{"id":457,"date":"2019-01-03T14:16:10","date_gmt":"2019-01-03T05:16:10","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/correlation-coefficient-test-and-confidence-interval-in-r\/"},"modified":"2024-10-12T17:23:33","modified_gmt":"2024-10-12T08:23:33","slug":"correlation-coefficient-test-and-confidence-interval-in-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/correlation-coefficient-test-and-confidence-interval-in-r\/","title":{"rendered":"R \u3067\u76f8\u95a2\u4fc2\u6570\u691c\u5b9a\u306e\u5b9f\u884c\u3068\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

R \u3067\u76f8\u95a2\u4fc2\u6570\u306e\u691c\u5b9a\u3068\u63a8\u5b9a\u306f cor.test() \u3067\u3067\u304d\u308b\u304c\u3001\u500b\u3005\u306e\u30c7\u30fc\u30bf\u304c\u5fc5\u8981\u3060\u3002<\/p>\n\n\n\n

\u500b\u3005\u306e\u30c7\u30fc\u30bf\u3092\u4f7f\u308f\u306a\u304f\u3066\u3082\u3001\u691c\u5b9a\u3084\u63a8\u5b9a\u306f\u3067\u304d\u306a\u3044\u3060\u308d\u3046\u304b\uff1f<\/p>\n\n\n\n\n\n\n\n

\u76f8\u95a2\u4fc2\u6570\u306e\u691c\u5b9a<\/h2>\n\n\n\n

\u6bcd\u76f8\u95a2\u4fc2\u6570 \u03c1\uff08\u30ed\u30fc\uff09 \u304c\u30bc\u30ed\u304b\u3069\u3046\u304b\u306e\u691c\u5b9a\u3002<\/p>\n\n\n\n

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

r \u304c\u30b5\u30f3\u30d7\u30eb\u306e\u76f8\u95a2\u4fc2\u6570\u3067\u3001n \u304c\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3002<\/p>\n\n\n\n

