{"id":694,"date":"2019-07-11T17:02:55","date_gmt":"2019-07-11T16:02:55","guid":{"rendered":"http:\/\/35.193.178.118\/?page_id=694"},"modified":"2019-07-29T16:21:17","modified_gmt":"2019-07-29T15:21:17","slug":"error-and-uncertainty","status":"publish","type":"page","link":"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/sensitivity-coefficients-errors-and-uncertainty\/error-and-uncertainty\/","title":{"rendered":"Error and uncertainty"},"content":{"rendered":"\r\n

Error and uncertainty<\/h2>\r\n\r\n\r\n\r\n

The terms \u2018error\u2019 and \u2018uncertainty\u2019 are not the same, although they are often confused. To understand the difference between these two terms, let\u2019s consider the result obtained from a measurement. If we could make a \u2018perfect\u2019 measurement, we would obtain the \u2018true value\u2019 of the measurand. However, in reality, the measurements that we make are never perfect, and the values obtained from measurement (measured values) are therefore estimates of this \u2018true value\u2019. A measured value will differ from the hypothetical \u2018true value\u2019 of the measurand for a number of reasons, some of which we may know about, others of which we may not.<\/p>\r\n\r\n\r\n\r\n

To account for known differences, we can apply a correction to the measured value. For instance, a measured value may be multiplied by a gain determined during the instrument\u2019s calibration, or a measured optical signal may have a dark reading subtracted from it. It is, however, important to realise that the correction will never be perfectly known. In other words, there will always be some difference between the corrected measured value and the (unknown and, in fact, unknowable) \u2018true value\u2019 of the measurand. We call the difference between a measured (or corrected) value and the \u2018true value\u2019 of the measurand the error, as shown in the diagram below.<\/p>\r\n\r\n\r\n\r\n

\"\"<\/figure>\r\n\r\n\r\n\r\n

Since we can never know the \u2018true value\u2019 of the measurand, we can never know the difference between it and the measured values that we obtain. This means that we can never know the value of an error.<\/p>\r\n\r\n\r\n\r\n

We can, however, describe the error in the result of a particular measurement as a draw from a probability distribution. The uncertainty associated with a measured value is a measure of that probability distribution. In particular, the standard uncertainty is the standard deviation of this probability distribution.<\/p>\r\n\r\n\r\n\r\n

although errors are unknown and unknowable, we can evaluate the uncertainty associated with a measured value. As we have seen, any measurement is sensitive to several different \u2018effects\u2019, or \u2018sources of uncertainty\u2019 such as noise, non-linearity, non-uniformity, etc. Each of these effects gives rise to an unknown error drawn from a probability distribution described by the uncertainty.<\/p>\r\n\r\n\r\n\r\n

There are two approaches to evaluating this uncertainty:<\/p>\r\n\r\n\r\n\r\n