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?

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(本文于 2016-11-25 09:12 首发于 “科学网”)

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



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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

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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

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参考：

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.

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