Several nonparametric tests are proposed for a mixed design consisting of a randomized complete block design (RCBD) and a completely randomized design (CRD) under the umbrella hypothesis with a known and an unknown peak. The combination of the two statistics is based on two different methods. A simulation study was conducted to investigate the performance of the proposed mixed design tests under many different cases. In either case of a known or an unknown peak umbrella hypothesis, the estimated power of the first method used for the proposed test statistics is better than the second method for all situations. We use a square distance as a weight in terms of assessing the power’s performance of the proposed test statistics for the known peak umbrella hypothesis. The square distance modification improves in increasing the test’s power; in particular, if the peak is indistinct with the first location parameter for four and five treatments, or if the location parameter on the left side of the umbrella hypothesis (upside) is greater than all the different location parameters on the right side of the umbrella hypothesis (downside) such as, (0.8 , 1.0 , 0.75 , 0.2) ; (0.75 , 0.8 , 0.6 , 0.4 , 0.2). Also, the modification improves the test’s power for five treatments and peak at 3 once the underlying distribution is symmetric, as long as the peak of the umbrella hypothesis is distinct. In general, for the unknown peak umbrella hypothesis, the result of the test’s power differs slightly between a modification and nonmodification cases. However, we can distinguish some cases based on the type of underlying distribution. In the case of having a symmetric distribution, the square distance modification is much better than test statistics without modification for some cases once we have four and five treatments. For the case of having three treatments; the estimated power for the proposed test statistics with a square distance modification (3.3.15), (3.3.16) is slightly different from the estimated power for the test statistic without modification (3.3.13), (3.3.14) in both cases of underlying distributions ”symmetric and skewed.”