Reliability vs Accuracy vs Precision vs Validity I am trying to distinguish the difference between Validity, Accuracy, Precision and Reliability. I understand that accuracy is a measure of how close something is to the true value and precision is how close repeated measurements are, but what are validity and reliability? It seems to me that precision and reliability are used interchangeably as well as accuracy and validity. Is this true?
 A: Say, our aim is to measure the diameter of an object. The true (unknown) diameter of this object is 5mm. We take our ruler and take 10 measurements, $\{x_1, \ldots, x_{10}\}$.

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*Accuracy describes the difference between the true value (=5mm) and the the sample average value of repeated measurements
$\bar x = \frac{1}{10}\sum_{i=1}^{10} x_i$. E.g. we could buy calibrated "standards" of certain lengths and a well-defined  uncertainties to estimate the accuracy of your measurement device across our needed value range.

*Precision describes the variability of repeated measurements. It is defined as the sample standard deviation,
$s = \sqrt{\frac{1}{10-1}\sum_{i=1}^{10} (x_i - \bar x)^2}$. Note that different types of precisions exists, and that they are used if we wish to describe the limitations in greater detail -- e.g. reproducibility, repeatability.

*Validity describes the ability to measure what we initially intended to measure. E.g. if the object consists of a material with a "large" thermal expansion coefficient and we do not document the temperature at which the measurement is taken, our readings could become useless. The same is true if our ruler possesses only marks with a distance of 10mm. In either case we would argue that the measurement is not valid. To my personal knowledge there exists no statistical exact definition of the term validity.  Thus, I have only  used the term "validity" in an informal manner.

*Reliability does not have an exact definition -- to my personal knowledge. It is considered to be the "overall consistency of a measure". I would argue that a measure possess a high reliability, if it is (1) repeatable, (2) reproducible by others, and (3) consistent by other measurement methods  -- e.g. if we would replace the ruler by an interferometer and obtain consistent results. However, again, I only used this term in an informal manner.

Hope this helps.
