To understand why there are so many inconsistencies and contradictory findings among hemispheric-asymmetry studies, data were analyzed from a large study of 300 left-handers. These data included information on familial sinistrality (FS), handwriting posture (HPO), a measure of cognitive performance, and five measures of hemispheric specialization. Using computer simulation methodology, 40 independent samples of 36 to 65 subjects each were drawn randomly with replacement. The sample data were analyzed and the results compared to those of the parent "population." Often, the samples poorly reflected the parent "population," and some procedures substantially inflated error rates. These procedures are discussed and specific guidelines suggested. These results are also discussed in the broader context of the necessity for investigators in neuropsychology to differentiate between the statistical and clinical significance of research findings; and to develop a more positive attitude toward the design, execution, and publication of replication studies.