Topographic mapping of brain electrical activity has become a commonly used method in the clinical as well as research laboratory. To enhance analytic power and accuracy, mapping applications often involve statistical paradigms for the detection of abnormality or difference. Because mapping studies involve many measurements and variables, the appearance of a large data dimensionality may be created. If abnormality is sought by statistical mapping procedures and if the many variables are uncorrelated, certain positive findings could be attributable to chance. To protect against this undesirable possibility we advocate the replication of initial findings on independent data sets. Statistical difference attributable to chance will not replicate, whereas real difference will reproduce. Clinical studies must, therefore, provide for repeat measurements and research studies must involve analysis of second populations. Furthermore, Principal Components Analysis can be employed to demonstrate that variables derived from mapping studies are highly intercorrelated and data dimensionality substantially less than the total number of variables initially created. This reduces the likelihood of capitalization on chance. The need to constrain alpha levels is not necessary when dimensionality is low and/or a second data set is available. When only one data set is available in research applications, techniques such as the Bonferroni correction, the "leave-one-out" method, and Descriptive Data Analysis (DDA) are available. These techniques are discussed, clinical and research examples are given, and differences between Exploratory (EDA) and Confirmatory Data Analysis (EDA) are reviewed.