A comparison of fold-change and the t-statistic for microarray data analysis，这文章是大神Robert Tibshirani和Daniela M. Witten（是Robert的一个学生，现在华盛顿大学生统专业做PI）写的。整篇文章每句话都非常重要！

### Introduction

Therefore, a researcher’s decision to use fold-change or a modified t-statistic should be based on biological, rather than statistical, considerations.

### Statistical measures of differential expression

$T_i=\frac{\bar{x_i}-\bar{y_i}}{s_i}$

$T^{"}_{i}= \frac{\bar{x_i}-\bar{y_i}}{s_i+s_0}$

$FC_i=\frac{\bar{x}^{'}_{i\cdot}}{\bar{y}^{'}_{i\cdot}}$

$FC_i=\bar{x}^{'}_{i\cdot}-\bar{y}^{'}_{i\cdot}$

$P_i=(\bar{x_{i\cdot}})^3-(\bar{y_{i\cdot}})^3$

P代表power，文中说不建议在实际中使用这个人工统计量。

### Analysis of the accuracy of the different measures

Control Treatment FCdifference FCratio T
Gene1 150, 200, 250 1, 50, 100 3.51 3.97 1.69
Gene2 101.1, 101.2, 101.3 100.1, 100.2, 100.3 0.014 1.01 12.25

t.test(c(101.1,101.2,101.3),c(100.1,100.2,100.3))

Welch Two Sample t-test

data:  c(101.1, 101.2, 101.3) and c(100.1, 100.2, 100.3)
t = 12.247, df = 4, p-value = 0.0002552
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.7733042 1.2266958
sample estimates:
mean of x mean of y
101.2     100.2

t.test(c(150,200,250),c(1,50,100))

Welch Two Sample t-test

data:  c(150, 200, 250) and c(1, 50, 100)
t = 3.6844, df = 3.9996, p-value = 0.02113
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
36.87866 262.45467
sample estimates:
mean of x mean of y
200.00000  50.33333



From this perspective, the question of whether the fold-changes or a modified t-statistic results in more accurate gene orderings is really a biological one, rather than a statistical one, as it depends on what types of expression differences between control and treatment have biological relevance.

### Conclusions

1. $FC_{difference}$和改良的t检验都是t检验的一种改良形式，也就是有不同的$s_0$。一些$s_0$的选取可以提高精确性。
2. 别用普通的t检验。
3. 可重复性高并不暗示着精确性高，The issues of reproducibility and accuracy should be kept separate when evaluating the performance of a statistic.
4. 在实际分析中并没有FC和t统计量谁好谁坏的说法，都要看生物学意义。有噪声干扰就用改良的t检验，没有噪声干扰就用FC。