u306e\u5224\u65ad\u6750\u6599\u3067\u3042\u308a\u3001\u5909\u5316\u306e\u5927\u304d\u3055\u306e\u7269\u5dee\u3057\u3067\u306f\u306a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5927\u304d\u3055\u3092\u8a9e\u308b\u3068\u304d\u306b\u4f7f\u3046\u306e\u304c\u3001<strong>Sen&#8217;s slope\uff08\u30bb\u30f3\u306e\u50be\u304d\uff09<\/strong> \u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5168\u30da\u30a2\u306e\u50be\u304d\u306e\u300c\u771f\u3093\u4e2d\u300d\u3092\u53d6\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Sen&#8217;s slope\u306e\u8003\u3048\u65b9\u3082\u3001\u63e1\u624b\u306e\u6bd4\u55a9\u3067\u8aac\u660e\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u63e1\u624b\u3057\u305f2\u3064\u306e\u6708\u306e\u30da\u30a2\u3054\u3068\u306b\u3001\u300c2\u304b\u6708\u306e\u58f2\u4e0a\u306e\u5dee \u00f7 2\u304b\u6708\u306e\u9593\u9694\u300d\u3092\u8a08\u7b97\u3059\u308c\u3070\u3001\u305d\u306e\u30da\u30a2\u306a\u308a\u306e\u300c\u50be\u304d\u300d\u304c1\u3064\u51fa\u308b\u30027,140\u7d44\u3042\u308c\u3070\u30017,140\u901a\u308a\u306e\u50be\u304d\u304c\u624b\u306b\u5165\u308b\u3002\u305d\u306e <strong>\u4e2d\u592e\u5024<\/strong> \u3092\u53d6\u3063\u305f\u3082\u306e\u304cSen&#8217;s slope\u3067\u3042\u308b\uff08Sen, 1968\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">7,140\u4eba\u306b\u300c\u3053\u306e10\u5e74\u30671\u304b\u6708\u3042\u305f\u308a\u4f55\u676f\u5897\u3048\u305f\u3068\u601d\u3046\uff1f\u300d\u3068\u805e\u304d\u3001\u305d\u306e\u7b54\u3048\u3092\u5c0f\u3055\u3044\u9806\u306b\u4e26\u3079\u3066\u771f\u3093\u4e2d\u306e\u4eba\u306e\u7b54\u3048\u3092\u63a1\u7528\u3059\u308b\u3002\u305d\u3093\u306a\u300c\u591a\u6570\u6c7a\u306e\u771f\u3093\u4e2d\u300d\u3092\u30a4\u30e1\u30fc\u30b8\u3059\u308b\u3068\u3088\u3044\u3002\u4e2d\u592e\u5024\u306a\u306e\u3067\u3001\u6975\u7aef\u306a\u7b54\u3048\uff08\u5916\u308c\u5024\u306e\u5f71\u97ff\u3092\u53d7\u3051\u305f\u30da\u30a2\uff09\u304c\u7d1b\u308c\u8fbc\u3093\u3067\u3082\u3001\u7d50\u679c\u306f\u307b\u3068\u3093\u3069\u52d5\u304b\u306a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sen&#8217;s slope\u306f\u5143\u306e\u30c7\u30fc\u30bf\u3068\u540c\u3058\u5358\u4f4d\uff08\u3053\u3053\u3067\u306f\u300c\u676f\uff0f\u6708\u300d\uff09\u3092\u6301\u3064\u305f\u3081\u3001\u300c1\u304b\u6708\u3042\u305f\u308a\u7d040.5\u676f\u30011\u5e74\u3067\u7d046\u676f\u5897\u3048\u3066\u3044\u308b\u300d\u306e\u3088\u3046\u306b\u3001\u305d\u306e\u307e\u307e\u73fe\u5834\u306e\u8a00\u8449\u306b\u7ffb\u8a33\u3067\u304d\u308b\u3002\u8ad6\u6587\u3084\u5831\u544a\u3067\u306f\u3001<strong>MK\u691c\u5b9a\u306eP\u5024\u3068Sen&#8217;s slope\uff08\u3068\u305d\u306e95%\u4fe1\u983c\u533a\u9593\uff09\u3092\u30bb\u30c3\u30c8\u3067\u793a\u3059<\/strong>\u306e\u304c\u57fa\u672c\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div id=\"biost-350143196\" class=\"biost- biost-entity-placement\"><p style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><a href=\"https:\/\/best-biostatistics.com\/kmhl\">\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 href=\"https:\/\/best-biostatistics.com\/kmhl\"><img class=\"aligncenter wp-image-2794 size-full\" src=\"https:\/\/best-biostatistics.com\/wp\/wp-content\/uploads\/2023\/11\/bn_r_03.png\" alt=\"\" width=\"500\" height=\"327\" \/><\/a>\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000; font-size: 20px;\"><strong><span class=\"marker2\">\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div><h2 class=\"wp-block-heading\">3. \u521d\u5b66\u8005\u304c\u30cf\u30de\u308b3\u3064\u306e\u7f60<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">MK\u691c\u5b9a\u306f\u5358\u7d14\u3067\u9811\u5065\u306a\u624b\u6cd5\u3060\u304c\u3001\u4e07\u80fd\u3067\u306f\u306a\u3044\u3002\u7279\u306b\u6b21\u306e3\u3064\u306f\u3001\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u5206\u6790\u3067\u983b\u7e41\u306b\u554f\u984c\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7f60\u2460\uff1a\u81ea\u5df1\u76f8\u95a2 \u2015\u300c\u4ef2\u826f\u3057\u30b0\u30eb\u30fc\u30d7\u306e\u591a\u6570\u6c7a\u300d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">MK\u691c\u5b9a\u306f\u3001\u5404\u6708\u306e\u30c7\u30fc\u30bf\u304c <strong>\u4e92\u3044\u306b\u72ec\u7acb\u3067\u3042\u308b<\/strong> \u3053\u3068\u3092\u524d\u63d0\u306b\u3057\u3066\u3044\u308b\u3002\u3068\u3053\u308d\u304c\u5b9f\u969b\u306e\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u306f\u3001\u305f\u3044\u3066\u3044\u300c\u5148\u6708\u306e\u72b6\u614b\u3092\u5f15\u304d\u305a\u308b\u300d\u3002\u3088\u304f\u58f2\u308c\u305f\u6708\u306e\u7fcc\u6708\u3082\u3088\u304f\u58f2\u308c\u3084\u3059\u304f\u3001\u4e0d\u8abf\u306e\u6708\u306e\u7fcc\u6708\u3082\u4e0d\u8abf\u306b\u306a\u308a\u3084\u3059\u3044\u3002\u3053\u308c\u3092 <strong>\u81ea\u5df1\u76f8\u95a2<\/strong>\uff08\u7cfb\u5217\u76f8\u95a2\uff09\u3068\u3044\u3046\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u308c\u306f\u3001\u30af\u30e9\u30b9\u3067\u591a\u6570\u6c7a\u3092\u3068\u308b\u3068\u304d\u306b\u3001\u3044\u3064\u3082\u540c\u3058\u610f\u898b\u3092\u8a00\u3044\u5408\u3046\u4ef2\u826f\u3057\u30b0\u30eb\u30fc\u30d7\u304c\u6df7\u3056\u3063\u3066\u3044\u308b\u72b6\u6cc1\u306b\u4f3c\u3066\u3044\u308b\u300230\u4eba\u306e\u30af\u30e9\u30b9\u3067\u3082\u30015\u4eba\u7d44\u306e\u4ef2\u826f\u3057\u30b0\u30eb\u30fc\u30d7\u304c6\u3064\u3042\u308b\u306a\u3089\u3001\u5b9f\u8cea\u7684\u306b\u306f\u300c6\u7968\u5206\u306e\u72ec\u7acb\u3057\u305f\u610f\u898b\u300d\u3057\u304b\u306a\u3044\u3002\u305d\u308c\u309230\u7968\u3068\u3057\u3066\u6570\u3048\u308b\u3068\u3001\u300c\u5727\u5012\u7684\u591a\u6570\u3067\u53ef\u6c7a\uff01\u300d\u3068\u3001\u5b9f\u614b\u4ee5\u4e0a\u306b\u81ea\u4fe1\u6e80\u3005\u306a\u7d50\u8ad6\u304c\u51fa\u3066\u3057\u307e\u3046\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b63\u306e\u81ea\u5df1\u76f8\u95a2\u304c\u3042\u308b\u6642\u7cfb\u5217\u306b\u305d\u306e\u307e\u307eMK\u691c\u5b9a\u3092\u4f7f\u3046\u3068\u3001\u3053\u308c\u3068\u540c\u3058\u3053\u3068\u304c\u8d77\u304d\u308b\u3002S\u306e\u6563\u3089\u3070\u308a\u304c\u672c\u6765\u3088\u308a\u5c0f\u3055\u304f\u898b\u7a4d\u3082\u3089\u308c\u3001<strong>\u5b9f\u969b\u306b\u306f\u50be\u5411\u304c\u306a\u3044\u306e\u306b\u300c\u6709\u610f\u306a\u30c8\u30ec\u30f3\u30c9\u3042\u308a\u300d\u3068\u5224\u5b9a\u3057\u3066\u3057\u307e\u3046\u78ba\u7387\uff08\u7b2c\u4e00\u7a2e\u306e\u904e\u8aa4\uff09\u304c\u9ad8\u304f\u306a\u308b<\/strong> \u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\uff08Hamed &amp; Rao, 1998; Yue et al., 2002\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee3\u8868\u7684\u306a\u5bfe\u51e6\u6cd5\u306f2\u3064\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5206\u6563\u306e\u88dc\u6b63\uff08Hamed &amp; Rao, 1998\uff09<\/strong>\uff1a\u81ea\u5df1\u76f8\u95a2\u306e\u5f37\u3055\u304b\u3089\u300c\u5b9f\u8cea\u7684\u306a\u30c7\u30fc\u30bf\u6570\uff08\u6709\u52b9\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\uff09\u300d\u3092\u898b\u7a4d\u3082\u308a\u3001S\u306e\u5206\u6563\u3092\u5e83\u3052\u3066\u88dc\u6b63\u3059\u308b\u3002\u4ef2\u826f\u3057\u30b0\u30eb\u30fc\u30d7\u3092\u300c1\u30b0\u30eb\u30fc\u30d7\uff1d\u5b9f\u8cea1\u7968\u300d\u3068\u3057\u3066\u6570\u3048\u76f4\u3059\u30a4\u30e1\u30fc\u30b8\u3067\u3042\u308b<\/li>\n\n\n\n<li><strong>\u30d7\u30ea\u30db\u30ef\u30a4\u30c8\u30cb\u30f3\u30b0\uff08Yue et al., 2002 \u306a\u3069\uff09<\/strong>\uff1a\u30c7\u30fc\u30bf\u304b\u3089\u81ea\u5df1\u76f8\u95a2\u306e\u6210\u5206\u3092\u53d6\u308a\u9664\u3044\u3066\u304b\u3089\u691c\u5b9a\u3059\u308b<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u8a18\u4e8b\u3067\u306f\u3001\u8003\u3048\u65b9\u304c\u308f\u304b\u308a\u3084\u3059\u304f\u5b9f\u88c5\u3082\u7c21\u5358\u306a\u524d\u8005\uff08Hamed &amp; Rao\u306e\u88dc\u6b63\uff09\u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1a\u81ea\u5df1\u76f8\u95a2\u3068\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u306e\u8aad\u307f\u65b9<\/strong><br>\u81ea\u5df1\u76f8\u95a2\u306f\u3001\u300c\u30c7\u30fc\u30bf\u3092 k \u304b\u6708\u305a\u3089\u3057\u305f\u3082\u306e\u300d\u3068\u300c\u5143\u306e\u30c7\u30fc\u30bf\u300d\u306e\u76f8\u95a2\u4fc2\u6570\u3067\u3042\u308b\u3002k\u30921, 2, 3, \u2026\u3068\u5909\u3048\u306a\u304c\u3089\u76f8\u95a2\u4fc2\u6570\u3092\u68d2\u30b0\u30e9\u30d5\u306b\u3057\u305f\u3082\u306e\u3092 <strong>\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0<\/strong> \u3068\u547c\u3073\u3001R\u3067\u306f <code>acf()<\/code> \u95a2\u6570\u3067\u63cf\u3051\u308b\u3002\u9752\u3044\u70b9\u7dda\u306f\u300c\u81ea\u5df1\u76f8\u95a2\u304c\u30bc\u30ed\u3067\u3082\u5076\u7136\u3053\u306e\u7a0b\u5ea6\u306f\u51fa\u308b\u300d\u3068\u3044\u3046\u76ee\u5b89\u306e\u7bc4\u56f2\u3060\u3002\u68d2\u304c\u3053\u306e\u7bc4\u56f2\u3092\u5927\u304d\u304f\u306f\u307f\u51fa\u3057\u3066\u3044\u308c\u3070\u3001\u81ea\u5df1\u76f8\u95a2\u304c\u3042\u308b\u3002\u30e9\u30b01\uff081\u304b\u6708\u305a\u3089\u3057\uff09\u306e\u68d2\u304c\u9ad8\u3051\u308c\u3070\u300c\u5148\u6708\u3092\u5f15\u304d\u305a\u308b\u300d\u30bf\u30a4\u30d7\u3001\u30e9\u30b012\u306e\u68d2\u304c\u9ad8\u3051\u308c\u3070\u300c\u6bce\u5e74\u540c\u3058\u6708\u306b\u540c\u3058\u3088\u3046\u306a\u5024\u306b\u306a\u308b\u300d\u3001\u3064\u307e\u308a\u5b63\u7bc0\u6027\u304c\u3042\u308b\u30b5\u30a4\u30f3\u3067\u3042\u308b\u3002\u305f\u3060\u3057\u3001\u3086\u308b\u3084\u304b\u306a\u5b63\u7bc0\u306e\u6ce2\u3084\u30c8\u30ec\u30f3\u30c9\u304c\u3042\u308b\u3060\u3051\u3067\u3082\u30e9\u30b01\u306e\u68d2\u306f\u9ad8\u304f\u306a\u308b\uff08\u96a3\u306e\u6708\u540c\u58eb\u306f\u3001\u6ce2\u306e\u4e0a\u3067\u8fd1\u3044\u4f4d\u7f6e\u306b\u3044\u308b\u305f\u3081\uff09\u3002\u7d14\u7c8b\u306a\u300c\u5f15\u304d\u305a\u308a\u300d\u3092\u898b\u305f\u3044\u3068\u304d\u306f\u3001\u30c8\u30ec\u30f3\u30c9\u3068\u5b63\u7bc0\u3092\u53d6\u308a\u9664\u3044\u305f <strong>\u6b8b\u5dee<\/strong> \u306e\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u3092\u898b\u308b\u306e\u304c\u78ba\u5b9f\u3067\u3042\u308b\uff08Step 5\u3067\u5b9f\u6f14\u3059\u308b\uff09\u3002<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">\u7f60\u2461\uff1a\u5b63\u7bc0\u6027 \u2015\u300c7\u6708\u30681\u6708\u3067\u80cc\u6bd4\u3079\u3092\u3057\u306a\u3044\u300d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u30a2\u30a4\u30b9\u30b3\u30fc\u30d2\u30fc\u306f\u590f\u306b\u58f2\u308c\u3001\u51ac\u306b\u306f\u58f2\u308c\u306a\u3044\u3002\u3053\u306e\u3088\u3046\u306a\u5b63\u7bc0\u306e\u6ce2\u3092\u6301\u3064\u30c7\u30fc\u30bf\u306bMK\u691c\u5b9a\u3092\u305d\u306e\u307e\u307e\u4f7f\u3046\u3068\u3001\u63e1\u624b\u306e\u80cc\u6bd4\u3079\u306f\u300c7\u6708 vs \u7fcc\u5e741\u6708\u300d\u306e\u3088\u3046\u306a\u3001\u5b63\u7bc0\u306e\u9055\u3044\u304c\u4e38\u3054\u3068\u5165\u308a\u8fbc\u3093\u3060\u6bd4\u8f03\u3060\u3089\u3051\u306b\u306a\u308b\u3002\u3053\u308c\u3067\u306f\u3001\u5e74\u3054\u3068\u306b\u58f2\u4e0a\u304c\u4f38\u3073\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3068\u3044\u3046\u672c\u6765\u306e\u554f\u3044\u304c\u3001\u590f\u51ac\u306e\u6ce2\u306b\u57cb\u3082\u308c\u3066\u3057\u307e\u3046\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u305d\u3053\u3067\u4f7f\u3046\u306e\u304c <strong>Seasonal Kendall\u691c\u5b9a<\/strong>\uff08\u5b63\u7bc0\u578bMann-Kendall\u691c\u5b9a\u3001Hirsch et al., 1982\uff09\u3067\u3042\u308b\u3002\u3084\u308a\u65b9\u306f\u5358\u7d14\u3067\u3001<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>1\u6708\u306f1\u6708\u540c\u58eb\u30012\u6708\u306f2\u6708\u540c\u58eb\u2026\u2026\u3068 <strong>\u540c\u3058\u6708\u306e\u4e2d\u3060\u3051\u3067<\/strong> \u80cc\u6bd4\u3079\uff08MK\u691c\u5b9a\u306eS\uff09\u3092\u884c\u3046<\/li>\n\n\n\n<li>12\u304b\u6708\u5206\u306eS\u3068\u5206\u6563\u3092\u5408\u8a08\u3057\u3066\u3001\u5168\u4f53\u3068\u3057\u3066\u5224\u5b9a\u3059\u308b<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u3068\u3044\u3046\u3082\u306e\u3060\u3002\u300c7\u6708\u306e\u6210\u7e3e\u306f\u3001\u53bb\u5e74\u306e7\u6708\u3068\u6bd4\u3079\u308b\u300d\u3002\u524d\u5e74\u540c\u6708\u6bd4\u306e\u767a\u60f3\u3068\u540c\u3058\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u540c\u69d8\u306b\u3001\u50be\u304d\u3082\u540c\u3058\u6708\u540c\u58eb\u306e\u30da\u30a2\u3060\u3051\u304b\u3089\u8a08\u7b97\u3059\u308b <strong>\u5b63\u7bc0\u578bSen&#8217;s slope<\/strong> \u304c\u3042\u308b\u3002\u3053\u3061\u3089\u306f\u300c1\u5e74\u3042\u305f\u308a\u4f55\u676f\u5897\u3048\u305f\u304b\u300d\u3068\u3044\u3046\u5358\u4f4d\u3067\u5f97\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u305f\u3060\u3057\u3001\u5b63\u7bc0\u578b\u306b\u3057\u3066\u3082\u7f60\u2460\uff08\u81ea\u5df1\u76f8\u95a2\uff09\u304c\u6d88\u3048\u308b\u308f\u3051\u3067\u306f\u306a\u3044\u3002\u6708\u3068\u6708\u304c\u9023\u52d5\u3057\u3066\u3044\u308b\u30c7\u30fc\u30bf\u3067\u306f\u3001\u3055\u3089\u306b\u88dc\u6b63\u304c\u5fc5\u8981\u306b\u306a\u308b\uff08Hirsch &amp; Slack, 1984\uff09\u3002\u3053\u306e\u70b9\u306fR\u306e\u5b9f\u88c5\u7de8\uff08Step 8\uff09\u3067\u78ba\u304b\u3081\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7f60\u2462\uff1a\u9014\u4e2d\u3067\u6d41\u308c\u304c\u5909\u308f\u308b \u2015\u300c\u5c71\u767b\u308a\u306e\u9014\u4e2d\u3067\u5f15\u304d\u8fd4\u3057\u305f\u300d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u30b3\u30e9\u30e0\u3067\u8ff0\u3079\u305f\u3068\u304a\u308a\u3001MK\u691c\u5b9a\u306f\u300c\u5168\u671f\u9593\u3092\u901a\u3057\u3066\u4e00\u65b9\u5411\u304b\u300d\u3057\u304b\u554f\u308f\u306a\u3044\u3002\u300c\u6700\u521d\u306e5\u5e74\u306f\u5897\u3048\u3066\u3044\u305f\u304c\u3001\u3042\u308b\u6642\u70b9\u304b\u3089\u6e1b\u308a\u59cb\u3081\u305f\u300d\u3088\u3046\u306a\u30c7\u30fc\u30bf\u3067\u306f\u3001MK\u691c\u5b9a\u306f\u300c\u50be\u5411\u306a\u3057\u300d\u3068\u7b54\u3048\u308b\u3053\u3068\u304c\u3042\u308a\u3001\u305d\u308c\u306f\u300c\u4f55\u3082\u8d77\u304d\u3066\u3044\u306a\u3044\u300d\u3068\u3044\u3046\u610f\u5473\u3067\u306f\u306a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c\u3069\u3053\u3067\u6d41\u308c\u304c\u5909\u308f\u3063\u305f\u306e\u304b\u300d\u3092\u77e5\u308a\u305f\u3044\u5834\u5408\u306f\u3001<strong>\u5909\u5316\u70b9\u691c\u51fa<\/strong> \u306e\u624b\u6cd5\uff08Pettitt\u691c\u5b9a\u306a\u3069\uff09\u3092\u4f7f\u3046\u3002\u533b\u5b66\u5206\u91ce\u3067\u3082\u3001Chen\u3089\uff082022\uff09\u304c\u7c73\u56fd\u5404\u5dde\u306eCOVID-19\u9031\u6b21\u75c7\u4f8b\u6570\u306b\u3001MK\u691c\u5b9a\u3092\u5fdc\u7528\u3057\u305f\u5909\u5316\u70b9\u691c\u51fa\u6cd5\uff08Mann-Kendall-Sneyers\u691c\u5b9a\uff09\u3092\u9069\u7528\u3057\u3001\u6d41\u884c\u306e\u5897\u52a0\u30fb\u6e1b\u5c11\u306e\u8ee2\u63db\u70b9\u3092\u7279\u5b9a\u3057\u3066\u3044\u308b\u3002\u672c\u8a18\u4e8b\u3067\u306f\u8a73\u3057\u304f\u6271\u308f\u306a\u3044\u304c\u3001\u300cMK\u691c\u5b9a\u3067\u6709\u610f\u3067\u306a\u3044\uff1d\u5909\u5316\u306a\u3057\u3001\u3068\u306f\u9650\u3089\u306a\u3044\u300d\u3053\u3068\u306f\u982d\u306b\u5165\u308c\u3066\u304a\u304d\u305f\u3044\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">4. R\u3067\u5b9f\u88c5\u3057\u3066\u307f\u3088\u3046\uff08Step by Step\uff09<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u304b\u3089\u306f\u3001\u55ab\u8336\u5e97\u306e\u30a2\u30a4\u30b9\u30b3\u30fc\u30d2\u30fc\u58f2\u4e0a\u3092\u6a21\u3057\u305f\u7591\u4f3c\u30c7\u30fc\u30bf\u3067\u3001\u3053\u3053\u307e\u3067\u306e\u5185\u5bb9\u3092\u78ba\u8a8d\u3057\u3066\u3044\u304f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f7f\u7528\u3059\u308b\u30d1\u30c3\u30b1\u30fc\u30b8\u306f\u6b21\u306e3\u3064\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>Kendall<\/code>\uff1a\u524d\u56de\u306e\u8a18\u4e8b\u3067\u3082\u4f7f\u3063\u305f\u30d1\u30c3\u30b1\u30fc\u30b8\u3002<code>MannKendall()<\/code> \u95a2\u6570\u3067\u57fa\u672c\u306eMK\u691c\u5b9a\u304c\u3067\u304d\u308b<\/li>\n\n\n\n<li><code>trend<\/code>\uff1aSen&#8217;s