| Ordinal measures currently enjoy widespread use. The use of a limited number of categories with equal lengths between points (the placements of categorical labels) on the scale may cause a loss of information. Many well-known studies claim that only nonparametric tests are appropriate for the nominal or ordinal level data, that parametric tests are appropriate for the interval or ratio level data; and ordinal numbers (equal lengths between points) cannot be meaningfully added, subtracted, multiplied, and divided. This citation has been one of the most controversial statements in applied statistics.;The purpose of this research was to evaluate the effect on parametric and nonparametric tests using ordinal data when the distances between points changed on the measurement scale. The research examined the performance of Type I and Type II error rates using selected parametric and nonparametric tests.;Three experiments were conducted by generating simulation data on a seven-point Likert-scale using one uniform, three normal, and three gamma populations. Various unequal distance changes were made between points in the four phases of the experiments.;One and two random samples of simulation data were selected from seven populations. Selected parametric tests and nonparametric tests were used to examine the equality of means, medians, deviations, and distributions between two populations. Several computer programs were written in FORTRAN 77 to implement the algorithm of data simulation, parametric tests, and nonparametric tests. The simulation data were tested by the programs.;The results were analyzed in terms of Type I and Type II error rates with different sample sizes, populations, and phases. In summary, the nonparametric tests produced the same results when the distances between points changed on the scale. However, parametric tests show different results when the distances between points changed. The power of parametric and nonparametric tests were evaluated as underlying assumptions were violated in the location parameters. |
