Standardized Test - Scoring Information Loss

Scoring Information Loss

Base = 5 cm; Height = 3 cm
Area = 1/₂(Base × Height)
Area = 1/₂(5 cm × 3 cm)
Area = 7.5 cm2 The first shows scoring information loss. The teacher knows whether the student got the right answer, but does not know how the student arrived at the answer. If the answer is wrong, the teacher does not know whether the student was guessing, made a simple error, or fundamentally misunderstands the subject.

When tests are scored right-wrong, an important assumption has been made about learning. The number of right answers or the sum of item scores (where partial credit is given) is assumed to be the appropriate and sufficient measure of current performance status. In addition, a secondary assumption is made that there is no meaningful information in the wrong answers.

In the first place, a correct answer can be achieved using memorization without any profound understanding of the underlying content or conceptual structure of the problem posed. Second, when more than one step for solution is required, there are often a variety of approaches to answering that will lead to a correct result. The fact that the answer is correct does not indicate which of the several possible procedures were used. When the student supplies the answer (or shows the work) this information is readily available from the original documents.

Second, if the wrong answers were blind guesses, there would be no information to be found among these answers. On the other hand, if wrong answers reflect interpretation departures from the expected one, these answers should show an ordered relationship to whatever the overall test is measuring. This departure should be dependent upon the level of psycholinguistic maturity of the student choosing or giving the answer in the vernacular in which the test is written.

In this second case it should be possible to extract this order from the responses to the test items. Such extraction processes, the Rasch model for instance, are standard practice for item development among professionals. However, because the wrong answers are discarded during the scoring process, attempts to interpret these answers for the information they might contain is seldom undertaken.

Third, although topic-based subtest scores are sometimes provided, the more common practice is to report the total score or a rescaled version of it. This rescaling is intended to compare these scores to a standard of some sort. This further collapse of the test results systematically removes all the information about which particular items were missed.

Thus, scoring a test right–wrong loses 1) how students achieved their correct answers, 2) what led them astray towards unacceptable answers and 3) where within the body of the test this departure from expectation occurred.

This commentary suggests that the current scoring procedure conceals the dynamics of the test-taking process and obscures the capabilities of the students being assessed. Current scoring practice oversimplifies these data in the initial scoring step. The result of this procedural error is to obscure of the diagnostic information that could help teachers serve their students better. It further prevents those who are diligently preparing these tests from being able to observe the information that would otherwise have alerted them to the presence of this error.

A solution to this problem, known as Response Spectrum Evaluation (RSE), is currently being developed that appears to be capable of recovering all three of these forms of information loss, while still providing a numerical scale to establish current performance status and to track performance change.

This RSE approach provides an interpretation of the thinking processes behind every answer (both the right and the wrong ones) that tells teachers how they were thinking for every answer they provide. Among other findings, this chapter reports that the recoverable information explains between two and three times more of the test variability than considering only the right answers. This massive loss of information can be explained by the fact that the "wrong" answers are removed from the test information being collected during the scoring process and is no longer available to reveal the procedural error inherent in right-wrong scoring. The procedure bypasses the limitations produced by the linear dependencies inherent in test data.

Testing bias occurs when a test systematically favors one group over another, even though both groups are equal on the trait the test measures. Critics allege that test makers and facilitators tend to represent a middle class, white background. Critics claim that standardized testing match the values, habits, and language of the test makers. However, being that most tests come from a white, middle-class background, it is important to note that the highest scoring groups are not people of that background, but rather tend to come from Asian populations.

Not all tests are well-written, for example, containing multiple-choice questions with ambiguous answers, or poor coverage of the desired curriculum. Some standardized tests include essay questions, and some have criticized the effectiveness of the grading methods. Recently, partial computerized grading of essays has been introduced for some tests, which is even more controversial.