11/27 Reading & Translation article & figure out the basic concept of statistical

標準差standard deviation,SD:一組數值自平均值分散開來的程度
一個較大的標準差代表大部分的數值和其平均值之間差異較大;一個較小的標準差代表這些數值較接近平均值。

標準誤standard error,SE是一種 standard deviation
但通常的 standard deviation 是指原始資料的標準差;standard error 是指統計量或估計量的標準差
1.相當於統計母群的標準差。其公式隨統計項目不同而異。例如：樣本平均的標準誤＝樣本的標準差／根號（樣本大小）。The standard error is the estimated standard deviation of a statistic. The formula depends on what statistic you are talking about. For example, the standard error of a sample mean is just the sample standard deviation divided by the square root of the sample size.
http://www.cmh.edu/stats/definitions/stderr.htm

2.如果我們從同個母群中取出多個樣本，那我們必然可得到多個樣本數值的平均。若我們計算這些樣本數平均相對於未知母群平均的標準差，即稱為「標準誤」。標準誤是用來測量樣本平均的變異性。然而，我們可以用以下公式來計算標準誤：(即不需用到未知的母群平均) 標準誤 = 標準差/根號(樣本數-1)。Standard error. If we took several samples of the same thing we would, of course, be able to compute several means, one for each sample. If we computed the standard deviation of these sample means as an estimate of their variation around the true but unknown population mean, that standard deviation of means is called the standard error. Standard error measures the variability of sample means. However, since we normally have only one sample but still wish to assess its variability, we can compute estimated standard error by this formula:
SE = sd/SQRT(n - 1)
where sd is the standard deviation for a variable and n is sample size. Often estimated standard error is just called 'standard error.'
http://www2.chass.ncsu.edu/garson/pa765/normal.htm

測量標準誤(standard error of measurement,SEM):=測驗誤差的標準差
1.可以顯示對個別病患進行測量之誤差,也可計算95%信賴區間(confidence interval,CI)之SEM藉以表示個案之真實結果有95%的機會將落在此區間。
例:一個人接受某一測驗N 次 所得的分數應是以其真實分數為中心而構成的常態分配,這個分配的標準差就是測量標準誤。
2.另一個解釋-->:測驗分數之誤差程度的量數與其信度之間成反比的關係
亦即信度愈高 測量標準誤愈小;反之 信度愈低 測量標準誤愈大。
分數的分析理論，是比較「母群」的施測結果和預期結果，但在實行比較時，我們通常只能比較樣本的結果。（例如：我們記錄了100位個案的收縮壓，並計算其平均和標準差，我們就能知道單個個體數據離樣本平均的距離。但如果我們重複執行此測驗多次，就能了解單個個體數據離所有樣本平均的平均值的差距。)「所有樣本平均的平均值」的“標準差”就稱為 SEM。在正負一個測量標準誤之外的數據被解釋為和其它大部分數據(67%)有差異。
The theoretical (i.e. statistical) analysis of scores depends on comparisons between obtained scores (or statistics) and expected scores (or statistics) from the population based on happenstance (chance). But in practice our comparisons are based almost without exception on scores obtained from samples, not on populations. For example, if we record systolic blood pressure in a large number of volunteers (n=100) and calculate the mean and standard deviation of our sample scores, we would know on average how far away any particular individual's score was from the (sample) average. But now if we repeat the effort (i.e. the measurement of systolic blood pressure in multiple separate samples of 100 individuals) over and over again (say, 100 times) we would know on average how far away any particular sample's average score was from the mean of all the (100) samples tested. The "standard deviation" of the mean of all the sample means (i.e. the population mean) is the standard error of measurement (SEM). Scores that fall beyond ± 1 SEMs are interpreted as unlike most (~67%) of the other scores.
http://symptomresearch.nih.gov/chapter_23/sec29/cahs29pg1.htm

相關性分析correlation coefficient
若我們想知道兩個連續變數之間的關係,例如身高和體重,是不是兩個會一起變化,就要用相關性分析
相關就是兩個變數會一起變化,如果一起變大及變小,就是正相關,如果一個變大另一個就變小,則是負相關。例如體重和腰圍的關係。
低度相關就是兩個變數各變各的,例如血脂肪和血鈣濃度的關係。
表示相關程度的數字,就是相關係數,介於-1至1之間,愈接近-1(負相關) 或1(正相關),相關程度愈高;愈接近0,相關程度愈低。常用的有Pearson相關係數(母數方法)及Spearman相關係數(無母數方法).前者需要較大的樣本及較多數學假設,所以Spearman相關係數的適用範圍較廣。
MCID (最小臨床重要差異值)
Jaeschke最早定義「最小臨床重要差異值 MCID」為："在病人有獲利且執行上沒有困難或副作用的情況下，所得到臨床上最小的分數改變。" 而在那之後MCID的定義有些改變。例如："被認為有用或重要的最小分數差異"；"降低最小的風險，讓答應接受治療的病人事前知道不接受治療的風險"。這些定義顯示了MCID建構的多個層面；有些著重在潛在危險的改變，有些著重在治療決策的影響，有些則單純著重改變的大小。最常見的定義是：MCID為重要改變的最低界線。
Jaeschke first defined an MCID as being “the smallest difference in score in the domain of interest which patients perceive as beneficial and which would mandate, in the absence of troublesome side effects and excessive cost, a change in the patient's management” [6]. Since then the definition has varied. We see definitions such as “the smallest difference in a score that is considered to be worthwhile or important” [4], the “minimum absolute risk reduction for which patients would take a treatment given their understanding of the risk without that treatment” [7], or the mean score for patients with an optimal result minus the mean score for a group with a suboptimal result [8]. The definitions show the varied constructs with the common label of MCID; some weighing change against potential risks, others weighing the impact on treatment decision making, others weighing the impact on the magnitude of change alone. The common thread is that it is the lower boundary of change that has been defined, in some way, to be important.
MCID 的主要功能是協助研究及臨床人員解釋, 評量分數變化或差異之意義。
研究上，療效的判斷常以是否「統計顯著(statistical significance)」判定之，然而具有統計顯著之差異值，不一定具有「臨床意義(clinical significance)」。
MCID值可作為判斷群組分數改變/差異（組內(within-group)/組間(between-group)）是否具有臨床重要意義的最小閾值，決定評量工具的MCID值，可協助臨床及研究人員判斷研究結果所造成的差異是否具備「臨床意義」！MCID值的另一用途是判斷評估工具是否具備反應性(responsiveness)(within-group)。