Coefficient Alpha

Coefficient alpha, or Cronbach's alpha, is one way to quantify reliability and represents the proportion of observed score variance that is true score variance. Reliability is a property of a test that is derived from true scores, observed scores, and measurement error. Scores or values that are obtained from the measurement of some attribute or characteristic of a person (e.g., level of intelligence, preference for types of foods, spelling achievement, body length) are referred to as observed scores. In contrast, true scores are the scores one would obtain if these characteristics were measured without any random error. For example, every time you go to the doctor, the nurse measures your height. That is the observed height or observed “score” by that particular nurse. You return for another visit 6 months later, and another nurse measures your height. Again, that is an observed score. If you are an adult, it is expected that your true height has not changed in the 6 months since you last went to the doctor, but the two values might be different by .5 inch. When measuring the quantity of anything, whether it is a physical characteristic such as height or a psychological characteristic such as food preferences, spelling achievement, or level of intelligence, it is expected that the measurement will always be unreliable to some extent. That is, there is no perfectly reliable measure. Therefore, the observed score is the true score plus some amount of error, or an error score.

Measurement error can come from many different sources. For example, one nurse may have taken a more careful measurement of your height than the other nurse. Or you may have stood up straighter the first time you were measured. Measurement error for psychological attributes such as preferences, values, attitudes, achievement, and intelligence can also influence observed scores. For example, on the day of a spelling test, a child could have a cold that may negatively influence how well she would perform on the test. She may get a 70% on a test when she actually knew 80% of the material. That is, her observed score may be lower than her true score in spelling achievement. Thus, temporary factors such as physical health, emotional state of mind, guessing, outside distractions, misreading answers, or misre-cording answers would artificially inflate or deflate the true scores for a characteristic. Characteristics of the test or the test administration can also create measurement error.

Ideally, test users would like to interpret individual's observed scores on a measure to reflect the person's true characteristic, whether it is physical (e.g., blood pressure, weight) or psychological (e.g., knowledge of world history, level of self-esteem). In order to evaluate the reliability of scores for any measure, one must estimate the extent to which individual differences are of function of the real or true score differences among respondents versus the extent to which they are a function of measurement error. A test that is considered reliable minimizes the measurement error so that error is not highly correlated with true score. That is, the relationship between the true score and observed score should be strong.

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