Censored vs Truncated

Censored vs Truncated:

Censored data have unknown values beyond a bound on either end of the number line or both.When the data is observed and reported at the boundary, the researcher has made the decision to restrict the range of the scale.

An example of a lower censoring boundary is 

The recording of pollutants in our water. The researcher may not care about (or instruments may not be able to detect) the level of pollutants if it falls below a certain threshold (e.g., .005 parts per million). In this case, any pollutant level below .005 ppm is reported as “<.005 ppm.”

Truncation occurs when values beyond a boundary are either excluded when gathered or excluded when analyzed. 

For example, if someone conducting a survey asks you if you make more than $100,000, and you answer “yes” and the surveyor says “thanks but no thanks”, then you’ve been truncated.

So to summarize, data are censored when we have partial information about the value of a variable—we know it is beyond some boundary, but not how far above or below it.

In contrast, data are truncated when the data set does not include observations in the analysis that are beyond a boundary value.