# Essay about Standard Error Of Measurement, By Leo M. Harvill

729 Words
Nov 8th, 2015
3 Pages

The article, “Standard Error of Measurement” by Leo M. Harvill from East Tennessee State University, provided a general introduction of Standard Error of Measurement (SEM).

First, it introduced the basic concepts of test reliability. An obtained score or a raw score refers to the number of points obtained by an examinee. The obtained score could be influenced by several factors such as the ambiguity of test items, the fatigue of the examinee, and these factors make the obtained score unlikely to reflect the true abilities of examines. A true score is such a score that could not influenced by those random events and could represent the true abilities of examinees. The error score or error of measurement is the difference between an obtained score and its true score. The relationship among obtained, true, and error scores could be expressed as the equation X=T+E, where X is the observed score, T is the true score, and E is the error score. The relationship among obtained, true, and error variances could be expressed as S_X^2=S_T^2+S_E^2, where S_X^2 is the variance of observed scores, S_T^2 is the variance of true scores, and S_E^2 is the variance of error scores.

Reliability refers to the ratio of the true score variance to the observed score variance, which can be expressed as r_(XX^ ' )=S_T^2/S_X^2. According to this equation, if the test is perfectly reliable, the true score variance would equal to the observed score variance and the reliability would equal to 1.…

First, it introduced the basic concepts of test reliability. An obtained score or a raw score refers to the number of points obtained by an examinee. The obtained score could be influenced by several factors such as the ambiguity of test items, the fatigue of the examinee, and these factors make the obtained score unlikely to reflect the true abilities of examines. A true score is such a score that could not influenced by those random events and could represent the true abilities of examinees. The error score or error of measurement is the difference between an obtained score and its true score. The relationship among obtained, true, and error scores could be expressed as the equation X=T+E, where X is the observed score, T is the true score, and E is the error score. The relationship among obtained, true, and error variances could be expressed as S_X^2=S_T^2+S_E^2, where S_X^2 is the variance of observed scores, S_T^2 is the variance of true scores, and S_E^2 is the variance of error scores.

Reliability refers to the ratio of the true score variance to the observed score variance, which can be expressed as r_(XX^ ' )=S_T^2/S_X^2. According to this equation, if the test is perfectly reliable, the true score variance would equal to the observed score variance and the reliability would equal to 1.…