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樣本量的計(jì)算是任何研究（包括動(dòng)物研究）設(shè)計(jì)的重要組成部分之一。如果選取的動(dòng)物數(shù)量過(guò)少，可能會(huì)導(dǎo)致總體中存在的顯著差異未能發(fā)現(xiàn)；而如果選取的動(dòng)物數(shù)量過(guò)多，則可能會(huì)造成資源的不必要的浪費(fèi)，并可能引發(fā)倫理問(wèn)題。基本上，在動(dòng)物研究中存在兩種樣本量計(jì)算方法。最受歡迎且最科學(xué)的方法是通過(guò)功效分析來(lái)計(jì)算樣本量。這種方法與用于計(jì)算臨床試驗(yàn)和臨床研究樣本量的方法類似。簡(jiǎn)單計(jì)算可以通過(guò)一些公式手動(dòng)進(jìn)行，但對(duì)于復(fù)雜的計(jì)算，可以使用統(tǒng)計(jì)軟件或由統(tǒng)計(jì)學(xué)家進(jìn)行。

第一種方式：采用功效分析的方式計(jì)算樣本量，相關(guān)概念和信息如下：

效應(yīng)量：這指的是兩個(gè)組的平均值（定量數(shù)據(jù)）之間的差異，或者是兩個(gè)組中事件發(fā)生比例之間的差異（定性數(shù)據(jù)）。研究人員在研究開(kāi)始前應(yīng)決定，在研究中，兩個(gè)組之間最小能被視為具有臨床意義的差異值應(yīng)該是多少。關(guān)于兩個(gè)組之間具有臨床意義的差異的概念，最好參考先前已發(fā)表的研究。

• Effect size: This is the difference between the mean of two groups (quantitative data) or proportions of events in two groups (qualitative data). A researcher should decide before the start of the study that how much minimum difference between two groups can be considered as clinically significant. The idea about clinically significant difference between the groups should be taken preferably from previously published studies

標(biāo)準(zhǔn)差：標(biāo)準(zhǔn)差用于衡量樣本內(nèi)的變異程度。只有在處理定量變量時(shí)才需要有關(guān)標(biāo)準(zhǔn)差的信息。有關(guān)特定變量的標(biāo)準(zhǔn)差信息可從先前發(fā)表的研究中獲取。如果沒(méi)有此類研究，則作者應(yīng)首先進(jìn)行試點(diǎn)研究，然后根據(jù)試點(diǎn)研究計(jì)算標(biāo)準(zhǔn)差。

• Standard deviation: Standard deviation measures variability within the sample. Information about standard deviation is needed only in the case of quantitative variables. Information about the standard deviation of a particular variable can be taken from previously published studies. If no such study is available then author should conduct a pilot study first and standard deviation can be calculated from the pilot study

Type I誤差：衡量標(biāo)準(zhǔn)是顯著性水平，通常固定在 5%（P = 0.05）這一水平。這是一個(gè)任意設(shè)定的值，可根據(jù)研究問(wèn)題進(jìn)行調(diào)整，即可以降低也可以提高。

• Type 1 error: This is measured by significance level, which is usually fixed at the level of 5% (P = 0.05). This is an arbitrary value and can be decreased or increased according to the research question

功效：研究的效力是指發(fā)現(xiàn)研究旨在尋找的效應(yīng)的概率。這一概率可根據(jù)研究問(wèn)題的不同而保持在80%至甚至99%之間，但通常保持在 80% 。

• Power: Power of a study is probability of finding an effect, which the study is aimed to find. This may be kept between 80% to even 99% depending on research question, but usually, it is kept at 80%

效應(yīng)方向（單尾檢驗(yàn)或雙尾檢驗(yàn)）：當(dāng)研究人員想要探究某種干預(yù)措施的效果時(shí)，樣本中觀察到的實(shí)際效應(yīng)可能與研究人員的預(yù)期方向一致，也可能恰好相反。如果研究人員認(rèn)為效應(yīng)可能存在于兩個(gè)方向中，那么他應(yīng)該使用雙尾檢驗(yàn)；如果他有充分的理由相信效應(yīng)會(huì)偏向某一特定方向，那么他可以使用單尾檢驗(yàn)。在動(dòng)物研究中，通常使用雙尾檢驗(yàn)。

