The robust rank-order test was improved to reduce errors when comparing samples with different variances. A new method was developed to calculate critical values directly, improving accuracy especially for small sample sizes and low significance levels. By estimating population parameters and using Monte-Carlo simulations, the new method outperformed the standard normal approximation, even for larger sample sizes. A sample size of 10^4 was found to be sufficient for better performance. This study opens the door for a more reliable way to conduct the robust rank-order test without relying on specific distributions.