pop.rho.test <-<\/span> function<\/span>(<\/span>r,<\/span>n){<\/span>\nT<\/span> <-<\/span> r\/<\/span>(<\/span>sqrt<\/span>(<\/span>1<\/span>-<\/span>r^<\/span>2<\/span>)<\/span>\/<\/span>sqrt<\/span>(<\/span>n-<\/span>2<\/span>))<\/span>\np <-<\/span> pt<\/span>(<\/span>abs<\/span>(<\/span>T<\/span>),<\/span> df=<\/span>n-<\/span>2<\/span>,<\/span>lower.tail=<\/span>F<\/span>)<\/span>*<\/span>2<\/span>\nlist<\/span>(<\/span>c<\/span>(<\/span>t=<\/span>T<\/span>,<\/span> df=<\/span>n-<\/span>2<\/span>,<\/span> \"p-value\"<\/span>=<\/span>p))<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
r = -0.533, n = 53 \u306e\u3068\u304d\u306e\u691c\u5b9a\u7d50\u679c\u306f\u3001\u4ee5\u4e0b\u306e\u901a\u308a\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
><\/span> pop.rho.test<\/span>(<\/span>r=-<\/span>0.533<\/span>,<\/span>n=<\/span>35<\/span>)<\/span>\n[[<\/span>1<\/span>]]<\/span>\nt            df       p-<\/span>value\n-<\/span>3.6187173384<\/span> 33.0000000000<\/span>  0.0009787127<\/span>\n<\/code><\/pre>\n\n\n\n
p = 0.0009787127 \u3067\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u6bcd\u76f8\u95a2\u4fc2\u6570\u306f 0 \u3068\u7570\u306a\u308b\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n
\u76f8\u95a2\u4fc2\u6570\u306e\u4fe1\u983c\u533a\u9593<\/h2>\n\n\n\n
\u6bcd\u76f8\u95a2\u4fc2\u6570 \u03c1 \u306e95%\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
pop.rho.ci <-<\/span> function<\/span>(<\/span>r,<\/span>n){<\/span>\nZ <-<\/span> 1<\/span>\/<\/span>2<\/span>*<\/span>log<\/span>((<\/span>1<\/span>+<\/span>r)<\/span>\/<\/span>(<\/span>1<\/span>-<\/span>r))<\/span>\nZl <-<\/span> Z-<\/span>1<\/span>\/<\/span>sqrt<\/span>(<\/span>n-<\/span>3<\/span>)<\/span>*<\/span>qnorm<\/span>(<\/span>1<\/span>-<\/span>0.05<\/span>\/<\/span>2<\/span>)<\/span>\nZu <-<\/span> Z+<\/span>1<\/span>\/<\/span>sqrt<\/span>(<\/span>n-<\/span>3<\/span>)<\/span>*<\/span>qnorm<\/span>(<\/span>1<\/span>-<\/span>0.05<\/span>\/<\/span>2<\/span>)<\/span>\nrl <-<\/span> (<\/span>exp<\/span>(<\/span>2<\/span>*<\/span>Zl)<\/span>-<\/span>1<\/span>)<\/span>\/<\/span>(<\/span>exp<\/span>(<\/span>2<\/span>*<\/span>Zl)<\/span>+<\/span>1<\/span>)<\/span>\nru <-<\/span> (<\/span>exp<\/span>(<\/span>2<\/span>*<\/span>Zu)<\/span>-<\/span>1<\/span>)<\/span>\/<\/span>(<\/span>exp<\/span>(<\/span>2<\/span>*<\/span>Zu)<\/span>+<\/span>1<\/span>)<\/span>\nlist<\/span>(<\/span>c<\/span>(<\/span>Estimate=<\/span>r,<\/span> LL=<\/span>rl,<\/span> UL=<\/span>ru))<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
\u4e0a\u8ff0\u306e\u76f8\u95a2\u4fc2\u6570\u306e\u4fe1\u983c\u533a\u9593\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
><\/span> pop.rho.ci<\/span>(<\/span>r=-<\/span>0.533<\/span>,<\/span>n=<\/span>35<\/span>)<\/span>\n[[<\/span>1<\/span>]]<\/span>\nEstimate         LL         UL\n-<\/span>0.5330000<\/span> -<\/span>0.7355906<\/span> -<\/span>0.2428969<\/span>\n<\/code><\/pre>\n\n\n\n
\u4e0b\u9650\u304c -0.7355906, \u4e0a\u9650\u304c -0.2428969 \u3067\u3042\u3063\u305f\u3002<\/p>\n\n\n\n
\u76f8\u95a2\u4fc2\u6570\u306e\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u969b\u306eFisher\u306e\u5206\u6563\u5b89\u5b9a\u5316\u5909\u63db<\/h3>\n\n\n\n
\u4e0a\u8ff0\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u4e2d\u306e Z \u306e\u5f0f\u306f\u3001Fisher\u306e\u5206\u6563\u5b89\u5b9a\u5316\u5909\u63db\u3068\u547c\u3070\u308c\u308b\u3082\u306e\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\u3053\u308c\u306f hyperbolic tangent \u306e\u9006\u95a2\u6570\u306e hyperbolic arc-tangent \u3067\u3001R \u3067\u306f atanh() \u3067\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
><\/span> r <-<\/span> -<\/span>0.533<\/span>\n><\/span>\n><\/span> 1<\/span>\/<\/span>2<\/span>*<\/span>log<\/span>((<\/span>1<\/span>+<\/span>r)<\/span>\/<\/span>(<\/span>1<\/span>-<\/span>r))<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.5943263<\/span>\n><\/span>\n><\/span> atanh<\/span>(<\/span>r)<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.5943263<\/span>\n<\/code><\/pre>\n\n\n\n
\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n\"\"<\/a>\r\n
\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div>
\u76f8\u95a2\u4fc2\u6570\u306e\u5dee\u306e\u691c\u5b9a<\/h2>\n\n\n\n
\u4e8c\u3064\u306e\u6bcd\u76f8\u95a2\u4fc2\u6570 $ \\rho_A $ \u3068 $ \\rho_B $ \u306e\u5dee\u306e\u691c\u5b9a\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
