A tool for systematically comparing the power of tests for normality

Breton, Marc D.; DeVore, Michael D.; Brown, Donald E.

doi:10.1080/00949650701377984

Cited by 6 publications

(3 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, based on the Johnson family of distributions,18 we approximated the probability distribution of the sensor error, using a transformation of the normal density 19…”

Section: Methodsmentioning

confidence: 99%

Analysis, Modeling, and Simulation of the Accuracy of Continuous Glucose Sensors

Breton

Kovatchev

2008

J Diabetes Sci Technol

157

134

View full text Add to dashboard Cite

Background: Continuous glucose monitors (CGMs) collect a detailed time series of consecutive observations of the underlying process of glucose fluctuations. To some extent, however, the high temporal resolution of the data is accompanied by increased probability of error in any single data point. Due to both physiological and technical reasons, the structure of these errors is complex and their analysis is not straightforward. In this article, we describe some of the methods needed to obtain a description of the sensor error that is detailed enough for simulation. Methods: Data were provided by Abbott Diabetes Care and included two data sets collected by the FreeStyle Navigator™ CGM: The first set consisted of 1032 time series of glucose readings from 136 patients with type 1 diabetes and parallel time series of reference blood glucose (BG) collected via self-monitoring at irregular intervals. The average duration of a time series was 5 days; the total number of sensor-reference data pairs was approximately 20,600. The second data set consisted of 56 time series of glucose readings from 28 patients with type 1 diabetes and a parallel time series of reference BG measured via the YSI 2300 Stat Plus™ analyzer every 15 minutes. The average duration of a time series was 2 days; the total number of sensor-reference data pairs was approximately 7000. Results: Three sets of results are discussed: analysis of sensor errors with respect to the BG rate of change, mathematical modeling of sensor error patterns and distribution, and computer simulation of sensor errors: Sensor errors depend nonlinearly on the BG rate of change: Errors tend to be positive (high readings) when the BG rate of change is negative and negative (low readings) when the BG rate of change is positive, which is indicative of an underlying time delay. In addition, the sensor noise is non-white (non-Gaussian) and the consecutive sensor errors are highly interdependent. Thus, the modeling of sensor errors is based on a diffusion model of blood-to-interstitial glucose transport, which accounts for the time delay, and a time-series approach, which includes autoregressive moving average (ARMA) noise to account for the interdependence of consecutive sensor errors. Based on modeling, we have developed a computer simulator of sensor errors that includes both generic and sensor-specific error components. A χ2 test showed that no significant difference exists between the observed and the simulated distribution of sensor errors and the distribution of errors of the FreeStyle Navigator ( p > .46). Conclusions: CGM accuracy was modeled via diffusion and additive ARMA noise, which allowed for designing a computer simulator of sensor errors. The simulator, a component of a larger simulation platform approved by the Food and Drug Administration in January 2008 for pre-clinical testing of closed-loop strategies, has been successfully applied to in silico testing of closed-loop control algorithms, resulting in an investigational device exemption for closed-loop trials at the University of Virginia.

show abstract

“…Finally, based on the Johnson family of distributions,18 we approximated the probability distribution of the sensor error, using a transformation of the normal density 19…”

Section: Methodsmentioning

confidence: 99%

Analysis, Modeling, and Simulation of the Accuracy of Continuous Glucose Sensors

Breton

Kovatchev

2008

J Diabetes Sci Technol

157

134

View full text Add to dashboard Cite

show abstract

“…Normality testing requires nonparametric procedures that could be esoteric and which are known as the goodness-of-fit (GoF) testing. Among many methods that had been studied in literature, the KolmogorovSmirnov GoF had been proffered as the test of choice by researchers for studying continuous distribution, of which the Normal pdf is a widely used example (Breton et al, 2008;Yazici and Yolacan, 2007). In addition, the Kolmogorov-Smirnov GoF statistics is supported by many studies for small sample size (Breton et al, 2008;Yazici and Yolacan, 2007;DeCoursey, 2003) which makes it suitable for engineering data where availability of large sample size may be prohibitive for economical reasons.…”

Section: Expmentioning

confidence: 99%

“…Among many methods that had been studied in literature, the KolmogorovSmirnov GoF had been proffered as the test of choice by researchers for studying continuous distribution, of which the Normal pdf is a widely used example (Breton et al, 2008;Yazici and Yolacan, 2007). In addition, the Kolmogorov-Smirnov GoF statistics is supported by many studies for small sample size (Breton et al, 2008;Yazici and Yolacan, 2007;DeCoursey, 2003) which makes it suitable for engineering data where availability of large sample size may be prohibitive for economical reasons. However, the use of Kolmogorov-Smirnov goodness-offit testing, for ascertaining whether set of data comes from or is distributed like a particular distribution or not, requires analytical procedures that could be cumbersome for non-statisticians or nonmathematicians.…”

Section: Expmentioning

confidence: 99%

Programming Development of Kolmogorov-Smirnov Goodness-of-Fit Testing of Data Normality as a Microsoft Excel® Library Function

Olusegun¹,

Okeniyi²,

Atayero³

2015

JSSD

View full text Add to dashboard Cite

This paper deliberates on the programming development of the Kolmogorov-Smirnov goodness-of-fit testing of data Normality as a library function in the Microsoft Excel® spreadsheet software, in which researchers normally store data for analysis and processing. The algorithmic program procedure utilised developed implementation of the Normality Kolmogorov-Smirnov D statistics for the one-sided and the two-sided test criteria as a library function in the Microsoft Excel® environment. For these programming developments, the Visual Basic for Applications® was employed for deploying macro embedment in the spreadsheet software. Successful programming development of the Normality K-S D statistics fosters implementation of the Normality K-S p-value estimation procedure also as a library function in the Microsoft Excel® environment. Test-applications of these programming developments in the study portray potency of accurate, speedy and economical procedure for testing compatibility of univariate data of real numbers to the Normal distribution, for datasets of n ≤ 2000 sample size.

show abstract

Two Powerful Tests for Normality

Noughabi

2016

Ann. Data. Sci.

View full text Add to dashboard Cite

A tool for systematically comparing the power of tests for normality

Cited by 6 publications

References 35 publications

Analysis, Modeling, and Simulation of the Accuracy of Continuous Glucose Sensors

Analysis, Modeling, and Simulation of the Accuracy of Continuous Glucose Sensors

Programming Development of Kolmogorov-Smirnov Goodness-of-Fit Testing of Data Normality as a Microsoft Excel® Library Function

Two Powerful Tests for Normality

Contact Info

Product

Resources

About