醫學統計

intraclass correlation coefficient（組內相關係數）

Explain the use of intraclass correlation in relation to inter-rater reliability.

組內相關係數用來測量施測者間信度。ICC可被表示為組間的變異和總變異的比值。Intraclass correlation (ICC) is used to measure inter-rater reliability. ICC may be conceptualized as the ratio of between-groups variance to total variance.
資料建立：ICC的目的是用來評論施測者間的影響和受測族群間的關係。Data setup:The purpose of ICC is to assess the inter-rater (column) effect in relation to the grouping (row) effect, using two-way ANOVA.
解釋：當受測目標間沒有差異時，ICC的值會接近1，顯示總變異全來自受測者自身的不同。Interpretation: ICC will approach 1.0 when there is no variance within targets, indicating total variation in measurements on the Likert scale is due solely to the target (ex., subject, neighborhood) variable.
模型：ICC會隨著以下幾種原因而改變：評估者是包括所有施測者或是由可能的施測者中隨機抽來的；受測者是否包括所有受測者或是只是由隨機抽樣選出；信度的驗證是建立在個別的評估者上或是所有評者的平均。Models: ICC varies depending on whether the judges are all judges of interest or are conceived as a random sample of possible judges, and whether all targets are rated or only a random sample, and whether reliability is to be measured based on individual ratings or mean ratings of all judges. Shrout and Fleiss (1979).
ICC公式由來：令A代表個案真實的改變，令B代表由施測者間信度不良所造成的誤差，則ICC=A/(A+B)。B是個案間差異(一群施測者施測同樣個案時所給的不同分數)的均方(一組數的平方的平均值)，由ANOVA計算。個案間變異的均方則為(A的k倍+B)Derivation of the ICC formula, following Ebel (1951: 409-411): Let A be the true variance in subjects' ratings due to the normal expectation that different subjects will have true different scores on the rating variable. Let B be the error variance in subjects' ratings attributable to inter-rater unreliability. The intent of ICC is to form the ratio, ICC = A/(A + B). B is simply the mean-square estimate of within-subjects variance (variance in the ratings for a given subject by a group of raters), computed in ANOVA. The mean-square estimate of between-subjects variance equals k times A (the true component) plus B (the inter-rater error component), since each mean contains a true component and an error component.
將B用MSwithin、A用(MSbetween –B)/k表示(因為MSbetween = kA + B)，則公式就可化為：

　　　　　　ICC = rI = (MSbetween - MSwithin)/( MSbetween + [k - 1] MSwithin)。

此時MSbtween 反應了不同的個案的真實分數也就不同。MSwithin則表示由施測者間的誤差造成的分數不同。k代表了(施測者人數/受測者人數）。
Given B = MSwithin, and given MSbetween = kA + B, substituting these equalities into the intended equation (ICC = A/[A+B]), the equation for ICC reduces to the formula for the most-used version of intraclass correlation (Haggard, 1958: 60)　: ICC = rI = (MSbetween - MSwithin)/( MSbetween + [k - 1] MSwithin) where MSbetween is the mean-square estimate of between-subjects variance, reflecting the normal expectation that different subjects will have true different scores on the rating variable
MSwithin is the mean-square estimate of within-subjects variance, or error attributed to inter-rater unreliability in rating the same person or target (row). k is the number of raters/ratings per target (person, neighborhood, etc.) = number of columns.
當MSbetween 等於MSwithin時，ICC等於0，顯示此時分組方式不會對ICC造成影響。
ICC is 0 when within-groups variance equals between-groups variance, indicative of the grouping variable having no effect.