Central to theories of speech motor control are estimates on magnitudes of lip activity expressed in terms of central tendency, variability, and interrelatedness. In fact, the tenability of each of two competing theories of motor control for speech production rests solely on the observation of the predicted direction of the correlation coefficient (one positive and one negative) that indexes the relationship of concurrent lip activity. Each theory, however, predicts a relationship that is the complete opposite of the relationship predicted by the other. That is, one theory proposes that the labial system functions on the basis of complementary variation, whereas the other assumes positive covariation, or complementary modulation. In apparent contradiction, each prediction has been observed under laboratory conditions. The explanation for this apparent contradiction resides in the small sample sizes upon which each estimate was based. The minimum number of observations that are necessary to achieve accurate estimates of lip displacement parameters has remained unclear. This paper addresses three fundamental questions: (a) how many observations of on-task behavior are necessary to accurately estimate mean and variance values for the magnitude of upper lip displacement in a speech production experiment?, (b) what is the analogous number of observations for estimating the same values of lower lip displacement (together with the mandible) in the same context?, and (c) how many observations are necessary to accurately estimate the correlation coefficient indexing the relationship of lip displacements during the production of speech? Answers to these questions are accomplished through a review of estimator properties, a Monte Carlo computer simulation, and through laboratory observations.(ABSTRACT TRUNCATED AT 250 WORDS)