X = T + E

by | Sep 14, 2012 | Church Planting, Coaching

How many times have you filled in those little square boxes or circles next to items on test forms? Have many times have you tried to second guess how your answers might be interpreted? How many times have you questioned or found yourself perplexed by your test results?

The real question is this. Do tests make the grade? To answer this question, the interpretation of an examinee’s test results can be understood in terms of a combination of three elements:

X is the examinee’s score obtained on a test.

T is the “true” score or “true” amount of an examinee’s attribute being measured. Self-esteem, leadership style, anxiety, intelligence, and introversion-extroversion are examples of the many types of attributes tests attempt to measure.

E is the amount of random error that exists in the testing process. No written test is perfect, and no testing situation is perfect. Therefore, errors in measurement are common. Test items might be poorly written or misunderstood by the examinee. The examinee might have a headache during the testing. The examinee might misunderstand the test instructions. The test developers may have achieved poor reliability and validity, meaning the test is not a very accurate measure of the attribute.

Given these elements, an examinee’s test score (X) is actually a combination of “truth” (T) and error (E). This combination can be expressed in the equation: X = T + E.

Suppose your score on a test indicates that you are an introvert. Are you really an introvert? You might be if that is your true score. But you might not be as introverted as measured. Consider these possible sources of errors in measurement. You were so uptight taking the test that you answered the items carelessly. Your examiner inaccurately transposed data from the scoring sheet. The software in the computer malfunctioned.

We often take test results at face value. That is a mistake. Here are some suggestions to help you optimize your use of tests.

  1. Use tests in combination with other sources of data to make interpretations of examinees.
  2. Remember that behavioral data are more valid predictors of performance than written tests.
  3. Because of the first two points, use test results as the second line of offense in making an interpretation. They should be used to as additional sources of information.
  4. Avoid making personnel decisions exclusively on the basis of written tests.
  5. Find out the reliability and validity of a test to determine its overall usefulness.

In conclusion, not all examinees are created equal, and neither are all tests of high or equal validity.

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