Independent sampling is a sampling process in which the selection or measurement of one observation does not affect the selection or measurement of another observation.
In an independent sample, each observation provides its own information separately from the others.
Suppose researchers randomly select students from a school and record each student’s height.
If choosing one student does not change which other students are selected, the observations are approximately independent.
Many statistical methods and models assume that observations are independent.
Independence helps ensure that:
each observation contributes unique information
estimates are more reliable
models and statistical tests work properly
When observations are not independent, results can be misleading.
If each student was sampled separately and one student’s score does not affect another’s, the observations are treated as independent.
Observations may not be independent when they are connected in some way.
Examples:
Measuring the same person multiple times
Sampling groups of friends
Collecting repeated measurements from one classroom
Measuring family members in the same household
In these situations, observations may be more similar to each other than expected by chance.
Models often assume that residuals or observations are independent.
If independence is violated:
variation may be underestimated
models may appear more accurate than they really are
statistical tests may become unreliable
Random sampling often helps create independence, but they are not exactly the same idea.
A sample can be random but still contain non-independent observations.