slope\uff08<code>sens.slope()<\/code>\uff09\u3001Seasonal Kendall\u691c\u5b9a\uff08<code>smk.test()<\/code>\uff09\u3001\u76f8\u95a2\u88dc\u6b63\u4ed8\u304dSeasonal Kendall\u691c\u5b9a\uff08<code>csmk.test()<\/code>\uff09\u3001\u5b63\u7bc0\u578bSen&#8217;s slope\uff08<code>sea.sens.slope()<\/code>\uff09\u306a\u3069<\/li>\n\n\n\n<li><code>modifiedmk<\/code>\uff1a\u81ea\u5df1\u76f8\u95a2\u3092\u88dc\u6b63\u3057\u305fMK\u691c\u5b9a\uff08<code>mmkh()<\/code>\uff09<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>install.packages(c(\"Kendall\", \"trend\", \"modifiedmk\"))\n\nlibrary(Kendall)\nlibrary(trend)\nlibrary(modifiedmk)<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1\uff1a\u7591\u4f3c\u30c7\u30fc\u30bf\u3092\u4f5c\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2016\u5e741\u6708\u301c2025\u5e7412\u6708\u306e120\u304b\u6708\u5206\u306e\u58f2\u4e0a\uff08\u676f\uff0f\u6708\uff09\u3092\u3001\u6b21\u306e3\u3064\u306e\u8981\u7d20\u3092\u8db3\u3057\u5408\u308f\u305b\u3066\u4f5c\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u30c8\u30ec\u30f3\u30c9<\/strong>\uff1a1\u304b\u6708\u3042\u305f\u308a0.3\u676f\u305a\u3064\u5897\u3048\u308b\uff08\u3053\u308c\u304c\u300c\u771f\u306e\u50be\u304d\u300d\uff09<\/li>\n\n\n\n<li><strong>\u5b63\u7bc0\u6027<\/strong>\uff1a8\u6708\u3092\u30d4\u30fc\u30af\u306b\u3001\u590f\u306f\uff0b40\u676f\u3001\u51ac\u306f\u221240\u676f\u307b\u3069\u4e0a\u4e0b\u3059\u308b\u6ce2<\/li>\n\n\n\n<li><strong>\u81ea\u5df1\u76f8\u95a2\u306e\u3042\u308b\u8aa4\u5dee<\/strong>\uff1a\u524d\u6708\u306e\u8aa4\u5dee\u306e7\u5272\u3092\u5f15\u304d\u7d99\u3050\u30ce\u30a4\u30ba\uff08AR(1)\u30e2\u30c7\u30eb\u3001\u4fc2\u65700.7\uff09<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u7f60\u2460\u3068\u7f60\u2461\u304c\u3061\u3083\u3093\u3068\u518d\u73fe\u3055\u308c\u308b\u3088\u3046\u306b\u3001\u3042\u3048\u3066\u300c\u5b63\u7bc0\u306e\u6ce2\u300d\u3068\u300c\u5148\u6708\u3092\u5f15\u304d\u305a\u308b\u30af\u30bb\u300d\u3092\u4ed5\u8fbc\u3093\u3067\u3044\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>set.seed(32)\n\nn     &lt;- 120                        # 10\u5e74 \u00d7 12\u304b\u6708\nt     &lt;- 1:n                        # \u6642\u9593\uff081\u301c120\u304b\u6708\u76ee\uff09\nmonth &lt;- rep(1:12, times = 10)      # \u6708\uff081\u301c12\uff09\n\ntrend  &lt;- 0.3 * t                                  # \u771f\u306e\u30c8\u30ec\u30f3\u30c9\uff1a\u67080.3\u676f\u5897\nseason &lt;- 40 * cos(2 * pi * (month - 8) \/ 12)      # 8\u6708\u30d4\u30fc\u30af\u306e\u5b63\u7bc0\u306e\u6ce2\nnoise  &lt;- as.numeric(arima.sim(model = list(ar = 0.7), n = n, sd = 20))  # \u81ea\u5df1\u76f8\u95a2\u306e\u3042\u308b\u8aa4\u5dee\n\nsales &lt;- round(300 + trend + season + noise)\n\n# \u6642\u7cfb\u5217\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff08ts\uff09\u306b\u5909\u63db\uff1a2016\u5e741\u6708\u958b\u59cb\u30011\u5e74=12\u671f\nsales_ts &lt;- ts(sales, start = c(2016, 1), frequency = 12)<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2\uff1a\u307e\u305a\u306f\u30b0\u30e9\u30d5\u3067\u76ee\u8996\u3059\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u3069\u3093\u306a\u691c\u5b9a\u3092\u3059\u308b\u306b\u3057\u3066\u3082\u3001\u6700\u521d\u306b\u3084\u308b\u3079\u304d\u306f\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3053\u3068\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>plot(sales_ts, type = \"o\", pch = 16, cex = 0.6,\n     xlab = \"Year\", ylab = \"Iced coffee sales (cups\/month)\",\n     main = \"Monthly iced coffee sales\")<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"800\" height=\"500\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step2.png\" alt=\"\" class=\"wp-image-4828\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step2.png 800w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step2-300x188.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step2-768x480.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb\u3084\u8ef8\u30e9\u30d9\u30eb\u306f\u82f1\u8a9e\u306b\u3057\u3066\u3044\u308b\u3002Mac\u306a\u3069\u3067\u306f\u3001\u30d5\u30a9\u30f3\u30c8\u3092\u6307\u5b9a\u305b\u305a\u306b\u65e5\u672c\u8a9e\u3092\u4f7f\u3046\u3068\u6587\u5b57\u304c\u300c\u25a1\u300d\uff08\u3044\u308f\u3086\u308b\u8c46\u8150\uff09\u306b\u5316\u3051\u308b\u3053\u3068\u304c\u3042\u308b\u305f\u3081\u3060\u3002<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bce\u5e74\u590f\u306b\u5c71\u3001\u51ac\u306b\u8c37\u304c\u6765\u308b\u6ce2\u304c\u306f\u3063\u304d\u308a\u898b\u3048\u308b\u3002\u305d\u306e\u3046\u3048\u3067\u3001\u6ce2\u5168\u4f53\u304c\u3086\u308b\u3084\u304b\u306b\u53f3\u4e0a\u304c\u308a\u306b\u306a\u3063\u3066\u3044\u308b\u3088\u3046\u306b\u3082\u898b\u3048\u308b\u3002\u305f\u3060\u30572018\u301c2019\u5e74\u3054\u308d\u306b\u306f\u4e00\u5ea6\u843d\u3061\u8fbc\u3093\u3067\u304a\u308a\u3001\u300c10\u5e74\u3067\u4f38\u3073\u3066\u3044\u308b\u300d\u3068\u8a00\u3044\u5207\u3063\u3066\u3088\u3044\u304b\u306f\u3001\u76ee\u8996\u3060\u3051\u3067\u306f\u5224\u65ad\u3057\u306b\u304f\u3044\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3\uff1a\u57fa\u672c\u306eMK\u691c\u5b9a<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u307e\u305a\u306f\u7f60\u3092\u6c17\u306b\u305b\u305a\u3001\u305d\u306e\u307e\u307eMK\u691c\u5b9a\u3092\u304b\u3051\u3066\u307f\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>MannKendall(sales)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u51fa\u529b\u306b\u306f <code>tau<\/code>\uff08Kendall\u306e\u03c4\uff09\u3068 <code>2-sided pvalue<\/code>\uff08\u4e21\u5074P\u5024\uff09\u304c\u8868\u793a\u3055\u308c\u308b\u3002\u7d50\u679c\u306f <strong>\u03c4 = 0.242\u3001P = 9.7\u00d710\u207b\u2075<\/strong>\uff08P &lt; 0.001\uff09\u3067\u3042\u3063\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c\u6642\u9593\u304c\u9032\u3080\u307b\u3069\u58f2\u4e0a\u304c\u5927\u304d\u3044\u300d\u30da\u30a2\u306e\u65b9\u304c\u591a\u304f\u3001\u305d\u306e\u504f\u308a\u306f\u5076\u7136\u3068\u306f\u8003\u3048\u306b\u304f\u3044\u3002\u3064\u307e\u308a\u3001\u7d71\u8a08\u5b66\u7684\u306b\u6709\u610f\u306a\u5897\u52a0\u50be\u5411\u304c\u3042\u308b\u3068\u3044\u3046\u5224\u5b9a\u3067\u3042\u308b\u3002\u03c4 = 0.24 \u306f\u3001\u5b8c\u5168\u306a\u53f3\u80a9\u4e0a\u304c\u308a\uff08\u03c4 = 1\uff09\u306b\u306f\u7a0b\u9060\u3044\u3001\u300c\u6ce2\u3084\u30d6\u30ec\u3092\u542b\u307f\u3064\u3064\u3082\u5168\u4f53\u3068\u3057\u3066\u306f\u4e0a\u5411\u304d\u300d\u7a0b\u5ea6\u306e\u4e00\u8cab\u6027\u3092\u793a\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u53c2\u8003\u307e\u3067\u306b\u3001base R\u306e <code>cor.test(t, sales, method = \"kendall\")<\/code> \u3067\u3082 \u03c4 = 0.242\u3001P = 9.6\u00d710\u207b\u2075 \u3068\u3001\u307b\u307c\u540c\u3058\u7d50\u679c\u304c\u5f97\u3089\u308c\u308b\uff08P\u5024\u306e\u6700\u5f8c\u306e\u6841\u306e\u308f\u305a\u304b\u306a\u5dee\u306f\u3001\u540c\u9806\u4f4d\u306e\u6271\u3044\u3084\u9023\u7d9a\u4fee\u6b63\u3068\u3044\u3063\u305f\u8a08\u7b97\u4e0a\u306e\u7d30\u90e8\u306e\u9055\u3044\u306b\u3088\u308b\uff09\u3002MK\u691c\u5b9a\u304c\u300c\u6642\u9593\u3068\u306e\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u300d\u3067\u3042\u308b\u3053\u3068\u3092\u3001\u81ea\u5206\u306e\u624b\u3067\u78ba\u304b\u3081\u3066\u307f\u3066\u307b\u3057\u3044\u3002<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4\uff1aSen&#8217;s