鍢匡紝浣犳槸涓嶆槸涔熼亣鍒拌繃杩欑澶寸柤浜嬧€斺€旀墜閲屾敟鐫€涓夊洓缁勫疄楠屾暟鎹紝鐪肩潧鐪嬭姳浜嗕篃鍒嗕笉娓呭畠浠埌搴曟湁娌℃湁鏈川鍖哄埆锛燄煠?鍒厡锛佷粖澶╁挶浠氨鐢ㄢ€?strong>鈥嬫柟宸垎鏋愨€?/strong>鈥嬪拰鈥?strong>鈥婯ruskal-Wallis妫€楠屸€?/strong>鈥嬭繖瀵?榛勯噾鎼。"锛屾墜鎶婃墜鏁欎綘鐮磋В澶氱粍鏁版嵁宸紓鐨勫瘑鐮侊紒淇濊瘉鐪嬪畬浣犱細鎷嶅ぇ鑵匡細"鍘熸潵缁熻杩樿兘杩欎箞鐜╋紒"

馃攳 涓€銆佷负鍟ヨ鎼炴噦澶氱粍姣旇緝锛熺湡瀹炴渚嬪憡璇変綘锛?/h3>

鎯宠薄涓€涓嬶細浣犳槸鏌愰摱琛岀殑鏁版嵁鍒嗘瀽甯堬紝鑰佹澘鐢╃粰浣犱笁缁刅IP瀹㈡埛鐨勮处鎴蜂綑棰濇暟鎹紙鍒嗚A/B/C锛夛紝璁╀綘鍒ゆ柇鍝鍒嗚涓氱哗鏈€鐗涖€傛垨鑰呬綘鏄尰鑽爺绌跺憳锛岃姣旇緝涓夌鑽墿瀵瑰皬鐧介紶瀛樻椿澶╂暟鐨勫奖鍝?..杩欐椂鍊欏鏋滃彧浼氱敤T妫€楠屼袱涓ゆ瘮杈冣€斺€斺€?strong>鈥嬬粨鏋滃彲鑳介敊寰楃璋扁€?/strong>鈥嬶紒鍥犱负锛?/p>

馃挕 鈥?strong>鈥嬭嚧鍛介櫡闃扁€?/strong>鈥嬶細姣忓仛涓€娆妫€楠岋紝鐘敊姒傜巼灏卞彔鍔犱竴娆★紒姣旇緝3缁勯渶瑕?娆妫€楠岋紝鎬荤姱閿欑巼椋欏崌鍒?4.3%锛堣繙瓒呰繃5%鐨勫畨鍏ㄧ嚎锛?/p>

鎵€浠ユ垜浠渶瑕佹洿涓撲笟鐨勫伐鍏凤細鈥?strong>鈥嬫柟宸垎鏋愶紙ANOVA锛夆€?/strong>鈥?鍜屽畠鐨?鏁戠伀闃熷憳"鈥?strong>鈥婯ruskal-Wallis妫€楠屸€?/strong>鈥嬶紒

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馃搳 浜屻€佹柟宸垎鏋愶細鎷嗚В鏁版嵁鍙樺紓鐨?渚︽帰鏈?

鈥?strong>鈥嬫牳蹇冩€濇兂宸ㄧ畝鍗曗€?/strong>鈥嬶細鎶婃暟鎹尝鍔ㄦ媶鎴愪袱閮ㄥ垎鈥斺€?/p>

• 鈥?strong>鈥嬬粍闂村彉寮傗€?/strong>鈥嬶紙鍒嗚A/B/C涔嬮棿鐨勫樊寮傦級
• 鈥?strong>鈥嬬粍鍐呭彉寮傗€?/strong>鈥嬶紙鍚屼竴鍒嗚瀹㈡埛闂寸殑闅忔満娉㈠姩锛?/li>

