THPLOT.M: A MATLAB function to implement generalized Thompson–Howarth error analysis using replicate data

Abstract

Thompson and Howarth in the 1970s developed a set of two complementary quantitative data analysis procedures that may be used to establish a linear relationship between measurements and the magnitude (standard deviation) of their associated measurement errors. Although these methods are restricted to duplicate measurements, they have been generalized to accommodate replicate measurements, involving more than two repeat determinations. A MATLAB function ( THPLOT.M) facilitates use of these generalized Thompson–Howarth methods by allowing: (i) two replicate data input formats, (ii) flexibility in how many replicate statistics are grouped together in the linear regression that determines the measurement–error relationship, (iii) weighted and unweighted linear regression models involving fixed, proportional, or combined fixed and proportional error terms, (iv) two graphical outputs depicting absolute and relative measurement–error relationships, (v) sample and number of replicate measurement labels on these plots, and (vi) numerical output of all relevant statistics, including the calculated effective detection limit. In addition, the THPLOT.M function performs inference tests on both the regression and user supplied parameter estimates of the linear measurement error function using χ 2 critical values, and outputs the binomial probabilities associated with the observed scatter of the replicate standard deviations about the calculated or hypothesized measurement–error function. Consequently, the THPLOT.M function facilitates rigorous examination of quality control data, allowing the scientist to use replicate determinations from a subset of samples to establish a relationship between the measurements and their errors, so that estimates of the error magnitude can be assigned to every sample measurement in a dataset.