{"id":510,"date":"2018-08-20T21:45:55","date_gmt":"2018-08-20T12:45:55","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-in-trend-test\/"},"modified":"2024-10-21T13:56:13","modified_gmt":"2024-10-21T04:56:13","slug":"how-to-determine-sample-size-in-trend-test","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-in-trend-test\/","title":{"rendered":"R \u3067\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3002<\/p>\n\n\n\n\n\n\n\n

\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u3068\u306f<\/h2>\n\n\n\n

\u30c8\u30ec\u30f3\u30c9\u3068\u306f\u3001\u9806\u5e8f\u30ab\u30c6\u30b4\u30ea\u306e\u5c0f\u3055\u3044\u307b\u3046\u304b\u3089\u5927\u304d\u3044\u307b\u3046\u306b\u79fb\u308b\u306b\u3064\u308c\u3066\u3001\u30ab\u30c6\u30b4\u30ea\u306e\u5e73\u5747\u5024\u3084\u5272\u5408\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u304b\u5c0f\u3055\u304f\u306a\u308b\u3068\u304b\u3001\u50be\u5411\u3084\u76f8\u95a2\u304c\u3042\u308b\u3053\u3068\u3092\u6307\u3059\u3002<\/p>\n\n\n\n

\u30c8\u30ec\u30f3\u30c9\u304c\u306a\u304f\u540c\u3058\u3068\u3044\u3046\u306e\u304c\u5e30\u7121\u4eee\u8aac\u3067\u3001\u6bcd\u96c6\u56e3\u3067\u3001\u3060\u3093\u3060\u3093\u306b\u5927\u304d\u304f\u306a\u308b\u3001\u3082\u3057\u304f\u306f\u5c0f\u3055\u304f\u306a\u308b\u30c8\u30ec\u30f3\u30c9\u304c\u3042\u308b\u306e\u304b\u3092\u3001\u691c\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n

\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a \u5e73\u5747\u5024\u306e\u5834\u5408<\/h2>\n\n\n\n

\u6bcd\u6570\u3068\u30b9\u30b3\u30a2\u306e\u76f8\u95a2\u4fc2\u6570\u3092\u8003\u3048\u308b\u3002<\/p>\n\n\n\n

\u30dd\u30a4\u30f3\u30c8\u306f\u3001\u5408\u8a08\u304c0\u306b\u306a\u308b\u3088\u3046\u306b\u30b9\u30b3\u30a2\u3092\u4e0e\u3048\u308b\u3053\u3068\u3002<\/p>\n\n\n\n

c: \u7dda\u5f62\u5bfe\u6bd4\uff08\u30d9\u30af\u30c8\u30eb\uff09\u2190\u3053\u308c\u304c\u30dd\u30a4\u30f3\u30c8\u3002<\/p>\n\n\n\n

K=3(3\u30b0\u30eb\u30fc\u30d7)\u306e\u5834\u5408\u306fc(-1,0,1)<\/p>\n\n\n\n

K=4\u306e\u5834\u5408\u306fc(-3,-1,1,3):\u7b49\u9593\u9694\uff08\u9593\u9694\u306f2\uff09<\/p>\n\n\n\n

mu: \u6bcd\u5e73\u5747\uff08\u30d9\u30af\u30c8\u30eb\uff09<\/p>\n\n\n\n

sigma.sq: ANOVA\u304b\u3089\u8a08\u7b97\u3055\u308c\u308b\u8aa4\u5dee\u5206\u6563\uff08\u4e0b\u8a18\u5206\u6563\u5206\u6790\u8868\u306e\u592a\u5b57\u4e0b\u7dda\u90e8\u5206\uff09<\/p>\n\n\n\n

<\/th>Df<\/th>Sum Sq<\/th>Mean Sq<\/th>F value<\/th>Pr(>F)<\/th><\/th><\/tr><\/thead>
tension<\/td>2<\/td>2034<\/td>1017.1<\/td>7.206<\/td>0.00175<\/td>**<\/td><\/tr>
Residuals<\/td>51<\/td>7199<\/td>141.1<\/u><\/b><\/td><\/td><\/td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

