Statistical matching, or data fusion, merges microdata from sample surveys. The goal is to create a synthetic file with a merged set of variables. A typical scenario is that variables (X,Y) are collected in Survey A, and variables (X,Z) are collected in Survey B. Statistical matching creates a synthetic microdata file from the Survey A and Survey B data, with values of X, Y, and Z on each record. Uncertainty occurs during statistical matching because information is lacking about the distribution of (Y,Z). A method to exhibit the uncertainty in estimates due to the statistical matching procedure is to allow a variety of assumptions to be made about the distribution of (Y,Z), carry out statistical matching to create a dataset corresponding to each assumption, and then assess the variation in estimates made from the group of datasets created by this procedure. This book describes innovations of previous work by Kadane (1978) and Rubin (1986) that implements the method correctly. Practitioners in the fields of applied statistics and microsimulation modeling who carry out statistical matching will find the methodologies described in this book to be useful for their work.