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Abstract:
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In marketing research, the Likert-scale is often used to measure a construct through several indicators. Under satisfactory internal consistency and the assumption that the construct has a normal distribution with unknown mean and variance 1, if it is of interest to test if the construct mean achieves a specified level, the traditional t test, based on factor-based scores, may be used. However, its power depends on unknown variances and covariances of indicators, and is difficult to evaluate. To improve, an alternative t test, based on factor scores, is proposed. Its power depends only on sample size and the construct mean. It has been demonstrated by extensive Monte-Carlo simulation that the theoretical power of the test about a normal construct mean can be well approximated by the power of the proposed t test. Some limitations about its use have been discussed.
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