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# Testing Measurement Error

assumes that any observation is composed of the true value plus some random error value. But is that reasonable? What if all error is not random? Isn't it possible that some errors are systematic,

## Measurement Error Statistics

that they hold across most or all of the members of a group? types of measurement error One way to deal with this notion is to revise the simple true score model by dividing the error component into measurement error example two subcomponents, random error and systematic error. here, we'll look at the differences between these two types of errors and try to diagnose their effects on our research. What is Random Error? Random error

## Measurement Error In Research

is caused by any factors that randomly affect measurement of the variable across the sample. For instance, each person's mood can inflate or deflate their performance on any occasion. In a particular testing, some children may be feeling in a good mood and others may be depressed. If mood affects their performance on the measure, it may artificially inflate the observed scores for some children and artificially deflate them

## Measurement Error Calculation

for others. The important thing about random error is that it does not have any consistent effects across the entire sample. Instead, it pushes observed scores up or down randomly. This means that if we could see all of the random errors in a distribution they would have to sum to 0 -- there would be as many negative errors as positive ones. The important property of random error is that it adds variability to the data but does not affect average performance for the group. Because of this, random error is sometimes considered noise. What is Systematic Error? Systematic error is caused by any factors that systematically affect measurement of the variable across the sample. For instance, if there is loud traffic going by just outside of a classroom where students are taking a test, this noise is liable to affect all of the children's scores -- in this case, systematically lowering them. Unlike random error, systematic errors tend to be consistently either positive or negative -- because of this, systematic error is sometimes considered to be bias in measurement. Reducing Measurement Error So, how can we reduce measurement errors, random or systematic? One thing you can do is to pilot test your instr

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## Measurement Error Bias

Journal Citation Reports with Source: 2015 Web of Science Data Measuring Test Measurement Error A General Approach Donald Boyd Hamilton measurement error definition psychology Lankford University at Albany Susanna Loeb Stanford University James Wyckoff University of Virginia Abstract Test-based accountability as well as value-added asessments and much experimental and quasi-experimental research in education rely on achievement tests http://www.socialresearchmethods.net/kb/measerr.php to measure student skills and knowledge. Yet, we know little regarding fundamental properties of these tests, an important example being the extent of measurement error and its implications for educational policy and practice. While test vendors provide estimates of split-test reliability, these measures do not account for potentially important day-to-day differences in student performance. In this article, we demonstrate a credible, low-cost approach for estimating http://jeb.sagepub.com/content/38/6/629.abstract the overall extent of measurement error that can be applied when students take three or more tests in the subject of interest (e.g., state assessments in consecutive grades). Our method generalizes the test–retest framework by allowing for (a) growth or decay in knowledge and skills between tests, (b) tests being neither parallel nor vertically scaled, and (c) the degree of measurement error varying across tests. The approach maintains relatively unrestrictive, testable assumptions regarding the structure of student achievement growth. Estimation only requires descriptive statistics (e.g., test-score correlations). With student-level data, the extent and pattern of measurement-error heteroscedasticity also can be estimated. In turn, one can compute Bayesian posterior means of achievement and achievement gains given observed scores—estimators having statistical properties superior to those for the observed score (score gain). We employ math and English language arts test-score data from New York City to demonstrate these methods and estimate the overall extent of test measurement error is at least twice as large as that reported by the test vendor. generalizability theory reliability testing high-stakes testing correlational analysis longitudinal studies effect size Article Notes Declaration of Conflicting Interests The author(s) declared no potential conflicts of interest with

we can estimate the extent of error in a measurement. There are three chief sources of error: • in the thing being measured (my weight may fluctuate so it's difficult to get an accurate picture of it); • the observer (on Mondays I may knock a pound off my weight if I binged on my mother's cooking at the week-end. Obviously the binging doesn't reflect my true weight!); • or in the recording device (our clinic weigh scale has been acting up; we really should get it recalibrated). And there are two types of error: Random errors are not attributable to a specific cause. If sufficiently large numbers of observations are made, random errors average to zero, because some readings over-estimate and some under-estimate. Systematic errors tend to fall in a particular direction and are likely due to a specific cause. Because systematic errors fall in one direction (e.g., I always exaggerate my athletic abilities) they bias a measurement. Random errors are considered part of the reliability of a measurement. Systematic errors are considered part of the validity of a measurement. RELIABILITY refers to consistency or dependability.Your patient Jim is unpredictable; sometimes he comes to his appointment on time, sometimes he's late and once or twice he was early. One way to estimate reliability of a measurement is to record its stability: do you get the same blood pressure reading if you repeat the measurement? This is sometimes called "test-retest stability" or "intra-rater reliability" and focuses on the observer and the instrument as potential sources of error. (Note that we must assume that no actual change in BP occurred between the measurements: there is no error in the thing being measured). You can also estimate reliability by comparing the agreement between different people making a rating (e.g., if several nurses measure a patient's blood pressure, do they get the same reading?). This can be called "inter-rater reliability" or "inter-rater agreement." Nerd's Corner: This is a simplification. Sometimes it's difficult to figure out if an error is random or systematic: the disagreement between the nu

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