## 关于统计-生物学家需要知道的五件事

Ewan Birney最近的一篇博文（Five statistical things I wished I had been taught 20 years ago ）讲述了统计对于生物学的重要性。

Ewan所谈及的五个方面分别是：

1. Non parametric statistics.
These are statistical tests which make a bare minimum of assumptions of underlying distributions; in biology we are rarely confident that we know the underlying distribution, and hand waving about central limit theorem can only get you so far. Wherever possible you should use a non parameteric test. This is Mann-Whitney (or Wilcoxon if you prefer) for testing "medians" (Medians is in quotes because this is not quite true. They test something which is closely related to the median) of two distributions, Spearman's Rho (rather pearson's r2) for correlation, and the Kruskal test rather than ANOVAs (though if I get this right, you can't in Kruskal do the more sophisticated nested models you can do with ANOVA). Finally, don't forget the rather wonderful Kolmogorov-Smirnov (I always think it sounds like really good vodka) test of whether two sets of observations come from the same distribution. All of these methods have a basic theme of doing things on the rank of items in a distribution, not the actual level. So - if in doubt, do things on the rank of metric, rather than the metric itself.

On the Effects of Non-Normality on the Distribution of the Sample Product-Moment Correlation Coefficient (Kowalski, 1975)

Newson R. Parameters behind "nonparametric" statistics: Kendall's tau,Somers' D and median differences. Stata Journal 2002; 2(1):45-64.

2. R (or I guess S).
R is a cranky, odd statistical language/system with a great scientific plotting package. Its a package written mainly by statisticians for statisticians, and is rather unforgiving the first time you use it. It is defnitely worth persevering. It's basically a combination of excel spreadsheets on steriods (with no data entry. an Rdata frame is really the same logical set as a excel workbook - able to handle millions of points, not 1,000s), a statistical methods compendium (it's usually the case that statistical methods are written first in R, and you can almost guarantee that there are no bugs in the major functions - unlike many other scenarios) and a graphical data exploration tool (in particular lattice and ggplot packages). The syntax is inconsistent, the documentation sometimes wonderful, often awful and the learning curve is like the face of the Eiger. But once you've met p.adjust(), xyplot() and apply(), you can never turn back.

R实在是太好用了，习惯用矢量运算之后，我就很少用perl了。不过学生物的，我所见过的人，能用好excel的人不多（我也不会用-,-），会用SPSS的人非常少，SAS从没见过有人用。每次我告诉身边的人，我用的是R，几乎都没人听说过的。在国内，目前主要也就高校里有人用。但至少做生信的，是需要学R的，Bioconductor上面那一大堆的软件包，已然是无法回避。

3. The problem of multiple testing, and how to handle it, either with the Expected value, or FDR, and the backstop of many of piece of bioinformatics - large scale permutation.
Large scale permutation is sometimes frowned upon by more maths/distribution purists but often is the only way to get a sensible sense of whether something is likely "by chance" (whatever the latter phrase means - it's a very open question) given the complex, hetreogenous data we have. 10 years ago perhaps the lack of large scale compute resources meant this option was less open to people, but these days basically everyone should be working out how to appropriate permute the data to allow a good estimate of "surprisingness" of an observation.

4. The relationship between Pvalue, Effect size, and Sample size
This needs to be drilled into everyone - we're far too trigger happy quoting Pvalues, when we should often be quoting Pvalues and Effect size. Once a Pvalue is significant, it's higher significance is sort of meaningless (or rather it compounds Effect size things with Sample size things, the latter often being about relative frequency). So - if something is significantly correlated/different, then you want to know about how much of an effect this observation has. This is not just about GWAS like statistics - in genomic biology we're all too happy about quoting some small Pvalue not realising that with a million or so points often, even very small deviations will be significant. Quote your r2, Rhos or proportion of variance explained...

power analysis就是四个变量，颠来倒去，知道三个，算第四个。

5. Linear models and PCA.
There is a tendency often to jump to quite complex models - networks, or biologically inspired combinations, when our first instinct should be to crack out the well established lm() (linear model) for prediction and princomp() (PCA) for dimensionality reduction. These are old school techniques - and often if you want to talk about statistical fits one needs to make gaussian assumptions about distributions - but most of the things we do could be either done well in a linear model, and most of the correlation we look at could have been found with a PCA biplot. The fact that these are 1970s bits of statistics doesn't mean they don't work well.

PCA就是把高维空间映射到低维空间，在保留尽可能多信息的情况下进行降维处理，

One may also see PCA as an analogue of the least squares method to find a line that goes as “near” the points as possible – to simplify, let us assume there are just two dimensions. But while the least squares method is asymetric (the two variables play different roles: they are not interchangeable, we try to predict one from the others, we measure the distance parallel to one coordinate axis), the PCA is symetric (the distance is measured orthogonally to the line we are looking for).

John Mark在评论里写道，进阶还需要学什么，一并记录下来。

The next level - number 6 - would be to get beyond P values, and instead compute probability distributions of the quantities of interest. This leads naturally to number 7, which is to delve into the generative models that are currently solved by MCMC methods. This is basically the Bayesian approach. Just as an aside "non parametrics" in some new work is also used to mean models where the number of parameters varies, as a consequence of the method.

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1. 好文章啊，不错~~

其实不仅仅是生物学家，我这种几乎没有统计背景的人在分析数据时也经常犯一些愚蠢的错误

BTW，可不可以把你网页的这个防点右键复制的功能去掉？这个实在没啥意义啊，呵呵

接受建议，去掉它。

2. Ewan Birney又写了篇文章，指出Bayesian statistics的重要性。
http://genomeinformatician.blogspot.com/2011/06/bayesian-vs-frequentist-pragmatic.html

3. PLoS Computational Biology的这两篇文章，同样很赞，值得推荐：

A Quick Guide for Developing Effective Bioinformatics Programming Skills