用数据说话系列(4): 独立样本、配对样本及单样本 t 检验 样本数 至少每组多少为宜

梅卫平

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姑且先不说 t检验前提要求数据服从正态分布，以下两点需要注意：

# 注意点一：一般来讲，希望有80% 以上的统计功效（Statistical Power Level）假设检验才有效。

# 注意点二：另外，效应量（Effect Size，或R语言中为delta），反映处理效应大小的度量。即，两样本平均数的差异，一般delta=1。

# n ：number of observations (per group).

结果显示：一般情况（即达到80%以上统计功效的前提下），

两独立样本双尾 t检验至少需要每组 17 个样本，

两独立样本单尾 t 检验最少需要每组 13 个样本。

补充：

power.t.test(power = 0.8,delta = 1,type = "paired")  

#  n=9.937864

#双尾 配对样本 t检验 至少每组 10 个样本

power.t.test(power = 0.8,delta =1,type = "paired",alternative = "one.side")

# n = 7.727622

#单尾配对样本t检验至少每组8个样本

power.t.test(power = 0.8,delta =1,type = "one.sample")

# n = 9.937864  

#双尾 单样本 t检验 至少每组 10 个样本

power.t.test(power = 0.8,delta =1,type = "one.sample",alternative = "one.side")

# n = 7.727622

#单尾单样本t检验至少每组8个样本

When delta=1,power against n for independent two-sample t-test("n" indicates sample number per group)

Note: two-side t-test.

# 计算过程（在R软件中运行）如下：

#----------------------------------------------------------

> power.t.test(n = 4, delta = 1)

    Two-sample t test power calculation

n = 4

delta = 1

sd = 1

sig.level = 0.05

power = 0.2224633     # 样本数为4的话，统计功效very bad

alternative = two.sided

NOTE: n is number in *each* group

> power.t.test(n = 20, delta = 1)

Two-sample t test power calculation

n = 20

delta = 1

sd = 1

sig.level = 0.05

power = 0.8689528   # 样本数为20 的话，统计功效 good

alternative = two.sided

NOTE: n is number in *each* group

> power.t.test(power = 0.80, delta = 1)

Two-sample t test power calculation

n = 16.71477   # very important  # 两样本双尾t test，至少每组17个样本

delta = 1

sd = 1

sig.level = 0.05

power = 0.8

alternative = two.sided

NOTE: n is number in *each* group

> power.t.test(power = 0.80, delta = 1, alternative = "one.sided")

Two-sample t test power calculation

n = 13.09777   # very important  # 两样本单尾t test，至少每组13个样本

delta = 1

sd = 1

sig.level = 0.05

power = 0.8

alternative = one.sided

NOTE: n is number in *each* group

# --------------------------------------------------

# 特定情况，比如：效用值（Effect Size或曰 delta）为2的时候

> power.t.test(power = 0.80, delta = 2)

Two-sample t test power calculation

n = 5.090008  # 特定条件，效用值=2 的情况，双尾只需要至少每组 5个样本

delta = 2

sd = 1

sig.level = 0.05

power = 0.8

alternative = two.sided

NOTE: n is number in *each* group

> power.t.test(power = 0.80, delta = 2, alternative = "one.sided")

Two-sample t test power calculation

n = 3.987012  # 特定条件，效用值=2 的情况，单尾只需要至少 每组 4 个样本

delta = 2

sd = 1

sig.level = 0.05

power = 0.8

alternative = one.sided

NOTE: n is number in *each* group

参考博文：

1. 李淼新：您的t检验显著结果只是因为你的运气吗？

2. Power calculations for one and two sample t tests

3. Statistical power

4.统计功效和效应值

5. t.test with varying delta

纰漏和错误之处在所难免，恳请您批评指正！

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