slope\u3067\u50be\u304d\u306e\u5927\u304d\u3055\u3092\u898b\u308b<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>sens.slope(sales)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u51fa\u529b\u306e <code>Sen's slope<\/code> \u304c\u50be\u304d\u306e\u63a8\u5b9a\u5024\u3001<code>95 percent confidence interval<\/code> \u304c\u305d\u306e95%\u4fe1\u983c\u533a\u9593\u3067\u3042\u308b\u3002\u7d50\u679c\u306f <strong>Sen&#8217;s slope = 0.465\u676f\uff0f\u6708\uff0895%\u4fe1\u983c\u533a\u9593 0.234\u301c0.682\uff09<\/strong> \u3067\u3042\u3063\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1\u304b\u6708\u3042\u305f\u308a\u7d040.46\u676f\u30011\u5e74\u306b\u76f4\u3059\u3068\u7d045.6\u676f\u306e\u5897\u52a0\u3067\u3042\u308b\u3002\u6708\u5e73\u5747\u306e\u58f2\u4e0a\u306f\u7d04314\u676f\u306a\u306e\u3067\u3001<strong>1\u5e74\u3042\u305f\u308a2%\u306b\u6e80\u305f\u306a\u3044\u3001\u3054\u304f\u3086\u308b\u3084\u304b\u306a\u4f38\u3073<\/strong>\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308b\u3002Step 3\u306eP\u5024\u306f0.001\u3092\u4e0b\u56de\u3063\u3066\u3044\u305f\u304c\u3001\u305d\u308c\u306f\u300c\u6025\u5897\u3057\u3066\u3044\u308b\u300d\u3053\u3068\u3092\u610f\u5473\u3057\u306a\u3044\u3002\u307e\u3055\u306b\u7b2c2\u7ae0\u3067\u8ff0\u3079\u305f\u3068\u304a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u306a\u304a\u3001\u7591\u4f3c\u30c7\u30fc\u30bf\u306e\u300c\u771f\u306e\u50be\u304d\u300d\u306f0.3\u676f\uff0f\u6708\u3067\u3042\u3063\u305f\u3002\u63a8\u5b9a\u50240.46\u306f\u30ce\u30a4\u30ba\u306e\u5f71\u97ff\u3067\u3084\u3084\u4e0a\u632f\u308c\u3057\u3066\u3044\u308b\u304c\u300195%\u4fe1\u983c\u533a\u9593\u306f\u3061\u3083\u3093\u30680.3\u3092\u542b\u3093\u3067\u3044\u308b\u3002\u70b9\u63a8\u5b9a\u3060\u3051\u3067\u306a\u304f\u4fe1\u983c\u533a\u9593\u3092\u793a\u3059\u610f\u5473\u304c\u3001\u3053\u3053\u304b\u3089\u3082\u308f\u304b\u308b\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u6ce8\u610f<\/strong>\uff1a<code>sens.slope()<\/code> \u306e95%\u4fe1\u983c\u533a\u9593\u306f\u3001MK\u691c\u5b9a\u3068\u540c\u3058\u304f\u300c\u30c7\u30fc\u30bf\u304c\u4e92\u3044\u306b\u72ec\u7acb\u300d\u3068\u3044\u3046\u524d\u63d0\u3067\u8a08\u7b97\u3055\u308c\u3066\u3044\u308b\u3002\u5f8c\u3067\u898b\u308b\u3088\u3046\u306b\u3001\u3053\u306e\u30c7\u30fc\u30bf\u306b\u306f\u81ea\u5df1\u76f8\u95a2\u304c\u3042\u308b\u305f\u3081\u3001\u5b9f\u969b\u306e\u4e0d\u78ba\u304b\u3055\u306f\u3053\u306e\u533a\u9593\u3088\u308a\u5927\u304d\u3044\uff08\u533a\u9593\u306f\u72ed\u3059\u304e\u308b\uff09\u3068\u8003\u3048\u308b\u3079\u304d\u3067\u3042\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5\uff1a\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u3067\u81ea\u5df1\u76f8\u95a2\u3092\u30c1\u30a7\u30c3\u30af\u3059\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u307e\u305a\u306f\u751f\u30c7\u30fc\u30bf\u306e\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u3092\u63cf\u304f\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>acf(sales, lag.max = 24,\n    main = \"Correlogram of monthly sales\")<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"800\" height=\"500\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step5a.png\" alt=\"\" class=\"wp-image-4829\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step5a.png 800w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step5a-300x188.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step5a-768x480.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6a2a\u8ef8\u306f\u305a\u3089\u3057\u305f\u6708\u6570\uff08\u30e9\u30b0\uff09\u3067\u3042\u308b\u3002\u30e9\u30b01\u301c3\u306e\u68d2\u304c\u9ad8\u304f\uff08\u30e9\u30b01\u3067\u7d040.8\uff09\u3001\u30e9\u30b012\u30fb24\u4ed8\u8fd1\u3067\u518d\u3073\u9ad8\u304f\u306a\u308a\u3001\u30e9\u30b06\u30fb18\u4ed8\u8fd1\u3067\u306f\u30de\u30a4\u30ca\u30b9\u306b\u306a\u3063\u3066\u3044\u308b\u30021\u5e74\u5468\u671f\u306e\u6ce2\u3001\u3064\u307e\u308a\u7f60\u2461\u306e\u5b63\u7bc0\u6027\u304c\u306f\u3063\u304d\u308a\u5199\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u3067\u6ce8\u610f\u3057\u305f\u3044\u306e\u306f\u3001<strong>\u30e9\u30b01\u301c3\u306e\u9ad8\u3055\u306f\u3001\u5b63\u7bc0\u306e\u6ce2\u3060\u3051\u3067\u3082\u751f\u3058\u308b<\/strong> \u3068\u3044\u3046\u70b9\u3067\u3042\u308b\u3002\u5b9f\u969b\u3001\u4eca\u56de\u306e\u30c7\u30fc\u30bf\u306b\u5165\u308c\u305f\u5b63\u7bc0\u306e\u6ce2\uff08\u30b3\u30b5\u30a4\u30f3\u66f2\u7dda\uff09\u3060\u3051\u3067\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u3092\u8a08\u7b97\u3057\u3066\u3082\u3001\u30e9\u30b01\u306f\u7d040.86\u306b\u306a\u308b\u3002\u751f\u30c7\u30fc\u30bf\u306e\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u3060\u3051\u3067\u306f\u3001\u300c\u5148\u6708\u3092\u5f15\u304d\u305a\u308b\u30af\u30bb\u300d\u306a\u306e\u304b\u300c\u5b63\u7bc0\u306e\u6ce2\u306e\u526f\u7523\u7269\u300d\u306a\u306e\u304b\u3092\u533a\u5225\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u305d\u3053\u3067\u3001\u30c8\u30ec\u30f3\u30c9\u3068\u5b63\u7bc0\u3092\u53d6\u308a\u9664\u3044\u305f <strong>\u6b8b\u5dee<\/strong> \u306e\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u3092\u63cf\u304f\u3002<code>lm()<\/code> \u306b\u6642\u9593 <code>t<\/code> \u3068\u6708 <code>factor(month)<\/code> \u3092\u5165\u308c\u3066\u56de\u5e30\u3057\u3001\u305d\u306e\u6b8b\u5dee\u3092\u53d6\u308a\u51fa\u3059\u3060\u3051\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u30c8\u30ec\u30f3\u30c9\uff08t\uff09\u3068\u5b63\u7bc0\uff08\u6708\u3054\u3068\u306e\u5e73\u5747\u306e\u9055\u3044\uff09\u3092\u53d6\u308a\u9664\u3044\u305f\u6b8b\u5dee\nresid_sales &lt;- residuals(lm(sales ~ t + factor(month)))\n\nacf(resid_sales, lag.max = 24,\n    main = \"Correlogram of residuals (trend and season removed)\")<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"800\" height=\"500\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step5b.png\" alt=\"\" class=\"wp-image-4830\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step5b.png 800w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step5b-300x188.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/step5b-768x480.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><code>factor(month)<\/code> \u306f\u3001\u300c\u6708\u3092\u6570\u5024\u3067\u306f\u306a\u304f1\u6708\u30fb2\u6708\u2026\u2026\u3068\u3044\u3046\u30ab\u30c6\u30b4\u30ea\u3068\u3057\u3066\u6271\u3046\u300d\u3068\u3044\u3046\u6307\u5b9a\u3067\u3042\u308b\u3002\u3053\u308c\u3067\u5404\u6708\u306e\u5e73\u5747\u7684\u306a\u6c34\u6e96\u306e\u9055\u3044\uff08\u5b63\u7bc0\u6027\uff09\u304c\u53d6\u308a\u9664\u304b\u308c\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u68d2\u306e\u9ad8\u3055\u3092\u6570\u5024\u3067\u78ba\u8a8d\u3057\u305f\u3044\u3068\u304d\u306f\u3001<code>plot = FALSE<\/code> \u3092\u6307\u5b9a\u3057\u3066\u5024\u3092\u53d6\u308a\u51fa\u3059\uff08\u5148\u982d\u306e\u8981\u7d20\u306f\u30e9\u30b00\uff1d\u5e38\u306b1\u306a\u306e\u3067\u9664\u304f\uff09\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u30e9\u30b01\u301c3\u306e\u81ea\u5df1\u76f8\u95a2\u4fc2\u6570\u3092\u6570\u5024\u3067\u8868\u793a\nround(acf(resid_sales, lag.max = 3, plot = FALSE)$acf&#91;2:4], 2)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b8b\u5dee\u306e\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u3067\u306f\u3001\u5b63\u7bc0\u306e\u6ce2\u306f\u6d88\u3048\u3066\u3044\u308b\u3002\u4e00\u65b9\u3067\u3001<strong>\u30e9\u30b01\u304c\u7d040.78\u3001\u30e9\u30b02\u304c\u7d040.59\u3001\u30e9\u30b03\u304c\u7d040.44\u3068\u3001\u306a\u3060\u3089\u304b\u306b\u6e1b\u3063\u3066\u3044\u304f<\/strong> \u5f62\u304c\u6b8b\u308b\u3002\u3053\u308c\u3053\u305d\u304c\u7f60\u2460\u306e\u81ea\u5df1\u76f8\u95a2\u3001\u300c\u5148\u6708\u3092\u5f15\u304d\u305a\u308b\u30af\u30bb\u300d\u306e\u6b63\u4f53\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u30c7\u30fc\u30bf\u306b\u306f\u3001\u7f60\u2460\u3068\u7f60\u2461\u306e\u4e21\u65b9\u304c\u6f5c\u3093\u3067\u3044\u308b\u3053\u3068\u304c\u306f\u3063\u304d\u308a\u3057\u305f\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 