... 如此類推。如果位研究者想做嗮成場析因實驗,就需要以下嘅組-0、a、b、c、ab、bc、ac、abc 總共 8 組;不過喺現實嘅科研當中,位研究者可能會決定唔做(例如) bc 嗰組-位研究者睇過前人做嘅研究,知道打前有好幾份研究經已發現咗結合 b 同 c 係冇嘢睇嘅,於是佢就為咗想慳人力物力,而決定索性唔做 bc 嗰組,淨係得 7 組受試者。由呢個例子睇得出,喺現實嘅析因實驗裏面,研究者好多時都有理由唔做嗮成場析因實驗,而呢種「由場析因實驗所有可能情況當中,淨係揀一部份嘅嚟做」嘅做法就係所謂嘅部份析因設計[13][14]。
獨立樣本 t 測試嘅情況,比較實驗組入面第一位受試者嘅 DV 值(DVexp 1)同對照組入面第一位受試者嘅 DV 值(DVcon 1),假如兩位受試者都係隨機噉抽嚟做樣本嘅話,DVexp 1 同 DVcon 1 呢兩個數(最少理論上)係可以獨立同分佈嘅;
用配對樣本 t 測試比較兩組數值,第一組係班受試者食藥之前嘅 DV 值,第二組係佢哋食藥之後嘅 DV 值,攞第一位受試者食藥前嘅 DV 值(DVpre 1)比較佢食藥後嘅 DV 值(DVpost 1),呢兩個數值必然係有關(DVpost 1 係 DVpre 1 嘅函數)嘅,因為兩個數值都係嚟自同一個人;
喺廿一世紀初嘅醫療領域上,唔少研究者就開始提倡比較「個人化」嘅實驗方法:人之間有個體差異,例如有啲人免疫系統勁啲冇咁易病,又有啲人免疫系統冇咁勁比較易病;想像 x 咁多劑量嘅藥,A 君食咗可能會完全好返嗮,但可能 B 君食咗就會因為劑量大得滯而唔舒服;不過傳統嘅實驗好多時都係追求一體適用[英 9]-實驗者攞一班受試者試咗隻新藥,班受試者冇唔舒服,實驗者就諗住第時撞到嘅病人冚唪唥都會頂得順隻藥,冇考慮到「病人之間可能會有個體差異」呢條問題;於是有醫學專家開始覺得唔滿意,想諗方法令醫療實驗考慮埋每位病人嘅獨特性質[19]:p. 1。
一場實驗一定要有返咁上下受控[英 10],即係要排除一啲研究者想忽略、但又有可能會左右實驗結果嘅因素:實驗方法其中一個最令人關注嘅問題係所謂嘅混淆變數[英 11]-混淆變數指有個變數已知係會對 IV 同 DV 產生影響,但研究者冇控制到嘅;舉例說明,想像家陣有位醫學研究者想同隻新藥做場實驗(臨床試驗),於是佢[22]
不過做完之後佢醒返起,佢搵受試者嗰陣冇隨機噉分組,淨係簡單噉按啲受試者「嚟自邊間醫院」分組-嚟自 X 醫院嘅受試者冚唪唥分嗮落實驗組,淨低嘅受試者冚唪唥分嗮落對照組;
問題係佢事後知道,因為 X 醫院係專醫 B 病嘅,所以嚟自 X 醫院嘅受試者全部都有 B 病,而對照組受試者嚟自第啲醫院而且全部冇 B 病;更大嘅問題係,打前嘅研究已知 B 病都會對 A 病啲症狀有影響;
-「嚟自邊間醫院」就係個混淆變數,影響咗啲受試者俾人分落邊組(IV),同時又間接影響咗啲受試者嘅最後症狀(DV),搞到研究者唔可以有信心噉話 DV 受影響真係純粹因為 IV [23]。
受控嘅考量係實驗室存在其中一個主因:喺現實嘅科學研究上,研究者做嘢嗰時實會盡力想確保有可能影響 IV 同 DV 嘅變數都受控,想排除混淆變數等因素嘅干擾;實驗室係俾人攞嚟做實驗嘅房,其中一個最重要嘅特徵係高度受控-例如一間做化學實驗嘅實驗室會將所有嘅檯櫈都整到乾乾淨淨,而且實驗用嘅化學物質冚唪唥都會攞密封嘅容器裝住,噉做其中一個重要嘅目的就係想防止做實驗嗰陣有啲意料之外嘅化學物質干擾研究緊嘅化學反應;做醫學同生物學等領域嘅實驗室都係同一道理[24][25]。
於是科學界就有咗實地實驗嘅諗頭-位經濟學家可以試吓(例如)搵兩間各條件相約嘅百貨公司(一個實驗室以外嘅環境),喺百貨公司 A 度落廣告,同時減少百貨公司 B 嘅廣告量,睇吓噉做(IV)會點樣改變啲人客嘅使錢方式(DV)[30][31]。
喺廿一世紀初嘅科學上,實地實驗有唔少爭議性:一方面,有好多社科(對人類行為嘅研究)嘅研究者都覺得,實地實驗可以達致實驗室做唔到嘅「自然度」-佢哋覺得實驗室嘅環境太唔自然,會搞到受試者展現出喺正常情況下唔會展現嘅行為;另一方面,又有好多研究者嫌實地實驗唔夠受控-好似係上述嘅百貨公司實驗噉,要搵兩間喺各因素上完全一樣嘅百貨公司係冇可能咁滯,但如果嗰兩間百貨公司喺某啲因素(例如大細或者地區)上唔完全一樣,第啲研究者就有理由質疑場實驗嘅結果係咪受咗呢啲唔一樣嘅因素干擾(兩者之間喺 DV 上有差異唔係因為 IV 操作,而係因為呢啲原先就唔一樣嘅條件嘅影響)。一般嚟講,社科研究者會考慮到雙方嘅道理,並且追求[32]:
然後研究者就觀察 A 同 B 跟住落嚟啲經濟指標變化嘅規律有咩差異;喺呢場實驗入面,天災係一個 IV,而啲經濟指標就係 DV,假設兩個經濟體真係喺各方面都相約,經濟體 A 跟住落嚟同經濟體 B 嘅差異應該主要係源自個 IV 嘅;不過同一般嘅實驗室實驗唔同嘅係,呢件 IV 操作係「自然」發生(唔係由研究者施加)嘅[註 5]。自然實驗常見於一啲專研究大規模現象嘅領域-好似係經濟學、社會學、地理學、考古學、地質學同生態學呀噉,噉係因為好似好多社會現象又或者係地殼變動呢啲咁大規模嘅現象,通常都好難喺實驗室裏面模擬[33][34]。
响跟住打後嘅幾個世紀裏面,有好多科學家都靠實驗(操作 IV 嚟睇 DV 會受咩影響)嚟做研究,喺物理學、化學、生物學以至心理學等嘅領域上都出咗重大嘅創新。到咗廿世紀初,實驗喺自然科學上經已係常態,社會科學亦都開始睇重實驗,而統計學上仲有咗實驗設計等嘅諗頭,專門諗「要點樣分析實驗出嘅數據」噉嘅問題[1]。
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