Properly structured, a sample can be used to make meaningful inferences about the larger population while gaining cost savings from analyzing fewer observations. Whether a sampling process and resulting sample provide these net benefits is context-specific and depends on a number of fundamental factors. My discussion here focuses on two of these factors: sample validity and sample precision. These in large measure appear to have figured into the Supreme Court’s acceptance of sampling in Tyson Foods, Inc. v. Bouaphakeo, 136 S. Ct. 1036 (2015), and its rejection of sampling in Wal-Mart Stores, Inc. v. Dukes, 131 S. Ct. 2541 (2011).
From Legal Case to the Target Population
As a gating issue, regardless of its size, a sample must be valid in order for the resulting parameter estimates and the inferences to be reliable. Validity refers to how accurately the sampling process and the sample itself capture the common and repeating features of the population according to what is intended to be measured. Whether a sample can provide valid information depends on several factors: