Consider search designs for identifying at most k nonzero effects under a search linear model. In the noisy case, the procedure for identifying these effects, which is based on the sum of squares due to error, is considered and its stochastic properties are studied. The errors of observations are assumed to be distributed independently with the normal distribution $N(0, \sigma^2)$ and, in particular, the case of $k = 1$ is considered. Some results on a searching probability under the procedure are presented. Probabilities with respect to search designs which are main effect plus one plans constructed in earlier works, are presented. A comparison between two search designs is given by using a criterion based on probability.