• Direction of effect (one tailed or two tailed): When a researcher wants to explore the effect of some intervention, the actual effect observed in sample may be in same direction as researcher thought or it may be just opposite to that. If researcher feels that effect may be in both directions then he should use two tailed test and if he has strong reason to believe for the effect to lie in one direction then he can use one tailed test. In animal research, two tailed tests are usually used

統(tǒng)計(jì)測(cè)試：在進(jìn)行樣本量計(jì)算時(shí)，了解將要應(yīng)用于數(shù)據(jù)的統(tǒng)計(jì)測(cè)試方法非常重要。對(duì)于像學(xué)生 t 檢驗(yàn)或卡方檢驗(yàn)這樣的簡(jiǎn)單統(tǒng)計(jì)測(cè)試，可以根據(jù)公式進(jìn)行手動(dòng)計(jì)算，但對(duì)于像方差分析或非參數(shù)測(cè)試這樣的復(fù)雜測(cè)試，則需要統(tǒng)計(jì)學(xué)家的幫助或使用軟件。

• Statistical tests: For sample size calculation, it is important to have an idea about statistical test, which is to be applied on data. For simple statistical tests such as Students ttest or Chisquare test, manual calculation based on formula can be carried out, but for complex tests like ANOVA or nonparametric tests help of statistician or use of software is needed

預(yù)計(jì)動(dòng)物的死亡或流失情況：最終樣本量應(yīng)根據(jù)預(yù)計(jì)的流失情況進(jìn)行調(diào)整。假設(shè)一位研究人員預(yù)計(jì)會(huì)有 10%的流失率，那么通過(guò)公式或軟件計(jì)算出的樣本量應(yīng)除以 0.9，以得到實(shí)際的樣本量。假設(shè)軟件計(jì)算出的樣本量是每組 10 只動(dòng)物，而研究人員預(yù)計(jì)會(huì)有 10%的流失率，那么他的最終樣本量將是每組 11 只動(dòng)物（10/0.9 = 11.11）。同樣，對(duì)于 20%的流失率，樣本量應(yīng)除以 0.8。這可以用結(jié)構(gòu)化的公式來(lái)解釋，即：

• Expected attrition or death of animals: Final sample size should be adjusted for expected attrition. Suppose a researcher is expecting 10% attrition then the sample size calculated by formula or software should be divided by 0.9 to get actual sample size. Suppose sample size calculated by software is 10 animals per group and researcher is expecting 10% attrition then his final sample size will be 11 animals per group (10/0.9 = 11.11). Similarly, for 20% attrition sample size should be divided by 0.8. This can be explained in the form of structured formula i.e.,

Corrected sample size = Sample size/ (1− [% attrition/100])

Second method of calculation is a crude method based on law of diminishing return. This method is called “resource equation” method

第二種方式：基于邊際收益遞減規(guī)律的簡(jiǎn)單方法。這種方法被稱為“資源等式（resource equation）”法

當(dāng)無(wú)法對(duì)效應(yīng)大小做出假設(shè)、無(wú)法根據(jù)先前的研究結(jié)果推斷出標(biāo)準(zhǔn)差、或者當(dāng)需要測(cè)量多個(gè)指標(biāo)或使用復(fù)雜的統(tǒng)計(jì)分析方法進(jìn)行分析時(shí)，可以采用這種方法。這種方法也可用于一些探索性研究，這類研究中檢驗(yàn)假設(shè)并非首要目標(biāo)，而研究人員僅希望找出不同組之間的任何差異程度。根據(jù)這種方法，會(huì)測(cè)量一個(gè)值“E”，它實(shí)際上就是方差分析（ANOVA）的自由度。E 的值應(yīng)在10到20之間。如果E小于10，則增加更多的動(dòng)物會(huì)增加獲得更顯著結(jié)果的機(jī)會(huì)；但如果E大于20，則增加更多的動(dòng)物不會(huì)增加獲得顯著結(jié)果的機(jī)會(huì)。盡管這種方法基于方差分析，但它適用于所有動(dòng)物實(shí)驗(yàn)。只要 E 保持在10到20之間，任何樣本量都可以被視為足夠的。E 可以通過(guò)以下公式計(jì)算：

E = 總的動(dòng)物數(shù)量（Total number of animals） −總的組數(shù)（Total number of groups）