6\uff1a\u81ea\u5df1\u76f8\u95a2\u3092\u88dc\u6b63\u3057\u305fMK\u691c\u5b9a\uff08Hamed &amp; Rao\u6cd5\uff09<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>mmkh(sales)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><code>mmkh()<\/code> \u306e\u51fa\u529b\u306b\u306f\u88dc\u6b63\u524d\u3068\u88dc\u6b63\u5f8c\u306e\u7d50\u679c\u304c\u4e26\u3093\u3067\u8868\u793a\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>Original Z<\/code> \/ <code>old P.value<\/code>\uff1a\u88dc\u6b63\u524d\uff08Step 3\u306b\u76f8\u5f53\uff09<\/li>\n\n\n\n<li><code>Corrected Zc<\/code> \/ <code>new P-value<\/code>\uff1a\u81ea\u5df1\u76f8\u95a2\u3092\u88dc\u6b63\u3057\u305f\u5f8c<\/li>\n\n\n\n<li><code>N\/N*<\/code>\uff1a\u5b9f\u30c7\u30fc\u30bf\u6570\u304c\u6709\u52b9\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306e\u4f55\u500d\u304b\u3002\u300c\u4ef2\u826f\u3057\u30b0\u30eb\u30fc\u30d7\u306b\u3088\u308b\u6c34\u5897\u3057\u7387\u300d\u306b\u76f8\u5f53\u3059\u308b<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u7d50\u679c\u306f\u3001Z\u304c\u88dc\u6b63\u524d\u306e3.90\u304b\u3089\u88dc\u6b63\u5f8c\u306f <strong>2.67<\/strong> \u306b\u7e2e\u307f\u3001P\u5024\u306f9.7\u00d710\u207b\u2075\u304b\u3089 <strong>0.0075<\/strong> \u306b\u5927\u304d\u304f\u306a\u3063\u305f\u3002N\/N*\u306f <strong>2.12<\/strong> \u3067\u3001\u300c120\u304b\u6708\u306e\u30c7\u30fc\u30bf\u306f\u3001\u72ec\u7acb\u306a\u30c7\u30fc\u30bf\u306b\u63db\u7b97\u3059\u308b\u3068\u534a\u5206\u7a0b\u5ea6\u306e\u60c5\u5831\u91cf\u3057\u304b\u306a\u3044\u300d\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u30c7\u30fc\u30bf\u3067\u306f\u88dc\u6b63\u5f8c\u3082\u6709\u610f\u3067\u306f\u3042\u3063\u305f\u304c\u3001\u81ea\u5df1\u76f8\u95a2\u3092\u7121\u8996\u3059\u308b\u3068\u300c\u5076\u7136\u3068\u306f\u8003\u3048\u306b\u304f\u3044\u5ea6\u5408\u3044\u300d\u3001\u3064\u307e\u308a\u8a3c\u62e0\u306e\u5f37\u3055\u3092\u304b\u306a\u308a\u904e\u5927\u306b\u898b\u7a4d\u3082\u3063\u3066\u3044\u305f\u3053\u3068\u304c\u308f\u304b\u308b\u3002\u7cfb\u5217\u306b\u3088\u3063\u3066\u306f\u3001\u88dc\u6b63\u306b\u3088\u3063\u3066\u6709\u610f\u3067\u306a\u304f\u306a\u308b\u3053\u3068\u3082\u73cd\u3057\u304f\u306a\u3044\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u6ce8\u610f<\/strong>\uff1aStep 5\u306e\u751f\u30c7\u30fc\u30bf\u306e\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u3067\u898b\u305f\u3068\u304a\u308a\u3001\u3053\u306e\u30c7\u30fc\u30bf\u306e\u81ea\u5df1\u76f8\u95a2\u306b\u306f\u5b63\u7bc0\u306e\u6ce2\u3082\u6df7\u3056\u3063\u3066\u3044\u308b\u3002<code>mmkh()<\/code> \u306f\u305d\u308c\u3082\u542b\u3081\u3066\u300c\u5f15\u304d\u305a\u308a\u300d\u3068\u3057\u3066\u88dc\u6b63\u3059\u308b\u305f\u3081\u3001\u5b63\u7bc0\u6027\u306e\u306f\u3063\u304d\u308a\u3057\u305f\u6708\u6b21\u30c7\u30fc\u30bf\u306b\u306f\u3001\u6b21\u306eStep 7\u30fbStep 8\u306e\u65b9\u6cd5\u306e\u65b9\u304c\u9069\u5207\u3067\u3042\u308b\u3002<code>mmkh()<\/code> \u304c\u672c\u9818\u3092\u767a\u63ee\u3059\u308b\u306e\u306f\u3001\u5e74\u6b21\u30c7\u30fc\u30bf\u306e\u3088\u3046\u306b\u5b63\u7bc0\u6027\u306e\u306a\u3044\u7cfb\u5217\u3067\u3042\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">Step 7\uff1a\u5b63\u7bc0\u6027\u306b\u914d\u616e\u3057\u305fSeasonal Kendall\u691c\u5b9a<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># \u5b63\u7bc0\u578bMK\u691c\u5b9a\uff08\u540c\u3058\u6708\u540c\u58eb\u3067\u6bd4\u8f03\uff09\nsmk.test(sales_ts)\n\n# \u5b63\u7bc0\u578bSen's slope\uff081\u5e74\u3042\u305f\u308a\u306e\u50be\u304d\uff09\nsea.sens.slope(sales_ts)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><code>smk.test()<\/code> \u306b\u306f\u3001<code>ts<\/code> \u5f62\u5f0f\uff08frequency = 12 \u3092\u6307\u5b9a\u3057\u305f\u3082\u306e\uff09\u306e\u30c7\u30fc\u30bf\u3092\u6e21\u3059\u70b9\u306b\u6ce8\u610f\u3059\u308b\u3002\u51fa\u529b\u306b\u306f\u5168\u4f53\u306eZ\u3068P\u5024\u3001\u305d\u3057\u306612\u304b\u6708\u5206\u3092\u5408\u8a08\u3057\u305fS\uff08<code>S<\/code>\uff09\u3068\u305d\u306e\u5206\u6563\uff08<code>varS<\/code>\uff09\u304c\u8868\u793a\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7d50\u679c\u306f <strong>Z = 4.32\u3001P = 1.6\u00d710\u207b\u2075<\/strong>\uff08P &lt; 0.001\uff09\u3067\u3042\u3063\u305f\u3002\u5b63\u7bc0\u578bSen&#8217;s slope\u306f <strong>4.5\u676f\uff0f\u5e74<\/strong>\uff08\u6708\u3042\u305f\u308a\u306b\u76f4\u3059\u3068\u7d040.38\u676f\uff09\u3067\u3042\u3063\u305f\u3002\u3053\u306e\u30c7\u30fc\u30bf\u3067\u306f\u3001Step 4\u306eSen&#8217;s slope\uff08\u5e74\u7d045.6\u676f\uff09\u3088\u308a\u3082\u771f\u306e\u5024\uff08\u5e743.6\u676f\uff09\u306b\u8fd1\u304b\u3063\u305f\u304c\u3001\u3053\u308c\u306f\u4e71\u65701\u56de\u5206\u306e\u7d50\u679c\u3067\u3042\u308a\u3001\u5b63\u7bc0\u578b\u306e\u65b9\u304c\u5e38\u306b\u6b63\u78ba\u3060\u3068\u3044\u3046\u610f\u5473\u3067\u306f\u306a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u540c\u3058\u6708\u540c\u58eb\u3067\u6bd4\u3079\u308b\u3068\u3001\u590f\u51ac\u306e\u6ce2\u306e\u5f71\u97ff\u3092\u53d7\u3051\u305a\u306b\u300c\u524d\u5e74\u540c\u6708\u3088\u308a\u5897\u3048\u3066\u3044\u308b\u304b\u300d\u3092\u554f\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6708\u3054\u3068\u306e\u7d50\u679c\u306f <code>summary()<\/code> \u3067\u78ba\u8a8d\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>summary(smk.test(sales_ts))<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u4eca\u56de\u306e\u30c7\u30fc\u30bf\u3067\u306f\u300112\u304b\u6708\u306e\u3046\u30612\u6708\uff08S = \u22121\uff09\u3092\u9664\u304f11\u304b\u6708\u3067S\u304c\u30d7\u30e9\u30b9\u3067\u3042\u3063\u305f\u3002\u300c\u3069\u306e\u6708\u3067\u3082\u3001\u304a\u304a\u3080\u306d\u524d\u5e74\u540c\u6708\u3088\u308a\u5897\u3048\u3066\u3044\u308b\u300d\u3068\u3044\u3046\u4e00\u8cab\u3057\u305f\u50be\u5411\u304c\u8aad\u307f\u53d6\u308c\u308b\u3002\u305f\u3060\u3057\u300112\u304b\u6708\u5206\u306e\u691c\u5b9a\u3092\u500b\u5225\u306b\u89e3\u91c8\u3059\u308b\u3068\u591a\u91cd\u6bd4\u8f03\u306e\u554f\u984c\u304c\u751f\u3058\u308b\u305f\u3081\u3001\u6708\u5225\u306eP\u5024\u306b\u4e00\u559c\u4e00\u6182\u305b\u305a\u3001\u6708\u5225\u306e\u7d50\u679c\u306f\u3042\u304f\u307e\u3067\u8a18\u8ff0\u7684\u306a\u53c2\u8003\u306b\u3068\u3069\u3081\u308b\u306e\u304c\u7121\u96e3\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 8\uff1a\u5b63\u7bc0\u578b\u3067\u3082\u300c\u4ef2\u826f\u3057\u30b0\u30eb\u30fc\u30d7\u300d\u306f\u6b8b\u308b\uff08\u76f8\u95a2\u88dc\u6b63\u4ed8\u304dSeasonal Kendall\u691c\u5b9a\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b9f\u306f\u3001Step 7\u306b\u3082\u843d\u3068\u3057\u7a74\u304c\u3042\u308b\u3002<code>smk.test()<\/code> \u306f\u3001<strong>12\u304b\u6708\u305d\u308c\u305e\u308c\u306e\u7cfb\u5217\u304c\u4e92\u3044\u306b\u72ec\u7acb\u3067\u3042\u308b<\/strong> \u3068\u4eee\u5b9a\u3057\u3066\u3044\u308b\u3002\u3068\u3053\u308d\u304cStep 