鐢ㄥ叕寮忚浜鸿瘽灏辨槸锛?br/> 鈥?strong>鈥嬫€绘尝鍔?= 缁勯棿娉㈠姩 + 缁勫唴娉㈠姩鈥?/strong>鈥?br/> 锛堢粺璁″鍙玈S鎬?SS缁勯棿+SS缁勫唴锛?/p>

鈻?涓夋鎼炲畾鏂瑰樊鍒嗘瀽锛?/h4>

1. 鈥?strong>鈥嬪厛杩囦袱閬撳畨妫€鈥?/strong>鈥嬶細

   • 鈥?strong>鈥嬫鎬佹€ф楠屸€?/strong>鈥嬶細QQ鍥炬垨Shapiro-Wilk妫€楠岋紙P>0.05鎵嶈繃鍏筹級
   • 鈥?strong>鈥嬫柟宸綈鎬ф楠屸€?/strong>鈥嬶細Bartlett妫€楠岋紙P>0.05鎵嶈兘缁х画锛?/li>

2. 鈥?strong>鈥嬬畻涓叧閿寚鏍囷細F鍊尖€?/strong>鈥?br/> F = (缁勯棿娉㈠姩/鑷敱搴? 梅 (缁勫唴娉㈠姩/鑷敱搴?
   鈥?strong>鈥嬬炕璇戔€?/strong>鈥嬶細濡傛灉缁勯棿宸紓杩滃ぇ浜庣粍鍐呭樊寮傦紝F鍊煎氨鐖嗚〃锛?/p>

3. 鈥?strong>鈥嬫煡琛ㄥ畾鑳滆礋鈥?/strong>鈥嬶紙瀹為檯鐢ㄨ蒋浠剁鍑虹粨鏋滐級锛?/p>

   鏂瑰樊鏉ユ簮	鑷敱搴?/th>	骞虫柟鍜?/th>	鍧囨柟鍜?/th>	F鍊?/th>	P鍊?/th>
   缁勯棿	2	2315	1158	82.68	<0.001
   缁勫唴	18	252	14
   鈥?strong>鈥嬬粨璁衡€?/strong>鈥嬶細P<0.001锛熶笁瀹跺垎琛孷IP浣欓鈥?strong>鈥嬬粷瀵规湁鐚吇鈥?/strong>鈥嬶紒

馃毃 鈥?strong>鈥嬫敞鎰忥紒鈥?/strong>鈥?鏂瑰樊鍒嗘瀽鏈夆€?strong>鈥嬩袱澶ф绌粹€?/strong>鈥嬶細

• 鏁版嵁蹇呴』鏈嶄粠姝ｆ€佸垎甯冿紙鍚﹀垯F鍊间細鎾掕皫锛?/li>
• 缁勯棿鏂瑰樊瑕侀綈鏁达紙涓嶇劧灏卞儚姣旇緝鑻规灉鍜岃タ鐡滐級

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馃Ω 涓夈€並ruskal-Wallis妫€楠岋細涓撴不"涓嶅惉璇濇暟鎹?鐨勭‖姹?/h3>

褰撲綘鍙戠幇鏁版嵁鈥?strong>鈥嬮暱寰楁鐡滆鏋ｂ€?/strong>鈥嬶紙姣斿姝讳骸鐜囥€佹敹鍏ヨ繖绉嶅父鍋忔€佺殑鏁版嵁锛夛紝鎴栬€呪€?strong>鈥嬫柟宸竷涓婂叓涓嬧€?/strong>鈥嬫椂鈥斺€斿埆鏀惧純锛佲€?strong>鈥婯ruskal-Wallis妫€楠屸€?/strong>鈥嬫潵鏁戝満锛?/p>

鈻?瀹冪殑缁濇嫑灏卞洓涓瓧锛氣€?strong>鈥嬫瘮澶у皬鎺掑簭锛佲€?/strong>鈥?/h4>

1. 鈥?strong>鈥嬫墍鏈変汉涓€璧锋帓搴ф鈥?/strong>鈥嬶細
   鎶婁笁缁勬暟鎹贩鍚堬紝浠庢渶灏忓埌鏈€澶ф帓鍚嶏紙1,2,3...锛?br/> 馃尠 閽夎灪姝讳骸鐜囨暟鎹細6.5%鎺掔1鍚嶏紝9.0%鎺掔2鍚?..49.0%鎺掔15鍚?/p>

