ANOVAと多重対比較の矛盾する結果の解釈の仕方は?
ãã®è¨äºã¯ãANOVA 㨠å¤é対æ¯è¼, ï¼äºå¾æ¯è¼ï¼post hoc comparisonsã¨ãããï¼ã®çç¾ããçµæãè§£éããæ¹æ³ã説æãã¾ãã
å¤éæ¯è¼ãã¼ã«ã«é¢ããç°¡åãªèª¬æ
ãªãå¤é対æ¯è¼æ¤å®ã使ç¨ããå¿ è¦ãããã®ã?
ANOVA ã®ç®çã¯ãããå åãå¾å±å¤æ°ã«å¯¾ãã¦å ¨ä½çã«ææãªå¹æãæã¤ãã©ãããæ¤åºãããã¨ã§ãããã¨ãã°ãå«ç ãèºã®å¥åº·ã«ã©ã®ããã«å½±é¿ããããç ç©¶ãã¦ããã¨ãã¾ããããå«ç ã¯ã4 ã¤ã®éå£ (non-smokers, passive smokers, light smokers and heavy smokers)ã«é¢ä¸ããå åã§ãã
ANOVAãå«ç ã®èºã®å¥åº·ã¸ã®ææãªå¹æãæ¤åºããã¨ä»®å®ãã¦ãæã ã¯ããã«ã¹ããããé²ãã¦ãç¹å®ã®éå£ãä»ã¨ææã«ç°ãªããã©ãããæ¤è¨ã§ãã¾ãããã®ç®çã®ããã«ãæã ã¯ãã¹ã¦ã®ç¾¤ã®å¯¾ã®éã®å·®ãæ¤å®ããå¿ è¦ãããã¾ãã å¤é対æ¯è¼æ¤å®ï¼Pairwise multiple comparisons testsï¼ãã¾ãã¯äºå¾æ¤å®ï¼Â post hoc testsï¼ã¯ããã®åé¡ã«åãçµãããã®ãã¼ã«ã§ãã
å¤éæ¯è¼åé¡ã¨ã¯ä½ã?
å¤é対æ¯è¼æ¤å®ã¯ãæ¯è¼ããã群ã®å対㮠på¤ã®è¨ç®ãä¼´ãã¾ããpå¤ã¯ããããçã§ã¯ãªãã«ããããããããã广ãçµ±è¨çã«ææã§ããã¨ä¸»å¼µããå±éºåº¦ã表ãã¾ãã対æ¯è¼ã®æ°ãå¢å¤§ããã¨ãpå¤ã®æ°ãå¢å¤§ããã®ã§ãç¾å®çãªå¶ç¶ã®ããã§ææãªå¹æãæ¤åºããããããªãã¾ãããã¨ãã°ã5%ã®æææ°´æºã¢ã«ãã¡ã ã¨ãã¦ã100åã®ææ på¤ãã5åã®ææpå¤ãå¶ç¶çã«è¦ã¤ãããã¨ã«ãªãã¾ãã
ãã®åé¡ã解決ããããã«ãå¤é対æ¯è¼æ¤å®ã§ã¯på¤ã®è£æ£ãè¡ãã¾ã: æ¯è¼ã®æ°ãå¢å¤§ããã»ã©ãpå¤ãããã«ãã£åããï¼= å¤ãå¢å¤§ãã)ã¾ãããããã£ã¦ãééã£ãæ¨è«ãå¼ãåºããã¨ãå°ãªããªãã¾ããpå¤ã®ããã«ãã£åæé ã¯ã*äºå¾æ¤å®*ã®éã§ç°ãªããã¨ã«æ³¨æãã¦ãã ããã
XLSTATãç¨ããExcelã§ã®ANOVAã¨ç¶ãå¤éæ¯è¼ã®å®è¡æ¹æ³ã«ã¤ãã¦ã¯ããã¡ãã®ãã¥ã¼ããªã¢ã«ãã確èªãã ããã
ANOVAã¨å¤é対æ¯è¼ã®çç¾ããçµæã®è§£é