pop.rho.diff <-<\/span> function<\/span>(<\/span>rA,<\/span>nA,<\/span>rB,<\/span>nB){<\/span>\nT<\/span> <-<\/span> abs<\/span>((<\/span>atanh<\/span>(<\/span>rA)<\/span>-<\/span>atanh<\/span>(<\/span>rB)))<\/span>\/<\/span>sqrt<\/span>(<\/span>1<\/span>\/<\/span>(<\/span>nA-<\/span>3<\/span>)<\/span>+<\/span>1<\/span>\/<\/span>(<\/span>nB-<\/span>3<\/span>))<\/span>\np <-<\/span> 2<\/span>*<\/span>(<\/span>1<\/span>-<\/span>pnorm<\/span>(<\/span>T<\/span>))<\/span>\nlist<\/span>(<\/span>c<\/span>(<\/span>rA=<\/span>rA,<\/span>nA=<\/span>nA,<\/span>rB=<\/span>rB,<\/span>nB=<\/span>nB,<\/span>T<\/span>=<\/span>T<\/span>,<\/span>\"p-value\"<\/span>=<\/span>p))<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
\u7537\u6027 -0.459 \u3068\u5973\u6027 -0.097 \u306e\u76f8\u95a2\u4fc2\u6570\u306e\u5dee\u3092\u691c\u5b9a\u3057\u305f\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
><\/span> pop.rho.diff<\/span>(<\/span>rA=-<\/span>0.459<\/span>,<\/span>nA=<\/span>30<\/span>,<\/span>rB=-<\/span>0.097<\/span>,<\/span>nB=<\/span>24<\/span>)<\/span>\n[[<\/span>1<\/span>]]<\/span>\nrA         nA         rB         nB          T<\/span>    p-<\/span>value\n-<\/span>0.4590000<\/span> 30.0000000<\/span> -<\/span>0.0970000<\/span> 24.0000000<\/span>  1.3704342<\/span>  0.1705514<\/span>\n<\/code><\/pre>\n\n\n\n
p = 0.1705514 \u3067\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3067\u306f\u306a\u304b\u3063\u305f\u304c\u3001-0.459 \u3068 -0.097 \u306f\u304b\u306a\u308a\u5927\u304d\u306a\u9055\u3044\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5c0f\u3055\u3059\u304e\u305f\u3053\u3068\u306b\u3088\u308b\u691c\u51fa\u529b\u4e0d\u8db3\u3068\u8003\u3048\u3089\u308c\u308b\u3002<\/p>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
R\u3067\u3001\u76f8\u95a2\u4fc2\u6570\u306e\u691c\u5b9a\u3068\u4fe1\u983c\u533a\u9593\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u3092\u7d39\u4ecb\u3057\u305f\u3002<\/p>\n\n\n\n
\u500b\u3005\u306e\u30c7\u30fc\u30bf\u304c\u4f7f\u3048\u308b\u5834\u5408\u306f\u3001cor.test() \u3067\u691c\u5b9a\u3068\u4fe1\u983c\u533a\u9593\u306f\u7c21\u5358\u306b\u5f97\u3089\u308c\u308b\u304c\u3001\u76f8\u95a2\u4fc2\u6570\u3068\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3057\u304b\u308f\u304b\u3089\u306a\u3044\u5834\u5408\u306f\u3001cor.test()\u306f\u4f7f\u3048\u306a\u3044\u306e\u3067\u3001\u4eca\u56de\u7d39\u4ecb\u3057\u305f\u30b9\u30af\u30ea\u30d7\u30c8\u304c\u5f79\u306b\u7acb\u3064\u3002<\/p>\n\n\n\n
\u307e\u305f\u30012\u3064\u306e\u76f8\u95a2\u4fc2\u6570\u306e\u5dee\u306e\u691c\u5b9a\u306f\u3001\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u306f\u88c5\u5099\u3055\u308c\u3066\u3044\u306a\u3044\u306e\u3067\u3001\u4eca\u56de\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u304c\u4f7f\u3048\u308b\u3002<\/p>\n\n\n\n
\u3088\u308a\u30b9\u30de\u30fc\u30c8\u306b\u307e\u3068\u307e\u3063\u3066\u3044\u308b\u30b9\u30af\u30ea\u30d7\u30c8\u306f cor.diff.test() \u3067\u691c\u7d22\u3059\u308b\u3068\u898b\u3064\u304b\u308b\u3002<\/p>\n\n\n\n
brainGraph\u30d1\u30c3\u30b1\u30fc\u30b8\u306b\u542b\u307e\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
cor.diff.test function – RDocumentation<\/a><\/p>\n\n\n\n
\u95a2\u9023\u8a18\u4e8b<\/h2>\n\n\n\n
cor.test()\u306e\u4f7f\u3044\u65b9\u306f\u3053\u3061\u3089\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\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t\u4f8b\u3048\u3070\u3001\u8eab\u9577\u304c\u9ad8\u3044\u3068\u4f53\u91cd\u304c\u91cd\u3044\u3068\u304b\u3001\u5e74\u9f62\u304c\u9ad8\u3044\u3068\u8840\u5727\u3082\u9ad8\u3044\u3068\u304b\u3001\u95a2\u4fc2\u3057\u3066\u3044\u308b\u4e8c\u3064\u306e\u4e8b\u67c4\u306f\u591a\u3044\u3002 \u3053\u308c\u3092\u76f8\u95a2\u95a2\u4fc2\u3068\u3044\u3046\u3002 R \u3067\u3001\u6563\u5e03\u56f3\u3001\u76f8\u95a2\u4fc2\u6570\u8a08\u7b97\u3001\u76f8\u95a2\u4fc2\u6570\u691c…<\/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
\u5f15\u7528\u66f8\u7c4d<\/h2>\n\n\n\n
\u51fa\u5178\u306f\u3001\u300c\u65b0\u7248\u533b\u5b66\u3078\u306e\u7d71\u8a08\u5b66\u300d\u306e6.1 \u76f8\u95a2\u4fc2\u6570\u306e\u691c\u5b9a\u3068\u4fe1\u983c\u533a\u9593\u306e\u4f8b\u984c<\/p>\n\n\n\n
\"\u533b\u5b66\u3078\u306e\u7d71\u8a08\u5b66<\/a><\/figure>\n\n\n\n
<\/div>\n\n\n\n
\n
\u533b\u5b66\u3078\u306e\u7d71\u8a08\u5b66 (\u7d71\u8a08\u30e9\u30a4\u30d6\u30e9\u30ea\u30fc)<\/a><\/p>\n