2. 鈥?strong>鈥嬭绠楀悇缁?鍦颁綅鍊?锛堢З鍜岋級鈥?/strong>鈥嬶細

   • 鐢茶嵂缁勶細32.5%鈫掔?鍚嶏紝35.5%鈫掔?鍚?..鍔犳€诲緱鈥?strong>鈥嬬З鍜孯1鈥?/strong>鈥?/li>
   • 鍚岀悊绠椾箼鑽粍R2銆佷笝鑽粍R3

3. 鈥?strong>鈥嬪叕寮忔毚鍑烩€?/strong>鈥嬶細
   H = [12/(N(N+1))] * 危(Ri虏/ni) - 3(N+1)
   锛堢湅涓嶆噦锛熺洿鎺ョ悊瑙ｄ负锛欻鍊艰秺澶э紝缁勯棿宸紓瓒婃樉钁楋紒锛?/p>

4. 鈥?strong>鈥嬬粨鏋滆В璇烩€?/strong>鈥嬶細

   • 閽夎灪瀹為獙H=9.74锛孭=0.008 鈫?鈥?strong>鈥嬩笁绉嶈嵂鏁堟灉缁濆涓嶅悓锛佲€?/strong>鈥?/li>

鉁?鈥?strong>鈥嬩紭鍔挎€荤粨鈥?/strong>鈥嬶細

• 涓嶈姹傛鎬佸垎甯冿紝鈥?strong>鈥嬭劯鐨帤鐨勬暟鎹篃鑳界敤鈥?/strong>鈥?/li>
• 瀵瑰紓甯稿€尖€?strong>鈥嬭秴绾у瀹光€?/strong>鈥嬶紙绠′綘鏄湡璞繕鏄篂涓愶紝缁熺粺鎸夋帓鍚嶈璇濓級

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鈿旓笍 鍥涖€丅attle鏃堕棿锛氭柟宸垎鏋?vs Kruskal-Wallis 鎬庝箞閫夛紵

閫氳繃涓€涓姣旇〃绉掓噦鍐崇瓥馃憞锛?/p>

鈥?strong>鈥嬩妇涓牀瀛愷煂扳€?/strong>鈥嬶細

• 鎯虫瘮杈冧笁绉嶆暀瀛︽柟娉曗€?strong>鈥嬪钩鍧囧垎鈥?/strong>鈥嬶紵鈫?鈥?strong>鈥嬮€夋柟宸垎鏋愨€?/strong>鈥?/li>
• 鎯虫瘮杈冧笁缁勬偅鑰呯柤鐥涒€?strong>鈥嬬瓑绾ц瘎鍒嗏€?/strong>鈥嬶紙1-10绾э級锛熲啋 鈥?strong>鈥嬮€塊ruskal-Wallis鈥?/strong>鈥?/li>

馃З 浜斻€佷簨鍚庢楠岋細鏄捐憲涔嬪悗鎬庝箞鍔烇紵

褰揚<0.05鏃讹紝浣犱細鍏村鍦板枈锛?鏈夊樊寮傦紒"...鐒跺悗鍛紵鈥?strong>鈥嬪埌搴曡皝鍜岃皝涓嶅悓锛熲€?/strong>鈥?杩欐椂鍊欓渶瑕?琛ュ垁鎶€鑳?鈥斺€斾簨鍚庢楠岋紒

鈻?鏂瑰樊鍒嗘瀽鐨?琛ュ垁"锛歍ukey HSD

python澶嶅埗
# Python绀轰緥
from statsmodels.stats.multicomp import pairwise_tukeyhsd
tukey = pairwise_tukeyhsd(鏁版嵁, 鍒嗙粍, alpha=0.05)
print(tukey) # 杈撳嚭姣忕粍PK缁撴灉