ä¸è¨ã§èª¬æãããããã«ãANOVAã¨å¤é対æ¯è¼æ¤å®ã¯ãç°ãªãåé¡ãæ¤è¨ãã¾ããANOVA ã§æä¾ãããåçããå¤é対æ¯è¼ã§æä¾ãããåçã¨çç¾ããå ´åãããã¾ãã
ANOVAãææã§å¤é対æ¯è¼ãéææ
ãã®çµè«ã¯ã次ã®ã¨ãã«å¼ãåºããã¾ã:
- ANOVAã§è¨ç®ãããpå¤ããæææ°´æºã¢ã«ãã¡ï¼ãã¨ãã°ã0,05ï¼ä»¥ä¸ã®ã¨ãã
- å¤é対æ¯è¼æ¤å®ã§è¨ç®ããããã¹ã¦ã®på¤ããæææ°´æºã¢ã«ãã¡ãããé«ãã¨ãã
以ä¸ã«äºä¾ã表示ãã¾ã:
ä¸»å¹æãææã§ããã¨è¦ãªãããææãªå·®ãäºå¾æ¤å®ãæ¤åºããªããããªè¤æ°ã®ã±ã¼ã¹ãããã¾ãã
ããã¯ãµã¤ãºã®å°ããæ¨æ¬ã§èµ·ãã¾ãããã®å ´åãæã ã¯çµ±è¨çæ¤å®åã®ä¸è¶³ã¨ãã¦ããã®çµæãè§£éã§ãã¾ãã対æ¯è¼æ¤å®ãçµ±è¨çã«å¼·åã§ã¯ãªãå ´åãææãªå·®ãæ¤åºãã«ãããªãã¾ãã
ã¾ãå åæ°´æºãå¤ãããå ´åã«ãããããèµ·ãã¾ãã対æ¯è¼ãå¤ãã»ã©ãpå¤ãããããã«ãã£åããã¾ãããããã£ã¦ããããçã§ããã«ããããããã帰ç¡ä»®èª¬ãæ£å´ããããªã¹ã¯ãæ¸å°ãã¾ããÂ
ã¾ã䏻广ããããã«ææãªï¼æææ°´æºã«çãããè¿ãï¼ã¨ãã«ãããããèµ·ãã¾ãã
çµæçã«ãå¤é対æ¯è¼ãã¼ã«ã®é¸æã¯ããã®ãããªçµæã®è§£éãå©ãã¾ããããä¿å®çãªãã¼ã«ã¯ãç¾å®ã«æå³ã®ããå¹³åéã®å·®ãæ£å´ããããã§ãã
ANOVAã éææã§å¤é対æ¯è¼ãææ
ãã®çµè«ã¯ã次ã®ã¨ãã«å¼ãåºããã¾ã:
- ANOVAã§è¨ç®ãããpå¤ã ãæææ°´æºã¢ã«ãã¡ï¼ãã¨ãã°ãe.g. 0,05ï¼ãããé«ãã¨ãã
- å¤é対æ¯è¼æ¤å®ã§è¨ç®ãããå°ãªãã¨ã1ã¤ã®på¤ããæææ°´æºã¢ã«ãã¡ãããä½ãã¨ãã
以ä¸ã«äºä¾ã表示ãã¾ã:

An unfortunate common practice is to pursue multiple comparisons only when the hull hypothesis of homogeneity is rejected. (Hsu, page 177).
å ´åã«ãã£ã¦ã¯ãANOVAãéè¦ãªã°ãã¼ãã«å¹æã示ããªãå ´åã§ãããã¹ãããã¯ãã¹ãã¯ã°ã«ã¼ãéã®éè¦ãªéããè¦ã¤ããã®ã«ååå¼·åã§ãã ä¸è¬ã«ããã®ãããªçµæã¯æå¹ã§ãã ãããããã¹ãããã¯ãã¹ãã®çµæãéè¦ã§ãªãANOVAï¼ãã£ãã·ã£ã¼LSDãªã©ï¼ã®å¾ã«æå¹ã§ããã¨èãããã¨ãã§ããªãã¨ããä¾å¤ãããã¾ãã
Was this article useful?
- Yes
- No