Power1D: a Python toolbox for numerical power estimates in experiments involving one-dimensional continua

The unit of experimental measurement in a variety of scientific applications is the one-dimensional (1D) continuum: a dependent variable whose value is measured repeatedly, often at regular intervals, in time or space. A variety of software packages exist for computing continuum-level descriptive statistics and also for conducting continuum-level hypothesis testing, but very few offer power computing capabilities, where 'power' is the probability that an experiment will detect a true continuum signal given experimental noise. Moreover, no software package yet exists for arbitrary continuum-level signal/noise modeling. This paper describes ',a package called powerld which implements (a) two analytical ID power solutions based on random field theory (RFT) and (b) a high-level framework for computational power analysis using arbitrary continuum-level signal/noise modeling. First powerld's two RFT-based analytical solutions are numerically validated using its random continuum generators. Second arbitrary signal/noise modeling is demonstrated to show how powerld can be used for flexible' modeling well beyond the assumptions of RFT-based analytical solutions. Its computational demands are non-excessive, requiring on the order of only 30's to execute on standard desktop computers, but with approximate solutions available much more rapidly. Its broad signal/noise modeling capabilities along with relatively rapid computations imply that powerld may be a useful tool for guiding experimentation involving multiple measurements of similar 1D continua, and in particular to ensure that an adequate number of measurements is made to detect assumed continuum signals.