R \u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n

samplesize.mean.trend.test <-<\/span> function<\/span>(<\/span>mu,<\/span> sigma.sq,<\/span> score,<\/span> sig.level=<\/span>.05<\/span>,<\/span> power=<\/span>.8<\/span>){<\/span>\nMETHOD <-<\/span> \"Sample size determination for trend test of the means\"<\/span>\nNOTE<\/span> <-<\/span> \"n is each number in groups\"<\/span>\nZa <-<\/span> qnorm<\/span>(<\/span>sig.level\/<\/span>2<\/span>,<\/span> lower.tail=<\/span>FALSE<\/span>)<\/span>\nZb <-<\/span> qnorm<\/span>(<\/span>power)<\/span>\nn <-<\/span> ((<\/span>Za+<\/span>Zb)<\/span>^<\/span>2<\/span> *<\/span> sigma.sq *<\/span> sum<\/span>(<\/span>score^<\/span>2<\/span>))<\/span>\/<\/span>(<\/span>sum<\/span>(<\/span>score*<\/span>mu)<\/span>^<\/span>2<\/span>)<\/span>\nstructure<\/span>(<\/span>list<\/span>(<\/span>n=<\/span>n,<\/span> mu=<\/span>mu,<\/span> sigma.sq=<\/span>sigma.sq,<\/span> score=<\/span>score,<\/span> sig.level=<\/span>sig.level,<\/span> power=<\/span>power,<\/span> method=<\/span>METHOD,<\/span> note=<\/span>NOTE<\/span>),<\/span> class =<\/span> \"power.htest\"<\/span>)<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
\u5e73\u5747\u5024\u306e\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97 \u4f8b1<\/h3>\n\n\n\n
\u53c2\u8003\u66f8\u7c4d<\/a>\u306e\u4f8b\u984c\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
\"\"
\u4e09\u7fa4\u306e\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u306e\u4f8b\u984c<\/figcaption><\/figure>\n\n\n\n
\u4f8b\u984c\u306f\u5206\u6563\u5206\u6790\u8868\u3067\u306a\u304fSE\uff08\u6a19\u6e96\u8aa4\u5dee\uff09\u306e\u5024\u304c\u308f\u304b\u308b\u30bf\u30a4\u30d7\u3002<\/p>\n\n\n\n
\u75c7\u72b6\u30b9\u30b3\u30a2\u306e\u5909\u5316\u91cf\u306f\u3001-2, -3.5, -3.5\u3068\u60f3\u5b9a\u3055\u308c\u308b\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
\u76f8\u95a2\u3092\u898b\u308b\u7dda\u5f62\u5bfe\u6bd4\u306f-2, 1, 1\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
\u5408\u8a08\u3067\u30bc\u30ed\u306b\u306a\u308b\u3088\u3046\u306b\u3059\u308b\u3053\u3068\u3068\u3001
\u75c7\u72b6\u30b9\u30b3\u30a2\u306e\u5909\u5316\u91cf\u3092\u8868\u3057\u3066\u3044\u308b\u6570\u5b57\u306b\u3059\u308b\u3053\u3068\u3002<\/p>\n\n\n\n
\u4e09\u7fa4\u306e\u3046\u3061\u3001-2\u306e\u7fa4\u3060\u3051\u9055\u3046\u308f\u3051\u306a\u306e\u3067\u3001
\u305d\u306e\u5834\u5408\u306f-2, 1, 1\u3068\u3044\u3046\u30b9\u30b3\u30a2\u304c\u59a5\u5f53\u3002<\/p>\n\n\n\n
\uff08\u5909\u5316\u91cf\u3068\u5272\u308a\u5f53\u3066\u308b\u30b9\u30b3\u30a2\u304c\u3068\u3082\u306b-2\u306a\u306e\u306f\u305f\u307e\u305f\u307e\u3002\u5ff5\u306e\u305f\u3081\uff09<\/p>\n\n\n\n
