{"id":92,"date":"2013-03-26T17:04:00","date_gmt":"2013-03-26T09:04:00","guid":{"rendered":"http:\/\/xuguang.info\/blog\/2013\/03\/the-games-howell-test-in-r"},"modified":"2015-01-27T22:45:49","modified_gmt":"2015-01-27T14:45:49","slug":"%e5%9c%a8r%e8%af%ad%e8%a8%80%e4%b8%ad%e8%bf%9b%e8%a1%8cgames-howell%e6%a3%80%e9%aa%8c","status":"publish","type":"post","link":"https:\/\/xg1990.com\/blog\/en\/archives\/92","title":{"rendered":"\u5728R\u8bed\u8a00\u4e2d\u8fdb\u884cGames-Howell\u68c0\u9a8c"},"content":{"rendered":"

\u4e3b\u8981\u53c2\u8003http:\/\/www.gcf.dkf.unibe.ch\/BCB\/files\/BCB_10Jan12_Alexander.pdf<\/a><\/p>\n

\u5f53\u65b9\u5dee\u5206\u6790\u53d1\u73b0\u7ec4\u95f4\u5747\u503c\u7684\u663e\u8457\u6027\u5dee\u5f02\u4e4b\u540e\uff0c\u6211\u4eec\u4f1a\u8fdb\u4e00\u6b65\u9700\u8981\u77e5\u9053\u54ea\u51e0\u7ec4\u6709\u663e\u8457\u6027\u5dee\u5f02\uff0c\u8fd9\u5c31\u8981\u7528\u5230\u591a\u91cd\u6bd4\u8f83(Multiple comparisons)<\/p>\n

\u4f46\u662f\u6211\u4eec\u4e0d\u80fd\u4f7f\u7528\u4f20\u7edf\u7684t\u68c0\u9a8c\u6765\u8fdb\u884c\u591a\u91cd\u6bd4\u8f83\uff0c\u56e0\u4e3a\u4f20\u7edf\u7684t\u68c0\u9a8c\u72af\u7b2c\u4e00\u7c7b\u9519\u8bef\u7684\u6982\u7387\u4e3aa\uff0c\u82e5\u7528t\u68c0\u9a8c\u8fdb\u884c\u591a\u91cd\u6bd4\u8f83\uff0c\u4f1a\u628a\u72af\u7b2c\u4e00\u7c7b\u9519\u8bef\u6982\u7387\u63d0\u5347\u52301-(1-a)^(n(n-1)\/2)\uff0c\u5176\u4e2dn\u662f\u7ec4\u6570\uff0cn\u8d8a\u5927\u591a\u91cd\u6bd4\u8f83\u7ed3\u679c\u72af\u7b2c\u4e00\u7c7b\u9519\u8bef\u6982\u7387\u8d8a\u5927\u3002<\/p>\n

<\/p>\n

\u56e0\u6b64\u9700\u8981\u4f7f\u7528\u5176\u4ed6\u7684\u591a\u91cd\u6bd4\u8f83\u65b9\u6cd5\uff0c\u4e00\u822c\u4f1a\u7528\u5230\u4ee5\u4e0b4\u79cd\uff1a<\/p>\n

1.Fisher LSD ,\u4f46\u662f\u9700\u8981\u6821\u6b63<\/p>\n

2.Tukey HSD ,\u4f46\u662f\u4ec5\u9650\u7b49\u6837\u672c\u91cf\u7684\u6761\u4ef6\u4e0b<\/p>\n

3.Duncan\u2019s test\uff0c \u4f46\u662f\u4ec5\u9650\u7b49\u6837\u672c\u91cf\u7684\u6761\u4ef6\u4e0b<\/p>\n

4.Games-Howell \uff0c \u53ef\u4ee5\u7528\u4e8e\u4e0d\u7b49\u6837\u672c\u91cf\u3001\u7ec4\u95f4\u65b9\u5dee\u4e0d\u540c\u7684\u60c5\u51b5\u4e0b<\/p>\n

\u53ef\u89c1\uff0c\u5728\u5b9e\u9645\u7814\u7a76\u4e2d\u6700\u9002\u7528\u7684\u8fd8\u662fGames-Howell\u65b9\u6cd5\uff0c
\n\u5177\u4f53\u65b9\u6cd5\u53d1\u8868\u5728\u8fd9\u91cc<\/p>\n

