顯著性差異

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跳去導覽 跳去搵嘢

統計學假說檢定[1][2]所講嘅顯著性差異(或統計學意義英文statistical significance,符號:ρ)係對數據之間差別嘅評價,一次實驗結果喺虛無假設之下冇乜可能發生時,就可以講呢個結果具有顯著性差異。更準確嚟講,譬如某項研究定咗個數值α(顯著水平),表示虛無假設原本係啱嘅但係俾研究者拒絕咗嘅出錯概率[3],跟住用p值表示虛無假設正確嘅條件下得到某結果抑或仲極端過呢個結果嘅情形嘅概率[4]。如果pα,噉就可以認為結果具有統計學意義,或數據之間有咗顯著性差異。[5][6][7][8][9][10][11]顯著水平應該喺開始搵數據前就諗掂,習慣係定喺5%[12]或以下,唔同學科領域可能要求唔一樣。[13]

喺任何涉及到響總體當中隨機揀樣本嘅實驗或觀察性研究裏,得到嘅結果都有可能只不過係抽樣誤差導致嘅。[14][15]但係,如果一次觀察結果嘅p值細過(或等於)顯著水平α,研究者就能夠講「今次結果反映到總體嘅特徵」嘅結論[1],並拒絕虛無假設[16]

顯著性差異嘅原因可能係:

  • 呢種差異可能因參與比對嘅數據係嚟自不同實驗對象,如比-西一般能力測驗中,大學學歷被試組嘅成績同小學學歷被試組會有顯著性差異。
  • 亦可能嚟自於實驗處理對實驗對象造成根本性狀改變,因而前測後測嘅數據會有顯著性差異。例如,記憶術研究發現,被試者學習某記憶法之前嘅成績同學咗記憶法後嘅記憶成績會有顯著性差異,呢個差異好可能來自於學呢種記憶法對被試記憶能力嘅改變。

歷史[編輯]

18世紀嗰時就有人提出顯著性差異,約翰·阿巴思諾特英文John Arbuthnot皮埃爾-西蒙·拉普拉斯做出男女出世嘅概率一樣呢個虛無假設,跟住計咗人類出世時嘅性別比p值[17][18][19][20][21][22][23]

1925年,羅納德·費沙英文Ronald Fisher喺佢本書《研究工作者的統計方法英文Statistical Methods for Research Workers》當中提出咗統計假說檢定嘅諗法,叫做「顯著性檢驗」(tests of significance)。[24][25][26]費沙建議將1/20(=0.05)嘅概率作為拒絕虛無假說嘅臨界值。[27]喺1933年嘅一篇論文中,耶日·內曼埃貢·皮爾遜嗌呢個值做「顯著水平」,畀咗個符號α畀佢。佢哋建議,α值要喺任何資料收集之前就諗定。[27][28]

費雪初初係將顯著水平定喺0.05,但又唔想將佢定死。佢喺1956年出版嘅《統計方法與科學推斷》裏面,建議根據具體情況確定顯著水平。[27]

相關概念[編輯]

顯著水平αp值嘅閾值,當pα時就拒絕虛無假設(就算零假設依然可能係啱嘅)。咁就表示α亦都係虛無假設啱嘅情況下錯誤噉將佢否定咗嘅概率[3],叫做假陽性第一型錯誤、棄真錯誤、α錯誤。

而有啲研究者就中意用置信水平γ = (1 − α),佢係虛無假設啱嘅時候唔將佢拒絕嘅概率。[29][30]置信水平同置信區間係Neyman喺1937年提出嘅。[31]

顯著水平[編輯]

雙尾檢驗英文one- and two-tailed tests中,顯著水平α = 0.05下嘅拒絕域分別喺抽樣分佈兩頭最尾,佔曲線底下面積嘅5%。

顯著水平significance level,符號:α)經常攞嚟喺假說檢定中睇假設同實驗結果係咪一致,佢代表虛無假設(寫成)冇錯嘅情況下,噉啱就將佢否定咗嘅概率,即係發生第一型錯誤(棄真錯誤、α錯誤)嘅機會。

譬如我哋響兩個總體裏便隨機揀出A、B兩組樣本數據,然後發現佢哋喺.05水平上具備顯著性差異,就係講兩組數據所代表嘅總體亦都有顯著性差異嘅可能性係95%;而佢哋代表嘅總體重有5%嘅可能性係冇乜分別嘅,呢個5%係由於抽樣誤差造成嘅。亦都可以噉講:

  • 如果拒絕「兩組數據一致(冇乜分別)」呢個虛無假設,噉會有5%嘅可能性犯第一型錯誤
  • 如果令A=兩個總體冇乜分別、B=揀出嚟兩組數有顯著差異,P(A|B) = 0.05

如果我哋喺檢驗某實驗(Hypothesis Test)中測得嘅數據之間有顯著性差異,就推翻到虛無假設備擇假設則得到支持;反之,如果數據之間冇顯著性差異,就推翻備擇假設,而唔拒絕虛無假設。通常情況下,實驗結果達到.05水平.01水平,先至可以認為數據之間具備顯著性差異,唔係嘅話就可能好似上邊講嘅咁會作出錯誤嘅判斷。作結論嗰時,要講清楚方向性(例如係顯著大過定係顯著細過)。

數學表述為:引入p值(p-value)作為檢驗樣本(test statistic)觀察值嘅最低顯著性差異水平。喺α = 0.01α = 0.05嘅情況下,若果虛無假設情況實際算得嘅概率p細過α,噉表示虛無假設成立時得到噉嘅結果嘅概率,重低過1%或5%,喺呢個顯著水平之下我哋可以拒絕虛無假設。

  • P(X=x)<ρ=0.05係「顯著(significant)」,統計分析軟件SPSS*標記;
  • P(X=x)<ρ=0.01係「極顯著(extremely significant)」,通常以**標記。

睇埋[編輯]

參考[編輯]

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