Estimating the population variance, standard deviation, and coefficient of variation: Sample size and accuracy

Area of Science:

• Evolutionary biology
• Anthropology
• Statistical inference

Background:

• Small sample sizes are common in human and primate evolutionary research for parameter estimation.
• Assessing the reliability of sample estimates for population parameters is crucial for valid inferences.
• Key parameters include mean, variance, standard deviation, and coefficient of variation.

Purpose of the Study:

• To present methods for a priori determination of the probability that sample variance and standard deviation approximate population parameters.
• To validate these methods using resampling from a large human craniometric dataset.
• To provide guidance on appropriate sample sizes for accurate evolutionary research.

Main Methods:

• Application of Cochran's theorem to calculate the probability of sample estimates being within a specified fraction of population parameters.
• Validation through random resampling with replacement of a variable from a large, global modern human craniometric dataset.
• Extension of validation methods to the coefficient of variation.

Main Results:

• Validated methods indicate that hundreds of observations are necessary for confident approximation of population variance.
• Tens of observations are sufficient for accurate estimation of population standard deviation.
• The coefficient of variation's estimation accuracy closely follows that of the standard deviation.

Conclusions:

• Sample size requirements differ significantly between estimating population variance and standard deviation in evolutionary studies.
• Cochran's theorem provides a reliable framework for determining a priori confidence in sample estimates.
• Researchers should consider these findings to ensure the statistical robustness of their evolutionary inferences.