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 …show more content…
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. Reliability can be also expressed as r_(XX^ ' )=〖1-S〗_E^2/S_X^2. Reliability coefficient could be estimated by several ways and through different ways the value of reliability coefficients may vary. However, the reliability coefficient cannot estimate the individual’s test score, we use standard error of measurement to estimate it.
Second, it provided the definition of standard error of measurement. The standard error of measurement is the standard deviation of errors of measurement, which can be expressed as the equation SEM=S_E=√(S_X^2 (1-r_(XX^ ' )))=S_X √(1-r_(XX^ ' ) ). If the test reliability is 0, SEM would be equal to the standard deviation of the observed scores; if the tess reliability is 1, SEM would be 0. In addition, different types of reliability coefficient used to calculate SEM could provide different SEM …show more content…
Score bands, also called confidence intervals, or confidence bands provide a range of possible test scores. We can use score band around true score to estimate the obtained score, for example, a 68 percent score band can be expressed as T±(1)(SEM); another expression including z score is written as z=(X-T)/SEM. On the other hand, we can use score band around obtained score to estimate true score, as the equation [X ̅+(r_(XX^ ' ) )(X-X ̅ )]±(1)〖(S〗_X)(√(1-r_(XX^ ' ) ))(√(r_(XX^ ' ) )), where X ̅ refers to mean score for an appropriate reference group, r_(XX^ ' ) refers to reliability coefficient, X refers to obtained test score, and S_X refers to standard deviation of test scores for an appropriate reference group. To measure the score difference between two individuals, we could use SEM_(X-Y)=〖(S〗_X)(√(2-r_(XX^ ' )-r_(YY^ ' )
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 …show more content…
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. Reliability can be also expressed as r_(XX^ ' )=〖1-S〗_E^2/S_X^2. Reliability coefficient could be estimated by several ways and through different ways the value of reliability coefficients may vary. However, the reliability coefficient cannot estimate the individual’s test score, we use standard error of measurement to estimate it.
Second, it provided the definition of standard error of measurement. The standard error of measurement is the standard deviation of errors of measurement, which can be expressed as the equation SEM=S_E=√(S_X^2 (1-r_(XX^ ' )))=S_X √(1-r_(XX^ ' ) ). If the test reliability is 0, SEM would be equal to the standard deviation of the observed scores; if the tess reliability is 1, SEM would be 0. In addition, different types of reliability coefficient used to calculate SEM could provide different SEM …show more content…
Score bands, also called confidence intervals, or confidence bands provide a range of possible test scores. We can use score band around true score to estimate the obtained score, for example, a 68 percent score band can be expressed as T±(1)(SEM); another expression including z score is written as z=(X-T)/SEM. On the other hand, we can use score band around obtained score to estimate true score, as the equation [X ̅+(r_(XX^ ' ) )(X-X ̅ )]±(1)〖(S〗_X)(√(1-r_(XX^ ' ) ))(√(r_(XX^ ' ) )), where X ̅ refers to mean score for an appropriate reference group, r_(XX^ ' ) refers to reliability coefficient, X refers to obtained test score, and S_X refers to standard deviation of test scores for an appropriate reference group. To measure the score difference between two individuals, we could use SEM_(X-Y)=〖(S〗_X)(√(2-r_(XX^ ' )-r_(YY^ ' )