Paul A. Games and John F. Howell\r\nPairwise Multiple Comparison Procedures with Unequal N's and\/or Variances: A Monte Carlo Study\r\nJournal of Educational Statistics,Vol.1, No. 2, 1976, pp. 113-125<\/pre>\n
\u8fd9\u4e2a\u65b9\u6cd5\u600e\u4e48\u5b9e\u65bd\u5462\uff1f
\n\u5982\u679c\u4f60\u6709SPSS\uff0c\u5c31\u4e0d\u7528\u62c5\u5fc3\u4e86\uff0c\u91cc\u9762\u6709\u8fd9\u4e2a\u529f\u80fd\u3002
\n\u800c\u81f3\u4eca\u6ca1\u6709\u4e00\u4e2aR\u5305\u80fd\u5b9e\u73b0\u8fd9\u4e2a\u529f\u80fd\u3002
\n\u4f46\u662f\uff0c\u8fd9\u91cc\u6709\u4efd\u65e5\u672c\u4eba\u5199\u7684\u4ee3\u7801\uff08\u4ee3\u7801\u94fe\u63a5<\/a>,\u8bf4\u660e\u94fe\u63a5<\/a>\uff09\u5b8c\u6210\u4e86\u8fd9\u4e2a\u529f\u80fd\uff0c<\/p>\n
\u5177\u4f53\u7528\u6cd5\u662f\u8fd9\u6837\u7684\uff0c\u5148\u7528\u4ee5\u4e0b\u547d\u4ee4\u8bfb\u5165\u4ee3\u7801\uff1a<\/p>\n
source("http:\/\/aoki2.si.gunma-u.ac.jp\/R\/src\/tukey.R", encoding="euc-jp")<\/pre>\n
\u6216\u8005\u76f4\u63a5\u62f7\u8d1d\u4ee5\u4e0b\u5185\u5bb9\uff1a<\/p>\n
# Tukey \u306e\u65b9\u6cd5\u306b\u3088\u308b\u591a\u91cd\u6bd4\u8f03\r\n# Games-Howell \u306e\u65b9\u6cd5\u3082\u9078\u629e\u3067\u304d\u308b\u3088\u3046\u306b\u62e1\u5f35 2009\/08\/03\r\ntukey <- function(\tdata,\t\t\t\t\t# \u89b3\u5bdf\u5024\u30d9\u30af\u30c8\u30eb\r\n\t\t\tgroup,\t\t\t\t\t# \u7fa4\u5909\u6570\u30d9\u30af\u30c8\u30eb\r\n\t\t\tmethod=c("Tukey", "Games-Howell"))\t# \u624b\u6cd5\u306e\u9078\u629e\r\n{\r\n\tOK <- complete.cases(data, group)\t\t\t# \u6b20\u640d\u5024\u3092\u6301\u3064\u30b1\u30fc\u30b9\u3092\u9664\u304f\r\n\tdata <- data[OK]\r\n\tgroup <- factor(group[OK])\r\n\tn <- tapply(data, group, length)\t\t\t# \u5404\u7fa4\u306e\u30b1\u30fc\u30b9\u6570\r\n\ta <- length(n)\t\t\t\t\t\t# \u7fa4\u306e\u6570\r\n\tphi.e <- sum(n)-a\t\t\t\t\t# \u8aa4\u5dee\u5206\u6563\uff08\u7fa4\u5185\u4e0d\u504f\u5206\u6563\uff09\u306e\u81ea\u7531\u5ea6\r\n\tMean <- tapply(data, group, mean)\t\t\t# \u5404\u7fa4\u306e\u5e73\u5747\u5024\r\n\tVariance <- tapply(data, group, var)\t\t\t# \u5404\u7fa4\u306e\u4e0d\u504f\u5206\u6563\r\n\tresult1 <- cbind(n, Mean, Variance)\t\t\t# \u5404\u7fa4\u306e\u7d71\u8a08\u91cf\r\n\trownames(result1) <- paste("Group", 1:a, sep="")\r\n\tmethod <- match.arg(method)\r\n\tif (method == "Tukey") {\t\t\t\t# Tukey \u306e\u65b9\u6cd5\r\n\t\tv.e <- sum((n-1)*Variance)\/phi.e\t\t# \u8aa4\u5dee\u5206\u6563\uff08\u7fa4\u5185\u4e0d\u504f\u5206\u6563\uff09\r\n\t\tt <- combn(a, 2, function(ij)\t\t\t# \u5bfe\u6bd4\u8f03\r\n\t\t\t\t\tabs(diff(Mean[ij]))\/sqrt(v.e*sum(1\/n[ij])) )\r\n\t\tp <- ptukey(t*sqrt(2), a, phi.e, lower.tail=FALSE)\t# \u6709\u610f\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\r\n\t\tTukey <- cbind(t, p)\t\t\t\t\t# \u5bfe\u6bd4\u8f03\u306e\u7d50\u679c\r\n\t\trownames(Tukey) <- combn(a, 2, paste, collapse=":")\r\n\t\treturn(list(result1=result1, Tukey=Tukey, phi=phi.e, v=v.e))\r\n\t}\r\n\telse {\t\t\t\t\t\t\t# Games-Howell \u306e\u65b9\u6cd5\r\n\t\tt.df <- combn(a, 2, function(ij) {\t\t# \u5bfe\u6bd4\u8f03\r\n\t\t\t\t\tt <- abs(diff(Mean[ij]))\/sqrt(sum(Variance[ij]\/n[ij]))\r\n\t\t\t\t\tdf <- sum(Variance[ij]\/n[ij])^2\/sum((Variance[ij]\/n[ij])^2\/(n[ij]-1))\r\n\t\t\t\t\treturn(c(t, df))} )\r\n\t\tt <- t.df[1,]\r\n\t\tdf <- t.df[2,]\r\n\t\tp <- ptukey(t*sqrt(2), a, df, lower.tail=FALSE)\t# \u6709\u610f\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\r\n\t\tGames.Howell <- cbind(t, df, p)\t\t\t# \u5bfe\u6bd4\u8f03\u306e\u7d50\u679c\r\n\t\trownames(Games.Howell) <- combn(a, 2, paste, collapse=":")\r\n\t\treturn(list(result1=result1, Games.Howell=Games.Howell))\r\n\t}\r\n}<\/pre>\n
\u5f53\u7136\u4e5f\u53ef\u4ee5\u628a\u4ee3\u7801\u4e0b\u8f7d\u5230\u672c\u5730\u518d\u8bfb\u53d6\u3002<\/p>\n
\u82e5\u8981\u4f7f\u7528Games-Howell\u65b9\u6cd5\u8fdb\u884c\u591a\u91cd\u6bd4\u8f83\uff0c\u8c03\u7528\u51fd\u6570<\/p>\n
<code>tukey(data, group, method="G")\r\n<\/code><\/pre>\n
\u5373\u53ef\uff0c\u5176\u4e2ddata\u4e3a\u503c\uff0c\u5373\u8fde\u7eed\u53d8\u91cf\uff1bgroup\u4e3a\u540d\u4e49\u53d8\u91cf\uff0c\u5373\u5206\u7c7b\u53d8\u91cf\uff1bmethod=\u201dG\u201d\u544a\u8bc9\u51fd\u6570\u4f7f\u7528Games-Howell\u65b9\u6cd5\u8fdb\u884c\u591a\u91cd\u6bd4\u8f83\u3002<\/p>\n
\u5206\u6790\u7ed3\u679c\u8ddfSPSS\u7ed3\u679c\u5dee\u5f02\u4e0d\u5927\uff0c\u8fd9\u4efd\u4ee3\u7801\u7528\u8d77\u6765\u6ca1\u4ec0\u4e48\u5927\u95ee\u9898\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u4e3b\u8981\u53c2\u8003http:\/\/www.gcf.dkf.unibe.ch\/BCB\/files\/BCB_10Jan12_Alexander.pdf \u5f53\u65b9\u5dee\u5206\u6790\u53d1\u73b0\u7ec4\u95f4\u5747\u503c\u7684\u663e\u8457\u6027\u5dee\u5f02\u4e4b\u540e\uff0c\u6211\u4eec\u4f1a\u8fdb\u4e00\u6b65\u9700\u8981\u77e5\u9053\u54ea\u51e0\u7ec4\u6709\u663e\u8457\u6027\u5dee\u5f02\uff0c\u8fd9\u5c31\u8981\u7528\u5230\u591a\u91cd\u6bd4\u8f83(Multiple comparisons) \u4f46\u662f\u6211\u4eec\u4e0d\u80fd\u4f7f\u7528\u4f20\u7edf\u7684t\u68c0\u9a8c\u6765\u8fdb\u884c\u591a\u91cd\u6bd4\u8f83\uff0c\u56e0\u4e3a\u4f20\u7edf\u7684t\u68c0\u9a8c\u72af\u7b2c\u4e00\u7c7b\u9519\u8bef\u7684\u6982\u7387\u4e3aa\uff0c\u82e5\u7528t\u68c0\u9a8c\u8fdb\u884c\u591a\u91cd\u6bd4\u8f83\uff0c\u4f1a\u628a\u72af\u7b2c\u4e00\u7c7b\u9519\u8bef\u6982\u7387\u63d0\u5347\u52301-(1-a)^(n(n-1)\/2)\uff0c\u5176\u4e2dn\u662f\u7ec4\u6570\uff0cn\u8d8a\u5927\u591a\u91cd\u6bd4\u8f83\u7ed3\u679c\u72af\u7b2c\u4e00\u7c7b\u9519\u8bef\u6982\u7387\u8d8a\u5927\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":""},"categories":[4],"tags":[22,21,10],"translation":{"provider":"WPGlobus","version":"3.0.1","language":"en","enabled_languages":["zh","en"],"languages":{"zh":{"title":true,"content":true,"excerpt":false},"en":{"title":false,"content":false,"excerpt":false}}},"yoast_head":"\n\u5728R\u8bed\u8a00\u4e2d\u8fdb\u884cGames-Howell\u68c0\u9a8c - 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