Abstract
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 power1d which implements (a) two analytical 1D 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 power1d’s two RFT-based analytical solutions are numerically validated using its random continuum generators. Second arbitrary signal/noise modeling is demonstrated to show how power1d 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 power1d 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.
Highlights
Analyzing multiple measurements of one-dimensional (1D) continua is common to a variety of scientific applications ranging from annual temperature fluctuations in climatology (Fig. 1) to position trajectories in robotics
While this paper focuses on power analysis it is instructive to first consider continuum-level hypothesis testing because those results are what power analysis attempts to control
This paper has described a Python package called power1d for estimating power in experiments involving 1D continuum data
Summary
Analyzing multiple measurements of one-dimensional (1D) continua is common to a variety of scientific applications ranging from annual temperature fluctuations in climatology (Fig. 1) to position trajectories in robotics. These measurements can be denoted y(q) where y is the dependent variable, q specifies continuum position, usually in space or time, and where the continua are sampled at Q discrete points. The data are ‘registered’ in the sense that point q is homologous across multiple continuum measurements.
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