Implementation of Kolmogorov–Smirnov P-value computation in Visual Basic®: implication for Microsoft Excel® library function

Abstract

This paper investigates methodologies for evaluating the probabilistic value (P-value) of the Kolmogorov–Smirnov (K–S) goodness-of-fit test using algorithmic program development implemented in Microsoft® Visual Basic® (VB). Six methods were examined for the one-sided one-sample and two methods for the two-sided one-sample cumulative sampling distributions in the investigative software implementation that was based on machine-precision arithmetic. For sample sizes n≤2000 considered, results from the Smirnov iterative method found optimal accuracy for K–S P-values≥0.02, while those from the SmirnovD were more accurate for lower P-values for the one-sided one-sample distribution statistics. Also, the Durbin matrix method sustained better P-value results than the Durbin recursion method for the two-sided one-sample tests up to n≤700 sample sizes. Based on these results, an algorithm for Microsoft Excel® function was proposed from which a model function was developed and its implementation was used to test the performance of engineering students in a general engineering course across seven departments.

Keywords:

• Kolmogorov–Smirnov sampling distributions
• Kolmogorov–Smirnov probabilistic value
• machine-precision arithmetic
• one-sided one-sample cumulative statistics
• two-sided one-sample cumulative statistics
• Microsoft Excel library function

AMS Subject Classifications :

• 62-04
• 62G10
• 62P30