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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?


(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




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:

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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