5\u306e\u6b8b\u5dee\u306e\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u3067\u898b\u305f\u3068\u304a\u308a\u3001\u3053\u306e\u30c7\u30fc\u30bf\u306f\u300c\u5148\u6708\u3092\u5f15\u304d\u305a\u308b\u300d\u30027\u6708\u306b\u3088\u304f\u58f2\u308c\u305f\u5e74\u306f8\u6708\u3082\u3088\u304f\u58f2\u308c\u3084\u3059\u304f\u30017\u6708\u306e\u80cc\u6bd4\u3079\u306e\u7d50\u679c\uff08S\uff09\u30688\u6708\u306e\u80cc\u6bd4\u3079\u306e\u7d50\u679c\u306f\u9023\u52d5\u3057\u3066\u3057\u307e\u3046\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u308c\u306f\u7f60\u2460\u306e\u300c\u4ef2\u826f\u3057\u30b0\u30eb\u30fc\u30d7\u300d\u304c\u3001\u6708\u306e\u5358\u4f4d\u3067\u518d\u767b\u5834\u3057\u305f\u72b6\u614b\u3067\u3042\u308b\u300212\u304b\u6708\u5206\u306eS\u3092\u300c12\u306e\u72ec\u7acb\u3057\u305f\u610f\u898b\u300d\u3068\u3057\u3066\u5408\u8a08\u3059\u308b\u3068\u3001\u3084\u306f\u308a\u7968\u304c\u6c34\u5897\u3057\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u9023\u52d5\uff08\u6708\u3068\u6708\u306e\u9593\u306e\u76f8\u95a2\uff09\u307e\u3067\u8003\u616e\u3059\u308b\u306e\u304c\u3001<strong>\u76f8\u95a2\u88dc\u6b63\u4ed8\u304dSeasonal Kendall\u691c\u5b9a<\/strong>\uff08Hirsch &amp; Slack, 1984\uff09\u3067\u3042\u308b\u3002<code>trend<\/code> \u30d1\u30c3\u30b1\u30fc\u30b8\u306e <code>csmk.test()<\/code> \u3067\u5b9f\u884c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>csmk.test(sales_ts)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u7d50\u679c\u306f <strong>Z = 1.75\u3001P = 0.080<\/strong> \u3068\u306a\u308a\u3001\u6709\u610f\u6c34\u6e965%\u3067\u306f\u6709\u610f\u306b\u306a\u3089\u306a\u304b\u3063\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u3067\u65e9\u5408\u70b9\u3057\u3066\u306f\u3044\u3051\u306a\u3044\u3002\u3053\u306e\u7591\u4f3c\u30c7\u30fc\u30bf\u306b\u306f\u3001\u771f\u306e\u30c8\u30ec\u30f3\u30c9\uff08\u5e743.6\u676f\u306e\u5897\u52a0\uff09\u304c\u78ba\u304b\u306b\u5165\u3063\u3066\u3044\u308b\u3002\u305d\u308c\u3067\u3082\u6709\u610f\u306b\u306a\u3089\u306a\u304b\u3063\u305f\u306e\u306f\u3001\u300c10\u5e74\u5206\u30fb\u81ea\u5df1\u76f8\u95a2\u306e\u5f37\u3044\u30c7\u30fc\u30bf\u300d\u304b\u3089\u5e743\u301c4\u676f\u3068\u3044\u3046\u3086\u308b\u3084\u304b\u306a\u4f38\u3073\u3092\u78ba\u304b\u3081\u308b\u306b\u306f\u3001\u60c5\u5831\u91cf\u304c\u8db3\u308a\u306a\u304b\u3063\u305f\u304b\u3089\u3067\u3042\u308b\u3002<strong>\u6709\u610f\u3067\u306a\u3044\u3053\u3068\u306f\u3001\u300c\u4f38\u3073\u3066\u3044\u306a\u3044\u300d\u3053\u3068\u306e\u8a3c\u660e\u3067\u306f\u306a\u3044\u3002<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u65b9\u3001\u5b63\u7bc0\u578bSen&#8217;s slope\uff08\u5e744.5\u676f\uff09\u306f\u3001\u3069\u306e\u691c\u5b9a\u3092\u4f7f\u3063\u3066\u3082\u5909\u308f\u3089\u306a\u3044\u3002P\u5024\u304c\u300c\u78ba\u304b\u3081\u3089\u308c\u305f\u304b\u3069\u3046\u304b\u300d\u3092\u6559\u3048\u3066\u304f\u308c\u308b\u306e\u306b\u5bfe\u3057\u3001Sen&#8217;s slope\u306f\u300c\u3069\u308c\u304f\u3089\u3044\u5909\u5316\u3057\u3066\u3044\u305d\u3046\u304b\u300d\u3092\u6559\u3048\u3066\u304f\u308c\u308b\u3002\u4e21\u8005\u3092\u5206\u3051\u3066\u5831\u544a\u3059\u308b\u3053\u3068\u306e\u5927\u5207\u3055\u304c\u3001\u3053\u3053\u3067\u3082\u78ba\u8a8d\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u203b\u30b3\u30e9\u30e0\uff1aP = 0.080\u306f\u300c\u6709\u610f\u50be\u5411\u300d\uff1f<\/strong><br>\u8ad6\u6587\u3067\u306f\u3001P = 0.05\u301c0.10\u3092\u300c\u6709\u610f\u50be\u5411\uff08marginally significant\uff09\u300d\u3068\u66f8\u304f\u4f8b\u3092\u898b\u304b\u3051\u308b\u3002\u3057\u304b\u3057\u3001\u3053\u308c\u306fP\u5024\u3092\u300c\u50be\u5411\u306e\u5f37\u3055\u300d\u306e\u3088\u3046\u306b\u6271\u3046\u8868\u73fe\u3067\u3042\u308a\u3001\u907f\u3051\u305f\u65b9\u304c\u3088\u3044\u3002\u5831\u544a\u3059\u3079\u304d\u306f\u3001P\u5024\u305d\u306e\u3082\u306e\uff08P = 0.080\uff09\u3068\u3001Sen&#8217;s slope\u306a\u3069\u306e\u52b9\u679c\u306e\u5927\u304d\u3055\u3067\u3042\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">\u3069\u308c\u3092\u4f7f\u3048\u3070\u3088\u3044\u304b\uff1a\u5224\u65ad\u306e\u30d5\u30ed\u30fc\u30c1\u30e3\u30fc\u30c8<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u30c7\u30fc\u30bf\u306e\u7279\u5fb4<\/th><th>\u63a8\u5968\u3055\u308c\u308b\u65b9\u6cd5<\/th><th>R\u306e\u95a2\u6570<\/th><\/tr><\/thead><tbody><tr><td>\u5b63\u7bc0\u6027\u306a\u3057\u30fb\u81ea\u5df1\u76f8\u95a2\u306a\u3057<\/td><td>\u901a\u5e38\u306eMK\u691c\u5b9a \uff0b Sen&#8217;s slope<\/td><td><code>MannKendall()<\/code>, <code>sens.slope()<\/code><\/td><\/tr><tr><td>\u5b63\u7bc0\u6027\u306a\u3057\u30fb\u81ea\u5df1\u76f8\u95a2\u3042\u308a\uff08\u5e74\u6b21\u30c7\u30fc\u30bf\u306a\u3069\uff09<\/td><td>\u81ea\u5df1\u76f8\u95a2\u88dc\u6b63MK\u691c\u5b9a \uff0b Sen&#8217;s slope<\/td><td><code>mmkh()<\/code><\/td><\/tr><tr><td>\u5b63\u7bc0\u6027\u3042\u308a\u30fb\u81ea\u5df1\u76f8\u95a2\u306a\u3057\uff08\u6708\u6b21\u30fb\u56db\u534a\u671f\u30c7\u30fc\u30bf\u306a\u3069\uff09<\/td><td>Seasonal Kendall\u691c\u5b9a \uff0b \u5b63\u7bc0\u578bSen&#8217;s slope<\/td><td><code>smk.test()<\/code>, <code>sea.sens.slope()<\/code><\/td><\/tr><tr><td>\u5b63\u7bc0\u6027\u3042\u308a\u30fb\u81ea\u5df1\u76f8\u95a2\u3042\u308a<\/td><td>\u76f8\u95a2\u88dc\u6b63\u4ed8\u304dSeasonal Kendall\u691c\u5b9a \uff0b \u5b63\u7bc0\u578bSen&#8217;s slope<\/td><td><code>csmk.test()<\/code>, <code>sea.sens.slope()<\/code><\/td><\/tr><tr><td>\u9014\u4e2d\u3067\u5411\u304d\u304c\u5909\u308f\u308a\u305d\u3046<\/td><td>\u5909\u5316\u70b9\u691c\u51fa\uff08Pettitt\u691c\u5b9a\u306a\u3069\uff09\u3092\u691c\u8a0e<\/td><td><code>pettitt.test()<\/code> \u306a\u3069<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u3069\u306e\u5834\u5408\u3082\u3001<strong>\u6700\u521d\u306b\u30b0\u30e9\u30d5\uff08Step 2\uff09\u3068\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\uff08Step 5\uff09\u3067\u3001\u30c7\u30fc\u30bf\u306e\u7d20\u9854\u3092\u78ba\u8a8d\u3059\u308b<\/strong> \u3053\u3068\u304c\u51fa\u767a\u70b9\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3082\u3046\u4e00\u3064\u5927\u5207\u306a\u306e\u306f\u3001<strong>\u691c\u5b9a\u3092\u9078\u3076\u306e\u306f\u7d50\u679c\u3092\u898b\u308b\u524d<\/strong> \u3060\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002\u672c\u8a18\u4e8b\u3067\u306f\u8aac\u660e\u306e\u305f\u3081\u306b\u540c\u3058\u30c7\u30fc\u30bf\u306b\u4f55\u7a2e\u985e\u3082\u306e\u691c\u5b9a\u3092\u304b\u3051\u305f\u304c\u3001\u5b9f\u969b\u306e\u7814\u7a76\u3067\u300c\u4e00\u756aP\u5024\u304c\u5c0f\u3055\u304b\u3063\u305f\u691c\u5b9a\u3092\u5831\u544a\u3059\u308b\u300d\u306e\u306f\u3001\u3044\u308f\u3086\u308bP\u5024\u30cf\u30c3\u30ad\u30f3\u30b0\u3067\u3042\u308b\u3002\u30c7\u30fc\u30bf\u306e\u7279\u5fb4\uff08\u5b63\u7bc0\u6027\u30fb\u81ea\u5df1\u76f8\u95a2\uff09\u304b\u3089\u4e3b\u89e3\u6790\u3092\u4e8b\u524d\u306b\u6c7a\u3081\u3001\u305d\u308c\u4ee5\u5916\u306e\u691c\u5b9a\u306f\u611f\u5ea6\u5206\u6790\u3068\u3057\u3066\u3001\u7d50\u679c\u306b\u304b\u304b\u308f\u3089\u305a\u3059\u3079\u3066\u5831\u544a\u3059\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">5. \u8ad6\u6587\u3067\u305d\u306e\u307e\u307e\u4f7f\u3048\u308b\u82f1\u6587\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u306f\u3042\u304f\u307e\u3067 <strong>\u8a18\u8ff0\u4f8b<\/strong> \u3067\u3042\u308b\u3002\uff3b \uff3d\u5185\u306e\u6570\u5024\u306f\u3001\u3054\u81ea\u8eab\u306e\u30c7\u30fc\u30bf\u3067\u5b9f\u969b\u306b\u5f97\u3089\u308c\u305f\u5024\u306b\u5fc5\u305a\u7f6e\u304d\u63db\u3048\u3066\u307b\u3057\u3044\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Methods<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Temporal trends in [monthly sales] from [January 2016] to [December 2025] were assessed using non-parametric Mann-Kendall-type trend tests (Mann, 1945; Kendall, 1975), which do not assume normality of the data. Serial correlation was examined using the autocorrelation function of the residuals after removing the linear trend and monthly effects. Because the series showed marked seasonality and serial correlation, the seasonal Kendall test with correction for dependence among seasons (Hirsch and Slack, 1984) was used as the primary analysis. The seasonal Kendall test without this correction (Hirsch et al., 1982) was also reported for reference. The magnitude of the trend was estimated with the seasonal Sen&#8217;s slope estimator (Sen, 1968; Hirsch et al., 1982). All analyses were performed using R version [4.x.x] with the trend package. A two-sided P value &lt; 0.05 was considered statistically significant.