Anthony's Science Blog

Interpreting standard errors as confidence intervals

August 17, 2011 – 6:42 pm

A lot of people don’t realize that standard errors can be interpreted as confidence intervals that vary in the confidence level depending on sample size. And what better way to get the word out than on my widely read blog? Knowing that these two concepts are closely related can help to interpret graphs on which people use standard errors. Here’s a handy table:

  n    CI
  1 50.00
  2 57.73
  3 60.89
  4 62.60
  5 63.67
  6 64.40
  7 64.93
  8 65.34
  9 65.65
 10 65.91
 15 66.68
 20 67.07
 50 67.78
100 68.02
Inf 68.26

So, if your sample size is 3, your standard error will represent a 61% confidence interval. If your sample size is 100, it will represent a 68% confidence interval. So, if sample size is not equal between groups on a graph, standard errors will represent confidence intervals of varying confidence. This is kind of a weird approach to graphing things when you think about it, but a few percent difference isn’t big enough to be important in most cases.