absolute error definition
I have searched the Internet and our own archives and have come up with two different definitions. At most sites I have seen this definition: Relative error is the absolute error divided by the true measurement. Relative Absolute Error. The relative absolute error is very similar to the relative squared error in the sense that it is also relative to a simple predictor, which is just the average of the actual values. In this case, though, the error is just the total absolute error instead of the total squared error. Thus, the relative absolute error takes the total absolute error and normalizes it by dividing by the total absolute error of the simple predictor. For a perfect fit, the numerator is equal to 0 and Ei = 0. It is expressed by the following equation. Absolute error Ea Relative error = -------------- x 100% Er = -- x 100 Accepted value A Data can also be evaluated in terms of how many measurements that are made in the same manner deviate from one another. and the percent error is. In words, the absolute error is the magnitude of the difference between the exact value and the approximation. The relative error is the absolute error divided by the magnitude of the exact value. The percent error is the relative error expressed in terms of per 100. Written by Pam MS, NCSP | Fact checked by Psychology Dictionary staff. incorrect data with no designation as to which extreme it falls, low or high. The absolute error can be found by determining the difference among actual and expected values. ABSOLUTE ERROR: Jennifer subtracted the actual value on her data plot from the value she expected in order to find the absolute error.. Ignore any minus sign. Example: I estimated 260 people, but 325 came. 260 − 325 = −65, ignore the − sign, so my error is 65. Percentage Error: show the error as a percent of the exact value ... so divide by the exact value and make it a percentage: 65/325 = 0.2 = 20%. Percentage Error is all about comparing a guess or estimate to an exact value. See percentage change, difference and error for other options. As you suggest, they really are two different things entirely. Your first definition, absolute error divided by true value, is a measure of _accuracy_; it tells us how close a particular measurement is to the correct value. One commonly distinguishes between the relative error and the absolute error. Given some value v and its approximation vapprox, the absolute error is. where the vertical bars denote the absolute value. Psychology Dictionary is the most comprehensive source of psychology definitions online with over 20K definitions written by our global team of psychiatrist & psychology professionals. This is the definition with which I am the most familiar, and what I felt relative error was. Then I came across a different definition at http://www.glencoe.com/sec/math/mac/mac01/course3/pdf/m_31107.pdf : The relative error of a measurement is found by dividing the greatest possible error by the measurement itself.
The absolute error is the magnitude of the difference between the exact value and the approximation.