This study was designed to derive the distribution of a test statistic based on normal probability plots. The first purpose was to provide an empirical derivation of the critical values for the Line Test (LT) with an extensive computer simulation. The goal was to develop a test that is sensitive to a wide range of alternative distributions, applicable to a wide range of sample sizes, and easy to compute. The second purpose was to determine the power of LT and compare it to that of several other test statistics. Monte Carlo simulation was used to generate the critical values of LT by randomly generating 500,000 replications from a normal distribution for sample sizes 10(1)100(25)1000(250)5000. For each replication, the value of LT was calculated. The empirical critical values were determined for each of three levels of significance for each sample size. These critical values were then "smoothed" using nonlinear regression techniques. The results indicate that LT provides adequate control over Type I errors while at the same time providing statistical power comparable to the Shapiro-Wilk test. Results also indicate that LT is easy to compute, is powerful for detecting departures from normality under a wide variety of alternative distributions, and is available for sample sizes up to 5,000. An appendix contains the Statistical Package for the Social Sciences syntax for computing the LT for a given data set. (Contains 2 figures, 10 tables, and 45 references.) (Author/SLD)