\u8aa4\u5dee\u5206\u6563\u306f\u6700\u5927\u306eSE\uff1d0.36\u306e\u4e8c\u4e57\u306b\u4e09\u7fa4\u306e\u75c7\u4f8b\u6570\u306e\u771f\u3093\u4e2d\u3042\u305f\u308a70\u4f8b\u3092\u304b\u3051\u308b\u3002<\/p>\n\n\n\n
SE\u306f\u3053\u3093\u306a\u3075\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
$$ SE = \\sqrt{\\frac{\u5206\u6563}{n}} $$<\/p>\n\n\n\n\n\n\n\n
\u3088\u3063\u3066\u4e8c\u4e57\u3057\u3066\u75c7\u4f8b\u6570\u3092\u304b\u3051\u308b\u3068\u5206\u6563\u306b\u623b\u308b\u3002<\/p>\n\n\n\n
$$ \\left( \\sqrt{\\frac{\u5206\u6563}{n}} \\right)^2 \\times n = \\frac{\u5206\u6563}{n} \\times n = \u5206\u6563 $$<\/p>\n\n\n\n\n\n\n\n
\u7d50\u679c\u3068\u3057\u3066\u4e00\u7fa448\u4f8b\u5fc5\u8981\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
><\/span> samplesize.mean.trend.test<\/span>(<\/span>mu=<\/span>c<\/span>(<\/span>-<\/span>2<\/span>,<\/span>-<\/span>3.5<\/span>,<\/span>-<\/span>3.5<\/span>),<\/span> sigma.sq=<\/span>70<\/span>*<\/span>0.36<\/span>^<\/span>2<\/span>,<\/span> score=<\/span>c<\/span>(<\/span>-<\/span>2<\/span>,<\/span>1<\/span>,<\/span>1<\/span>))<\/span>\nSample size determination for<\/span> trend test of the means\nn =<\/span> 47.47002<\/span>\nmu =<\/span> -<\/span>2.0<\/span>,<\/span> -<\/span>3.5<\/span>,<\/span> -<\/span>3.5<\/span>\nsigma.sq =<\/span> 9.072<\/span>\nscore =<\/span> -<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\nNOTE:<\/span> n is each number in<\/span> groups\n<\/code><\/pre>\n\n\n\n
\u5e73\u5747\u5024\u306e\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97 \u4f8b2<\/h3>\n\n\n\n
\u3082\u3046\u4e00\u3064\u306e\u4f8b\u3068\u3057\u3066\u3001warpbreaks\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3067\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
warpbreaks\u306e\u30c7\u30fc\u30bf\u3067\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u3057\u3066\u307f\u305f\u7d50\u679c\u306f\u4ee5\u4e0b\u3092\u53c2\u7167\uff08\u30ea\u30f3\u30af\u5148\u8a18\u4e8b\u306e\u6700\u4e0b\u6bb5\uff09\u3002<\/p>\n\n\n
\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\tR \u3067\u50be\u5411\u691c\u5b9a\u3092\u884c\u3046\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t\u50be\u5411\u691c\u5b9a\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf\u3067\u89b3\u5bdf\u3055\u308c\u305f\u3001\u5e73\u5747\u5024\u3084\u5272\u5408\u304c\u3001\u3060\u3093\u3060\u3093\u306b\u5927\u304d\u304f\u306a\u308b\u3001\u3060\u3093\u3060\u3093\u306b\u5c0f\u3055\u304f\u306a\u308b\u3068\u3044\u3046\u50be\u5411\u304c\u3001\u6bcd\u96c6\u56e3\u3067\u3082\u305d\u306e\u901a\u308a\u304b\u691c\u5b9a\u3059\u308b\u3082\u306e\u3002 R\u3067\u3069\u306e\u3088…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n\n\n\n\n
\u5404\u7fa4\u306e\u5e73\u5747\u5024\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u300136.4, 26.4, 21.7\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
