BS in Statistics
Circular statistics are specialized statistical methods that deal specifically with directional data. Data that is angular require specialized techniques due to the modulo 2π (in radians) or modulo 360◦ (in degrees) nature of angles.
Correlation, typically in terms of Pearson’s correlation coefficient, is a measure of association between two linear random variables x and y. In this paper, the specific circular technique of the parametric and nonparametric linear-circular correlation coefficient will be explored where correlation is no longer between two linear variables x and y, but between a linear random variable x and circular random variable θ.
A simulation study of the parametric and nonparametric Linear-Circular Correlation Coefficient was carried out to evaluate the mathematical distribution the statistics followed. A further study was conducted to investigate the effect of ties on the nonparametric correlation coefficient. Lastly, a comparison of power between the parametric and nonparametric Linear-Circular Correlation coefficient was conducted with varying sample sizes, means, and distributions.
It was found that the nonparametric and parametric test statistics both follow their theoretical distributions (asymptotically for the nonparametric statistic). It was found that the nonparametric statistic was robust against ties. Additionally, it was also found that the power of the parametric statistic outperformed the nonparametric statistic for almost all values of λ for our exponential linear random variable.