Goodness-of-fit test statistics are widely used in surveys however little regard is given to the statistical power. This paper investigates the simulated power of a number of five categorical goodness-of-fit test statistics used on a 5-point Likert scale. The test statistics used in this power study are Pearson’s Chi-Square, the Kolmogorov- Smirnov test statistic for discrete data, the Log- Likelihood Ratio, the Freeman-Tukey and the Power Divergence statistic with λ=⅔. This paper aims to provide recommendations on which of these categorical goodness-of-fit test statistic is the most powerful overall and which is the most powerful for a uniform null distribution against alternative distributions with general shapes
The results of the simulated power studies in this paper lead to the following conclusions for these goodness-of-fit test statistics when used on a 5- point Likert scale:
• for sample sizes less than six per cell under the uniform null distribution, the simulated powers of all four test statistics were very poor for all alternative distributions with the exception of the decreasing trend distribution
• the simulated power of the Freeman- Tukey test statistic is generally shown to be relatively less than the power of all the other investigated test statistics
• there is generally no improvement in the simulated power for the Power Divergence test statistic with λ=⅔ over either Pearson’s Chi-Square or the Log- Likelihood Ratio test statistics.
Available at: http://works.bepress.com/mike_steele/4/