鈥?strong>鈥嬬粨鏋滆В璇烩€?/strong>鈥嬶細

• 鑻-B缁勭殑P<0.05 鈫?鈥?strong>鈥嬭繖淇╃湡鏈変粐鈥?/strong>鈥?/li>
• 鑻-C缁凱>0.05 鈫?鈥?strong>鈥嬭繖淇╁崐鏂ゅ叓涓も€?/strong>鈥?/li>

鈻?Kruskal-Wallis鐨?琛ュ垁"锛歂emenyi娉?/h4>

杩樻槸閽夎灪瀹為獙锛?/p>

缁勯棿瀵规瘮	P鍊?/th>	缁撹
鐢茶嵂vs涔欒嵂	0.006	鈥?strong>鈥嬫樉钁椾笉鍚岋紒鈥?/strong>鈥?/td>
涔欒嵂vs涓欒嵂	0.537	娌″尯鍒?/td>
鈥?strong>鈥嬬湡鐩糕€?/strong>鈥嬶細鐢茶嵂鏁堟灉鍚婃墦涔欒嵂锛屼笝鑽拰璋侀兘姣斾笉鍑哄樊鍒?/td>

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馃挕 鐙瑙傜偣锛氭暟鎹睙婀栫殑鐢熷瓨娉曞垯

骞蹭簡鍗佸勾鏁版嵁鍒嗘瀽锛屾垜鍙戠幇涓€?strong>鈥嬪弽鐩磋瑙勫緥鈥?/strong>鈥嬶細

馃搶 鈥?strong>鈥?0%鐨勪汉鍙仛妫€楠岋紝鍗村拷鐣ユ晥搴斿ぇ灏忥紒鈥?/strong>鈥?br/> 姣斿鏂瑰樊鍒嗘瀽P<0.001鍙憡璇変綘"鏈夊樊寮?锛屼絾鈥?strong>鈥嬪樊寮傛湁澶氬ぇ鈥?/strong>鈥嬶紵寰楃湅鈥?strong>鈥嬑仿插€尖€?/strong>鈥嬶紙缁勯棿骞虫柟鍜?鎬诲钩鏂瑰拰锛夆€斺€?/p>

• 畏虏>0.14绠楀ぇ鏁堝簲锛堣刀绱у啓杩涙姤鍛婇噸鐐规爣绾級
• 畏虏<0.01锛熷氨绠楁樉钁椾篃鍙兘鈥?strong>鈥嬫病瀹為檯浠峰€尖€?/strong>鈥嬶紒

鈥?strong>鈥嬫湭鏉ヨ秼鍔库€?/strong>鈥嬶細鐜板湪瓒婃潵瓒婂鐮旂┒鐢ㄢ€?strong>鈥婤ootstrap閲嶆娊鏍封€?/strong>鈥嬫浛浠ｄ紶缁熸楠岋紙灏ゅ叾灏忔牱鏈椂锛夈€傛瘮濡傚鍋忔€佹暟鎹娊1000娆★紝鐩存帴绠楀樊寮傜殑缃俊鍖洪棿鈥斺€旀瘮纭鍏紡鏇寸ǔ鍋ワ紒

鏈€鍚庨€佷綘涓€鍙ュ績娉曪細鈥?strong>鈥嬪伐鍏峰啀楂樼骇涔熷緱鎳傚師鐞嗏€?/strong>鈥嬶紒涓嬫闈㈠澶氱粍鏁版嵁锛屽厛闂嚜宸憋細

馃 鈥?strong>鈥?鎴戠殑鏁版嵁涔栧悧锛熻姣斿潎鍊艰繕鏄嫾涓綅鏁帮紵"鈥?/strong>鈥?br/> 閫夊浜嗘柟娉曪紝缁撴灉璇存湇鍔涚炕鍊嶅摝锝?/p>