Because tests are not an absolutely perfect measuring instrument then there is going to be some error in the obtained raw score. So if person A's obtained raw score is 30 and the test manual states the SEm is 3 then you would be reasonably confident that his true score lies 30 + or – 3, i.e. between 27 and 33. To be 95% confident you will need to go 6 either side ie. 24 to 36.
A measure of the amount of error to be expected in a score from a particular test. The smaller the standard error of measurement, the greater the accuracy of the test score. The standard error of measurement is the standard deviation of a theoretical distribution of a set of variations, each of which is the difference between the obtained score and true score. Thus, if a standard error of measurement is 5, the chances are two to one that an obtained score lies within five units of the true score.
Standard error of measurement (SEM) is a statistical phenomenon that all test and quiz scores are subject to. It is the amount of error in individual test scores if a student were to take the same test repeatedly, with no change in his or her level of knowledge and preparation. The difference between a student's actual score and his or her highest or lowest hypothetical score is known as the SEM.
The estimate of the error associated with pupils' obtained scores when compared with their hypothetical true score. The SEM, which varies from test to test, should be given in the test manual. The band of scores in which we can be fairly certain the true score lies can be calculated from this figure. For example, we can be 95 per cent certain that a pupilâ€™s true score lies in the range â€˜obtained score Â± 2 SEMâ€™ and 99 per cent certain that it lies in the range â€˜obtained score Â± 3 SEMâ€™.