><\/span> with<\/span>(<\/span>data=<\/span>warpbreaks,<\/span> tapply<\/span>(<\/span>breaks,<\/span> tension,<\/span> mean))<\/span>\nL        M        H\n36.38889<\/span> 26.38889<\/span> 21.66667<\/span>\n<\/code><\/pre>\n\n\n\n
\u307e\u305f\u3001\u8aa4\u5dee\u5206\u6563\u306f\u5206\u6563\u5206\u6790\u8868\u304b\u3089141.1\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
><\/span> aov.res <-<\/span> aov<\/span>(<\/span>breaks ~<\/span> tension,<\/span> data=<\/span>warpbreaks)<\/span>\n><\/span> summary<\/span>(<\/span>aov.res)<\/span>\n            Df Sum Sq Mean Sq F<\/span> value  Pr<\/span>(<\/span>><\/span>F<\/span>)<\/span>\ntension      2<\/span>   2034<\/span>  1017.1<\/span>   7.206<\/span> 0.00175<\/span> **<\/span>\nResiduals   51<\/span>   7199<\/span>   141.1<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span>\n<\/code><\/pre>\n\n\n\n
\u4e0a\u8a18\u306e\u6761\u4ef6\u3067\u8a08\u7b97\u3059\u308b\u3068\u3001\u5404\u7fa411\u4f8b\u5fc5\u8981\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u306f\u5404\u7fa418\u4f8b\u306a\u306e\u3067\u3001
\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u306e\u305f\u3081\u306b\u306f\u5c11\u3057\u591a\u3081\u3060\u304c\u60aa\u304f\u306f\u306a\u3044\u3002<\/p>\n\n\n\n
><\/span> samplesize.mean.trend.test<\/span>(<\/span>mu=<\/span>c<\/span>(<\/span>36.4<\/span>,<\/span> 26.4<\/span>,<\/span> 21.7<\/span>),<\/span> sigma.sq=<\/span>141.1<\/span>,<\/span> score=<\/span>c<\/span>(<\/span>1<\/span>,<\/span>0<\/span>,<\/span>-<\/span>1<\/span>))<\/span>\nSample size determination for<\/span> trend test of the means\nn =<\/span> 10.25015<\/span>\nmu =<\/span> 36.4<\/span>,<\/span> 26.4<\/span>,<\/span> 21.7<\/span>\nsigma.sq =<\/span> 141.1<\/span>\nscore =<\/span> 1<\/span>,<\/span> 0<\/span>,<\/span> -<\/span>1<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\nNOTE:<\/span> n is each number in<\/span> groups\n<\/code><\/pre>\n\n\n\n
\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97 \u5e73\u5747\u5024\u306e\u5834\u5408\u3092\u30a8\u30af\u30bb\u30eb\u3067<\/h3>\n\n\n\n
\u3088\u3051\u308c\u3070\u3001\u4e0b\u8a18\u306e\u30ea\u30f3\u30af\u5148\u304b\u3089\u3069\u3046\u305e\u3002<\/p>\n\n\n\n
5\u30b0\u30eb\u30fc\u30d7\u307e\u3067\u5bfe\u5fdc\u3002<\/p>\n\n\n\n
\u5e73\u5747\u5024\u306e\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a \u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3010\u30a8\u30af\u30bb\u30eb\u3067\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3011 | TKER SHOP<\/a><\/p>\n\n\n\n
\u4f7f\u3044\u65b9\u89e3\u8aac\u52d5\u753b\u3002<\/p>\n\n\n\n
\u3053\u3061\u3089\u3082\u3088\u3051\u308c\u3070\u3069\u3046\u305e\u3002<\/p>\n\n\n\n