<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">Results<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">The autocorrelation function of the residuals from a linear regression on time and calendar month indicated positive serial correlation (lag-1 autocorrelation, [0.78]). The seasonal Kendall test corrected for dependence among seasons did not show a statistically significant trend in [monthly sales] (Z = [1.75], P = [0.080]). The estimated seasonal Sen&#8217;s slope was [4.5] [cups] per year, corresponding to approximately [1.4]% of the mean monthly value per year. The seasonal Kendall test without correction for serial dependence yielded Z = [4.32] (P &lt; [0.001]); however, this test assumes independence among seasons, which was not supported by the data.<\/p>\n<\/blockquote>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u4f7f\u3046\u969b\u306e\u6ce8\u610f<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u300c\u5f37\u3044\u5897\u52a0\u50be\u5411\uff08strong trend\uff09\u300d\u306e\u3088\u3046\u306b\u3001P\u5024\u306e\u5c0f\u3055\u3055\u3092\u6839\u62e0\u306b\u50be\u5411\u306e\u5f37\u3055\u3092\u8868\u73fe\u3057\u306a\u3044\u3002\u50be\u5411\u306e\u5927\u304d\u3055\u306fSen&#8217;s slope\uff08\u3068\u4fe1\u983c\u533a\u9593\uff09\u3001\u4e00\u8cab\u6027\u306fKendall\u306e\u03c4\u3067\u8ff0\u3079\u308b<\/li>\n\n\n\n<li><code>sea.sens.slope()<\/code> \u306f\u4fe1\u983c\u533a\u9593\u3092\u51fa\u529b\u3057\u306a\u3044\u3002\u4fe1\u983c\u533a\u9593\u3092\u5831\u544a\u3057\u305f\u3044\u5834\u5408\u306f\u3001\u81ea\u5df1\u76f8\u95a2\u3092\u8003\u616e\u3057\u305f\u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\uff08\u30d6\u30ed\u30c3\u30af\u30fb\u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u306a\u3069\uff09\u306a\u3069\u3067\u5225\u9014\u6c42\u3081\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u306a\u304a <code>sens.slope()<\/code> \u304c\u51fa\u529b\u3059\u308b\u4fe1\u983c\u533a\u9593\u306f\u30c7\u30fc\u30bf\u306e\u72ec\u7acb\u6027\u3092\u524d\u63d0\u3068\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u81ea\u5df1\u76f8\u95a2\u304c\u3042\u308b\u5834\u5408\u306f\u72ed\u3059\u304e\u308b\u70b9\u306b\u6ce8\u610f\u3059\u308b<\/li>\n\n\n\n<li>\u6709\u610f\u306a\u7d50\u679c\u304c\u5f97\u3089\u308c\u305f\u5834\u5408\u306f\u3001Results\u306e1\u6587\u76ee\u3092 &#8220;showed a statistically significant increasing trend&#8221; \u306e\u3088\u3046\u306b\u66f8\u304d\u63db\u3048\u308b<\/li>\n\n\n\n<li>\u5b63\u7bc0\u6027\u306e\u306a\u3044\u30c7\u30fc\u30bf\u306e\u5834\u5408\u306f\u3001\u5b63\u7bc0\u578b\u306b\u95a2\u3059\u308b\u6587\u3092\u524a\u9664\u3057\u3001Mann-Kendall\u691c\u5b9a\uff0bSen&#8217;s slope\u3092\u57fa\u672c\u3068\u3057\u3001\u81ea\u5df1\u76f8\u95a2\u304c\u3042\u308b\u5834\u5408\u306fHamed and Rao (1998) \u306e\u88dc\u6b63\uff08<code>modifiedmk::mmkh()<\/code>\uff09\u3092\u4e3b\u89e3\u6790\u3068\u3057\u3066\u8a18\u8ff0\u3059\u308b<\/li>\n<\/ul>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u307e\u3068\u3081<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>MK\u691c\u5b9a\u306f\u300c\u5168\u54e1\u3068\u63e1\u624b\u3057\u3066\u80cc\u6bd4\u3079\u300d<\/strong>\u3002\u6642\u9593\u3068\u306e\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u305d\u306e\u3082\u306e\u3067\u3001\u6b63\u898f\u5206\u5e03\u3092\u4eee\u5b9a\u305b\u305a\u3001\u5916\u308c\u5024\u306b\u3082\u5f37\u3044<\/li>\n\n\n\n<li><strong>\u50be\u5411\u306e\u5927\u304d\u3055\u306fSen&#8217;s slope\u3067\u8a9e\u308b<\/strong>\u3002P\u5024\u306e\u5c0f\u3055\u3055\u306f\u300c\u6025\u5897\u300d\u3092\u610f\u5473\u3057\u306a\u3044\u3002P\u5024\u3068Sen&#8217;s slope\uff0895%\u4fe1\u983c\u533a\u9593\uff09\u3092\u30bb\u30c3\u30c8\u3067\u5831\u544a\u3059\u308b<\/li>\n\n\n\n<li><strong>3\u3064\u306e\u7f60\u306b\u6ce8\u610f\u3059\u308b<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u81ea\u5df1\u76f8\u95a2\uff08\u4ef2\u826f\u3057\u30b0\u30eb\u30fc\u30d7\u306e\u6c34\u5897\u3057\u7968\uff09\u2192 Hamed &amp; Rao\u306e\u88dc\u6b63\uff08<code>mmkh()<\/code>\uff09<\/li>\n\n\n\n<li>\u5b63\u7bc0\u6027\uff087\u6708\u30681\u6708\u3067\u80cc\u6bd4\u3079\u3057\u306a\u3044\uff09\u2192 Seasonal Kendall\u691c\u5b9a\uff08<code>smk.test()<\/code>\uff09\u3002\u81ea\u5df1\u76f8\u95a2\u3082\u3042\u308b\u306a\u3089\u76f8\u95a2\u88dc\u6b63\u4ed8\u304d\uff08<code>csmk.test()<\/code>\uff09<\/li>\n\n\n\n<li>\u9014\u4e2d\u3067\u306e\u65b9\u5411\u8ee2\u63db \u2192 \u5909\u5316\u70b9\u691c\u51fa\u3092\u691c\u8a0e<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u307e\u305a\u306f\u30b0\u30e9\u30d5\u3068\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0<\/strong>\u3002\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u306f\u3001\u30c8\u30ec\u30f3\u30c9\u3068\u5b63\u7bc0\u3092\u9664\u3044\u305f\u6b8b\u5dee\u3067\u3082\u78ba\u8a8d\u3059\u308b\u3002\u30c7\u30fc\u30bf\u306e\u7d20\u9854\u3092\u898b\u3066\u304b\u3089\u3001\u7d50\u679c\u3092\u898b\u308b\u524d\u306b\u4f7f\u3046\u691c\u5b9a\u3092\u9078\u3076<\/li>\n\n\n\n<li><strong>\u6709\u610f\u3067\u306a\u3044\uff1d\u5909\u5316\u306a\u3057\u3001\u3067\u306f\u306a\u3044<\/strong>\u3002\u300c\u78ba\u304b\u3081\u3089\u308c\u305f\u304b\uff08P\u5024\uff09\u300d\u3068\u300c\u3069\u308c\u304f\u3089\u3044\u5909\u5316\u3057\u3066\u3044\u305d\u3046\u304b\uff08Sen&#8217;s slope\uff09\u300d\u306f\u5206\u3051\u3066\u8a9e\u308b<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e00\u62ec\u30b3\u30d4\u30da\u7528R\u30b9\u30af\u30ea\u30d7\u30c8<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code># ============================================================\n# Mann-Kendall\u691c\u5b9a\u306b\u3088\u308b\u6642\u7cfb\u5217\u30c8\u30ec\u30f3\u30c9\u89e3\u6790\n# ============================================================\n\n# --- \u30d1\u30c3\u30b1\u30fc\u30b8 ---\n# install.packages(c(\"Kendall\", \"trend\", \"modifiedmk\"))\nlibrary(Kendall)\nlibrary(trend)\nlibrary(modifiedmk)\n\n# --- Step 1\uff1a\u7591\u4f3c\u30c7\u30fc\u30bf\u306e\u4f5c\u6210 ---\nset.seed(32)\nn     &lt;- 120\nt     &lt;- 1:n\nmonth &lt;- rep(1:12, times = 10)\n\ntrend  &lt;- 0.3 * t\nseason &lt;- 40 * cos(2 * pi * (month - 8) \/ 12)\nnoise  &lt;- as.numeric(arima.sim(model = list(ar = 0.7), n = n, sd = 20))\n\nsales    &lt;- round(300 + trend + season + noise)\nsales_ts &lt;- ts(sales, start = c(2016, 1), frequency = 12)\n\n# --- Step 2\uff1a\u6642\u7cfb\u5217\u30b0\u30e9\u30d5 ---\nplot(sales_ts, type = \"o\", pch = 16, cex = 0.6,\n     xlab = \"Year\", ylab = \"Iced coffee sales (cups\/month)\",\n     main = \"Monthly iced coffee sales\")\n\n# --- Step 3\uff1a\u57fa\u672c\u306eMK\u691c\u5b9a ---\nMannKendall(sales)\ncor.test(t, sales, method = \"kendall\")   # \u691c\u7b97\uff1a\u6642\u9593\u3068\u306e\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\n\n# --- Step 4\uff1aSen's slope ---\nsens.slope(sales)\n\n# --- Step 5\uff1a\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\uff08\u751f\u30c7\u30fc\u30bf\uff0f\u6b8b\u5dee\uff09---\nacf(sales, lag.max = 24, main = \"Correlogram of monthly sales\")\nresid_sales &lt;- residuals(lm(sales ~ t + factor(month)))\nacf(resid_sales, lag.max = 24,\n    main = \"Correlogram of residuals (trend and season removed)\")\nround(acf(resid_sales, lag.max = 3, plot = FALSE)$acf&#91;2:4], 2)   # \u30e9\u30b01\u301c3\u306e\u5024\n\n# --- Step 6\uff1a\u81ea\u5df1\u76f8\u95a2\u3092\u88dc\u6b63\u3057\u305fMK\u691c\u5b9a\uff08Hamed &amp; Rao\u6cd5\uff09---\nmmkh(sales)\n\n# --- Step 7\uff1a\u5b63\u7bc0\u578bMK\u691c\u5b9a\u3068\u5b63\u7bc0\u578bSen's slope ---\nsmk.test(sales_ts)\nsummary(smk.test(sales_ts))   # \u6708\u3054\u3068\u306e\u7d50\u679c\nsea.sens.slope(sales_ts)\n\n# --- Step 8\uff1a\u76f8\u95a2\u88dc\u6b63\u4ed8\u304d\u5b63\u7bc0\u578bMK\u691c\u5b9a ---\ncsmk.test(sales_ts)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u53c2\u8003\u6587\u732e<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Mann HB. Nonparametric tests against trend. <em>Econometrica<\/em>. 