Sampling error
Sampling error is the difference between the value of a sample statistic and the corresponding population
parameter when the sample is random and no mistakes were made. For the mean:
\[
\text{sampling error} = \bar{x} - \mu
\]
Sampling error occurs because of chance; it cannot be completely eliminated.
Nonsampling errors
Nonsampling errors are errors from collection, recording, coding, processing, unclear questions, or
inaccurate responses. These are not due to chance.
If the “recorded” sample differs from the correct sample, the calculator estimates the nonsampling component by:
\[
\text{nonsampling error} = \bar{x}_{\text{recorded}} - \bar{x}_{\text{correct}}
\]
How the pieces relate
The recorded difference from the population mean can be separated into a chance part (sampling) plus a mistake part
(nonsampling):
\[
\bar{x}_{\text{recorded}} - \mu
= (\bar{x}_{\text{correct}} - \mu) + (\bar{x}_{\text{recorded}} - \bar{x}_{\text{correct}})
\]
The visualization in the calculator shows these as segments on a number line.
Tip: Use the simulation to see how \(\bar{x}-\mu\) varies across many random samples (the sampling-error
distribution). Nonsampling errors won’t appear in that simulation because they come from mistakes, not chance.
