An independent sample is a sample that is selected randomly so that its observations do not depend on the values other observations. Many statistical analyses are based on the assumption that samples are independent. Others are designed to assess samples that are not independent.
For example, suppose quality inspectors want to compare two laboratories to determine whether their blood tests give similar results. They send blood samples drawn from the same 10 children to both labs for analysis.
|Child||Lab A||Lab B|
Because both labs tested blood specimens from the same 10 children, the test results are not independent. To compare the average blood test results from the two labs, the inspectors would need to do a paired t-test, which is based on the assumption that samples are dependent.
To obtain independent samples, the inspectors would need to randomly select and test 10 children using Lab A and then randomly select and test a different group of 10 different children using Lab B. Then they could compare the average blood test results from the two labs using a 2-sample t-test, which is based on the assumption that samples are independent.