# Censoring vs Truncation – Difference Between Censoring and Truncation

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In the book Statistical Models and Methods for Lifetime Data , it is written :

Censoring: When an observation is incomplete due to some random cause.
Truncation: When the incomplete nature of the observation is due to a systematic selection process inherent to the study design.

What is meant by "systematic selection process inherent to the study design" in the definition of truncation?

What is the difference between censoring and truncation?

Definitions vary, and the two terms are sometimes used interchangeably. I'll try to explain the most common uses using the following data set: $$1\qquad 1.25\qquad 2\qquad 4 \qquad 5$$
If the detection limit is 1.5, so that observations that fall below this limit is censored, our example data set would become: $$<1.5\qquad <1.5\qquad 2\qquad 4 \qquad 5,$$ that is, we don't know the actual values of the first two observations, but only that they are smaller than 1.5.
If the truncation limit is 1.5, our example data set would become $$2\qquad 4 \qquad 5$$ and we would not know that there in fact were two signals which were not recorded.