1945;13(3):245\u2013259. <a href=\"https:\/\/www.jstor.org\/stable\/1907187\">https:\/\/www.jstor.org\/stable\/1907187<\/a><\/li>\n\n\n\n<li>Kendall MG. <em>Rank Correlation Methods<\/em>. 4th ed. London: Charles Griffin; 1975.<\/li>\n\n\n\n<li>Sen PK. Estimates of the regression coefficient based on Kendall&#8217;s tau. <em>Journal of the American Statistical Association<\/em>. 1968;63(324):1379\u20131389. <a href=\"https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/01621459.1968.10480934\">https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/01621459.1968.10480934<\/a><\/li>\n\n\n\n<li>Hirsch RM, Slack JR, Smith RA. Techniques of trend analysis for monthly water quality data. <em>Water Resources Research<\/em>. 1982;18(1):107\u2013121. <a href=\"https:\/\/doi.org\/10.1029\/WR018i001p00107\">https:\/\/doi.org\/10.1029\/WR018i001p00107<\/a><\/li>\n\n\n\n<li>Hirsch RM, Slack JR. A nonparametric trend test for seasonal data with serial dependence. <em>Water Resources Research<\/em>. 1984;20(6):727\u2013732. <a href=\"https:\/\/doi.org\/10.1029\/WR020i006p00727\">https:\/\/doi.org\/10.1029\/WR020i006p00727<\/a><\/li>\n\n\n\n<li>Hamed KH, Rao AR. A modified Mann-Kendall trend test for autocorrelated data. <em>Journal of Hydrology<\/em>. 1998;204(1\u20134):182\u2013196. <a href=\"https:\/\/doi.org\/10.1016\/S0022-1694(97)00125-X\">https:\/\/doi.org\/10.1016\/S0022-1694(97)00125-X<\/a><\/li>\n\n\n\n<li>Yue S, Pilon P, Phinney B, Cavadias G. The influence of autocorrelation on the ability to detect trend in hydrological series. <em>Hydrological Processes<\/em>. 2002;16(9):1807\u20131829. <a href=\"https:\/\/doi.org\/10.1002\/hyp.1095\">https:\/\/doi.org\/10.1002\/hyp.1095<\/a><\/li>\n\n\n\n<li>Chen X, Wang H, Lyu W, Xu R. The Mann-Kendall-Sneyers test to identify the change points of COVID-19 time series in the United States. <em>BMC Medical Research Methodology<\/em>. 2022;22:233. <a href=\"https:\/\/doi.org\/10.1186\/s12874-022-01714-6\">https:\/\/doi.org\/10.1186\/s12874-022-01714-6<\/a><\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u304a\u3059\u3059\u3081\u66f8\u7c4d<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">MK\u691c\u5b9a\u305d\u306e\u3082\u306e\u3092\u4e3b\u984c\u306b\u3057\u305f\u548c\u66f8\u306f\u307b\u3068\u3093\u3069\u306a\u3044\u3002\u305d\u3053\u3067\u3001\u672c\u8a18\u4e8b\u3067\u6271\u3063\u305f\u300c\u81ea\u5df1\u76f8\u95a2\u300d\u300c\u5b63\u7bc0\u6027\u300d\u300c\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u300d\u3068\u3044\u3063\u305f\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u306e\u57fa\u790e\u4f53\u529b\u3092\u3064\u3051\u308b\u672c\u3068\u3001MK\u691c\u5b9a\u306e&#8221;\u672c\u5bb6&#8221;\u304c\u66f8\u3044\u305f\u7121\u6599\u306e\u6559\u79d1\u66f8\u3092\u7d39\u4ecb\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. \u99ac\u5834\u771f\u54c9\u300e\u6642\u7cfb\u5217\u5206\u6790\u3068\u72b6\u614b\u7a7a\u9593\u30e2\u30c7\u30eb\u306e\u57fa\u790e\uff1aR\u3068Stan\u3067\u5b66\u3076\u7406\u8ad6\u3068\u5b9f\u88c5\u300f\uff08\u30d7\u30ec\u30a2\u30c7\u30b9\u51fa\u7248, 2018\uff09<\/strong><br>\u81ea\u5df1\u76f8\u95a2\u3084\u30b3\u30ec\u30ed\u30b0\u30e9\u30e0\u3001\u5b63\u7bc0\u6027\u306e\u6271\u3044\u3068\u3044\u3063\u305f\u6642\u7cfb\u5217\u5206\u6790\u306e\u57fa\u672c\u3092\u3001R\u306e\u30b3\u30fc\u30c9\u3068\u3068\u3082\u306b\u4e00\u304b\u3089\u5b66\u3079\u308b\u3002\u6570\u5f0f\u306b\u82e6\u624b\u610f\u8b58\u304c\u3042\u308b\u4eba\u306e\u6700\u521d\u306e1\u518a\u3068\u3057\u3066\u6700\u9069\u3067\u3042\u308b\u3002<br>&#x1f449; <a href=\"https:\/\/amzn.to\/4Ar3xgj\">https:\/\/www.amazon.co.jp\/dp\/4903814874<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. \u6c96\u672c\u7adc\u7fa9\u300e\u7d4c\u6e08\u30fb\u30d5\u30a1\u30a4\u30ca\u30f3\u30b9\u30c7\u30fc\u30bf\u306e\u8a08\u91cf\u6642\u7cfb\u5217\u5206\u6790\u300f\uff08\u7d71\u8a08\u30e9\u30a4\u30d6\u30e9\u30ea\u30fc, \u671d\u5009\u66f8\u5e97, 2010\uff09<\/strong><br>\u81ea\u5df1\u76f8\u95a2\u30fb\u5b9a\u5e38\u6027\u30fbAR\u30e2\u30c7\u30eb\u306a\u3069\u3001\u672c\u8a18\u4e8b\u306e\u300c\u7f60\u2460\u300d\u306e\u80cc\u666f\u306b\u3042\u308b\u7406\u8ad6\u3092\u3001\u304d\u3061\u3093\u3068\u6570\u5f0f\u3067\u7406\u89e3\u3057\u305f\u3044\u4eba\u5411\u3051\u306e\u5b9a\u756a\u66f8\u3067\u3042\u308b\u3002<br>&#x1f449; <a href=\"https:\/\/amzn.to\/4h8S7pY\">https:\/\/www.amazon.co.jp\/dp\/4254127928<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. Helsel DR, Hirsch RM, Ryberg KR, Archfield SA, Gilroy EJ. <em>Statistical Methods in Water Resources<\/em>\uff08U.S. Geological Survey Techniques and Methods 4-A3, 2020\uff09<\/strong><br>Seasonal Kendall\u691c\u5b9a\u306e\u8003\u6848\u8005\u3067\u3042\u308bHirsch\u3089\u306b\u3088\u308b\u6559\u79d1\u66f8\u3067\u3001\u7c73\u56fd\u5730\u8cea\u8abf\u67fb\u6240\uff08USGS\uff09\u306e\u30b5\u30a4\u30c8\u304b\u3089\u7121\u6599\u3067PDF\u3092\u5165\u624b\u3067\u304d\u308b\u3002MK\u691c\u5b9a\u3001Sen&#8217;s slope\u3001Seasonal Kendall\u691c\u5b9a\u3001\u81ea\u5df1\u76f8\u95a2\u3078\u306e\u5bfe\u51e6\u307e\u3067\u304c\u30c8\u30ec\u30f3\u30c9\u89e3\u6790\u306e\u7ae0\u3067\u8a73\u3057\u304f\u89e3\u8aac\u3055\u308c\u3066\u304a\u308a\u3001\u82f1\u8a9e\u304c\u82e6\u306b\u306a\u3089\u306a\u3051\u308c\u3070\u3001\u672c\u8a18\u4e8b\u306e\u5185\u5bb9\u3092\u6700\u3082\u6df1\u304f\u5b66\u3079\u308b1\u518a\u3067\u3042\u308b\u3002<br>&#x1f449; <a href=\"https:\/\/doi.org\/10.3133\/tm4A3\">https:\/\/doi.org\/10.3133\/tm4A3<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5f8c\u8f29\uff1a\u300c\u5148\u8f29\u3001\u77e5\u308a\u5408\u3044\u306e\u55ab\u8336\u5e97\u306e\u30de\u30b9\u30bf\u30fc\u306b\u76f8\u8ac7\u3055\u308c\u305f\u3093\u3067\u3059\u3002\u30a2\u30a4\u30b9\u30b3\u30fc\u30d2\u30fc\u306e\u58f2\u4e0a\u304c10\u5e74\u3067\u3058\u308f\u3058\u308f\u4f38\u3073\u3066\u3044\u308b\u6c17\u304c\u3059\u308b\u304b\u3089\u3001\u305d\u308c\u3092\u6570\u5b57\u3067\u78ba\u304b\u3081\u305f\u3044\u3063\u3066\u300d \u5148\u8f29\uff1a\u300c\u6708\u3054\u3068\u306e\u58f2\u4e0a\u30c7\u30fc\u30bf\u304c\u3042\u308b\u306e\u304b\u3044\uff1f\u300d \u5f8c\u8f29\uff1a\u300c\u306f\u3044\u300110\u5e74\u5206\u3067 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":4832,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[54],"tags":[],"class_list":["post-4827","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-54"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/09\/Mann-Kendall_Sen_Slope-scaled.jpeg","_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4827","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/comments?post=4827"}],"version-history":[{"count":2,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4827\/revisions"}],"predecessor-version":[{"id":4833,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4827\/revisions\/4833"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/4832"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=4827"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=4827"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=4827"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}