A comparative study of tests for the difference of two Poisson means

Ng, Hon Keung Tony; Gu, K.; Tang, Man‐Lai

doi:10.1016/j.csda.2006.02.004

Cited by 20 publications

(34 citation statements)

References 15 publications

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“…For some decision rules, declared and actually observed values of this probability are poorly matched in the range of small count numbers; studying the difference between them is an important part in the evaluation of a decision rule. [5][6][7][8] Finally, in addition to the computational aspects above, discussing detection capabilities has a potential for terminological controversy. A record of such controversy is contained in the annals of chemical metrology.…”

Section: Introductionmentioning

confidence: 99%

Detection in LA-ICPMS: construction and performance evaluation of decision rules

Ulianov

Müntener

Schaltegger

et al. 2016

J. Anal. At. Spectrom.

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Laser ablation inductively coupled plasma mass spectrometry (LA-ICPMS) is frequently employed for the analysis of minute isotope contents in the presence of a background noise. Distinguishing between the sample signal and the background noise at a given confidence level thus represents a routine challenge. For count numbers Nb and Ns collected during (equally long) background and sample measurements, respectively, the statistical significance of their net value, Ns, Nb, can be evaluated: how probable is it to obtain such value by subtracting two count number estimates coming from a common statistical distribution (i.e., when Ns and Nb represent measured estimates of the same mean activity)? If, based on the analysis of a model distribution of the net count numbers, we decide that this is probable, the signal is statistically indistinguishable from the background: the analysed isotope is not detected. If the corresponding (one-sided) probability is below some threshold, it is detected. The net signal value on the divide between the above alternatives, given in net counts or mass (content) units, is called critical level; optionally, it can be complemented by the computation of the detection limit; such values are often reported in the literature. Less discussed is the appropriateness of computational methods used to estimate these values. Troubles arise from attempts to apply Gaussian confidence intervals to small, discretely distributed count numbers contained in real LA-ICPMS acquisitions, and from a non-optimal estimation of the net count number standard deviation in some of the methods used for the computation of critical levels for paired measurements. Combined, these factors may result in uncontrolled, excessively high rates of false detections (background reported as detection of analyte in the sample). Here, we provide a review of methods, otherwise called decision rules, available for the critical level estimation and discuss how to evaluate the performances of these rules to enable an educated computation of LA-ICPMS detection capabilities, including the case of small count numbers

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Section: Introductionmentioning

confidence: 99%

Detection in LA-ICPMS: construction and performance evaluation of decision rules

Ulianov

Müntener

Schaltegger

et al. 2016

J. Anal. At. Spectrom.

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“…Their method was based on the conditional distribution of a Poisson random variable given the sum of two Poisson random variables following a binomial distribution. The conditional approach can be readily applied to the hypothesis testing and interval estimation problems, and many papers have addressed these issues since then 2–9. Gail2 conducted both exact and approximate sample size estimation and power calculations, assuming equal sample size in two groups.…”

Section: Introductionmentioning

confidence: 99%

“…For unequal sample sizes, Shiue and Bain3 and Thode4 derived two approximate sample size formulae. Ng and Tang8, 9 conducted simulation studies to evaluate tests in comparing two Poisson variates over unequal sampling frames. For designing non‐randomized comparative studies where an external control cohort is used as the comparison group, Makuch and Simon10 developed an approximate sample size formula for binary data.…”

Section: Introductionmentioning

confidence: 99%

Sample size for post-marketing safety studies based on historical controls

Makuch

2010

Pharmacoepidem. Drug Safe.

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“…Those of which we are aware used the Monte Carlo methods, some with relatively few replications. These studies compared three confidence intervals [3], compared eight intervals under stratified sampling [4], and compared size and power of tests [5]. The case of rare arrivals is of particular interest because commonly used methods, based on asymptotic considerations, might provide poor results with a small number of 4031 arrivals.…”

Section: Introductionmentioning

confidence: 99%

An analysis of eight 95 per cent confidence intervals for a ratio of Poisson parameters when events are rare

Barker

Cadwell

2008

Statistics in Medicine

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We compared eight nominal 95 per cent confidence intervals for the ratio of two Poisson parameters, both assumed small, on their true coverage (the probability that the interval includes the ratio of Poisson parameters) and median width. The commonly used log-linear interval, justified by asymptotic considerations, provided coverage and relatively narrow intervals, despite small numbers of arrivals. However, the uniform and scores intervals, defined in the text, come very close to providing coverage while providing substantially narrower intervals. These intervals might have practical applications. In a sensitivity analysis, none of the intervals maintained coverage for negative binomial data, indicating that distributional assumptions should be checked before taking our recommendations.

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A comparative study of tests for the difference of two Poisson means

Cited by 20 publications

References 15 publications

Detection in LA-ICPMS: construction and performance evaluation of decision rules

Detection in LA-ICPMS: construction and performance evaluation of decision rules

Sample size for post-marketing safety studies based on historical controls

An analysis of eight 95 per cent confidence intervals for a ratio of Poisson parameters when events are rare

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