This article considers experiments in manufacturing where the response of interest is the geometric shape of a manufactured part and the goal is to determine whether the process settings varied during the experiment affect the resulting shape of the part. An approach in practice to determine factor effects is to estimate the form error of the part—if a standard definition of the form error of interest exists—and conduct an analysis of variance (ANOVA) on the form errors. Instead, we study the performance of several statistical shape analysis techniques to analyze this class of experiments. Simulated shape data were used to perform power comparisons for two- and three-dimensional shapes. The ANOVA on the form errors was found to have a poor performance in detecting mean shape differences in circular and cylindrical shapes. Procrustes-based tests such as an ANOVA test due to Goodall and a recently proposed ANOVA permutation test provide the highest power to detect differences in the mean shape. These tests can also be applied to parts produced in "free form" manufacturing, where no standard definition of form error exists, provided that correspondent points exist on each part.