Cronbach's Coefficient Alpha Analyzing latent constructs such as job satisfaction, motor ability, sensory recognition, or customer satisfaction requires instruments to accurately measure the constructs. Interrelated items may be summed to obtain an overall score for each participant. When a value is recorded, the observed value contains some degree of measurement error. Two sets of measurements on the same variable for the same individual may not have identical values. However, repeated measurements for a series of individuals will show some consistency.
Reliability measures internal consistency from one set of measurements to another.
The measurement error is assumed to be independent of the true value, that is, The reliability coefficient of a measurement test is defined as the squared correlation between the observed value Y and the true value T, that is, which is the proportion of the observed variance due to true differences among individuals in the sample. Suppose variables are used with for , where is the observed value, is the true value, and is the measurement error. Let be the total observed score and be the total true score. If the variances of the items vary widely, you can standardize the items to a standard deviation of 1 before computing the coefficient alpha. When the correlation between each pair of variables is 1, the coefficient alpha has a maximum value of 1.