Extended Tables of the Wilcoxon Matched Pair Signed Rank Statistic

McCornack, Robert L.

doi:10.2307/2283253

Cited by 33 publications

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“…Wilcoxon (1945) and Wilcoxon et al (1963) tabulated critical values for various sample sizes and probability levels up to 50 pairs of observations; extended tables were provided by McCornack (1965). These extensive tabulations were derived long before the use of modern and fast computers, requiring rather tedious work.…”

Section: The Wilcoxon Signed-rank Statistic For Paired Datamentioning

confidence: 99%

“…Afterwards, however, additional tables of critical values were provided for larger sample sizes and smaller significance levels for both paired (Wilcoxon 1947;McCornack 1965;Lehmann 1998) and unpaired data (Mann and Whitney 1947;Fix and Hodges 1955;Jacobson 1963;Verdooren 1963;Milton 1964;Lehmann 1998). Statisticians also focused on numerical evaluations of the asymptotic properties of the signed-rank (Wilcoxon 1947;Fellingham and Stocker 1964;McCornack 1965;Claypool and Holbert 1974) and ranksum statistics (Wilcoxon 1947;Buckle et al 1969;Di Bucchianico 1999;Bean et al 2004).…”

Section: Numerical Approachmentioning

confidence: 99%

“…Statisticians also focused on numerical evaluations of the asymptotic properties of the signed-rank (Wilcoxon 1947;Fellingham and Stocker 1964;McCornack 1965;Claypool and Holbert 1974) and ranksum statistics (Wilcoxon 1947;Buckle et al 1969;Di Bucchianico 1999;Bean et al 2004).…”

Section: Numerical Approachmentioning

confidence: 99%

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Normal Approximations to the Distributions of the Wilcoxon Statistics: Accurate to What N ? Graphical Insights

Bellera

Julien

Hanley

2010

Journal of Statistics Education

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The Wilcoxon statistics are usually taught as nonparametric alternatives for the 1-and 2-sample Student-t statistics in situations where the data appear to arise from non-normal distributions, or where sample sizes are so small that we cannot check whether they do. In the past, critical values, based on exact tail areas, were presented in tables, often laid out in a way that saves space but makes them confusing to look up. Recently, a number of textbooks have bypassed the tables altogether, and suggested using normal approximations to these distributions, but these texts are inconsistent as to the sample size n at which the standard normal distribution becomes more accurate as an approximation. In the context of non-normal data, students can find the use of this approximation confusing. This is unfortunate given that the reasoning behind-and even the derivation of-the exact distributions 1 Journal of Statistics Education, Volume 18, Number 2, (2010) can be so easy to teach but also help students understand the logic behind rank tests. This note describes a heuristic approach to the Wilcoxon statistics. Going back to first principles, we represent graphically their exact distributions. To our knowledge (and surprise) these pictorial representations have not been shown earlier. These plots illustrate very well the approximate normality of the statistics with increasing sample sizes, and importantly, their remarkably fast convergence.

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Section: The Wilcoxon Signed-rank Statistic For Paired Datamentioning

confidence: 99%

Section: Numerical Approachmentioning

confidence: 99%

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Normal Approximations to the Distributions of the Wilcoxon Statistics: Accurate to What N ? Graphical Insights

Bellera

Julien

Hanley

2010

Journal of Statistics Education

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“…I values of inspired gas volume an fractiona concentrations of Oz and COz' and appropriately corrected for temperature and pressure. Significance of difference between the results of the two exercise occasions was assessed statistically by the non-parametric Wilcoxon's rank-test for paired observations (McCornack, 1965). Table 1 shows the average maximal strengths and durations of exercise in the various studies for normal subjects and patients with sensory loss.…”

Section: Calculations and Statisticsmentioning

confidence: 99%

Role of Sensory Nerves in the Cardiovascular and Respiratory Changes with Isometric Forearm Exercise in Man

Duncan¹,

Johnson²,

Lambie³

1981

Clinical Science

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1. To investigate the stimulus to the cardiovascular and respiratory systems during isometric exercise, two patients with sensory neuropathies affecting forearm afferent nerves were studied and their circulatory and respiratory responses compared with those of normal subjects. The contribution of pain to the cardiorespiratory changes was also investigated in normal subjects by using hypnosis to relieve pain during and after isometric exercise. 2. The patients and normal subjects performed fatiguing isometric forearm exercises on a handgrip dynamometer on at least two occasions, once with normal forearm circulation and once with the forearm circulation occluded by an arterial cuff during and after exercise. Blood pressure, heart rate, minute ventilation, oxygen consumption and ventilatory equivalent were measured before, during and after exercise. 3. During exercises with and without occlusion increases in blood pressure and heart rate in patients and in subjects under hypnosis were similar to those in control subjects. Changes in oxygen consumption were also similar to those of controls, but the patients showed a smaller rise in ventilation and no increase in ventilatory equivalent. 4. After exercise in normal subjects occlusion of the forearm circulation produced continued elevation of blood pressure and respiration. Blood pressure also remained elevated after exercise with occlusion in subjects under hypnosis, but not in patients with sensory loss. Respiration did not remain elevated in either subjects under hypnosis or patients. 5. The results suggest that cardiovascular and respiratory changes during isometric exercise can occur without involvement of muscle sensory nerves and that pain contributes substantially to the increase in respiration. Normal sensory innervation is apparently necessary only for maintenance of raised blood pressure after exercise with occlusion.

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“…mean. Statistical analysis was performed using the Wilcoxon matched-pairs signed rank test (McCornack, 1965) and the Mann-Whitney two sample rank test (Milton, 1964 Figure 1. Urinary flow rate (13.7 ± 0.8 vs 18.3 ± 1.5 ml/min; P < 0.01) and urinary excretion of sodium (158 ± 12 vs 286 ± 48 ,umol/min; P < 0.01), chloride (73 ± 16 vs 189 ± 41 ,umol/min; P < 0.01) and inorganic phosphate (8.7 ± 1.9 vs 16.7 ± 2.3; P < 0.01) were significantly decreased during infusion of the angiotensin II-analogue.…”

Section: Methodsmentioning

confidence: 99%

Effect of angiotensin II and captopril on renal tubular function in man.

Düsing¹,

Moritz²,

Glänzer³

et al. 1985

Brit J Clinical Pharma

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1 The effects of nonpressor doses of intravenous angiotensin II and of the converting enzyme inhibitor captopril on renal excretory function were investigated in eight healthy volunteers during sustained water diuresis on a constant intake of 150 mmol sodium per day. 2 The angiotensin II-analogue val5-angiotensin II-aspl-p-amide was infused i.v. at an average dose of 2.6 ng kg-' min-' which was the highest dose without a significant effect on arterial blood pressure. This subpressor dose of angiotensin II significantly decreased urine volume, urinary excretion of sodium, chloride and phosphate and distal delivery [(CH20 + CC')/GFR 1001 in the absence of changes in GFR or distal fractional chloride absorption [CH20/(CH20 + CC1)]-3 In a second series of experiments, an oral dose of 50 mg of the angiotensin Iconverting enzyme inhibitor captopril was given to the sodium replete volunteers. In this study, captopril did not affect arterial blood pressure, GFR or any of the determined parameters of renal tubular function. 4 Our results strongly suggest that the nonpressor dose of angiotensin II induced renal retention of sodium chloride via increased absorption in the proximal tubule. Thus, they further support the concept that angiotensin II participates in the regulation of renal sodium chloride excretion by affecting proximal tubular absorptive capacity. However, in the sodium replete stage, angiotensin II is of no major importance in regulating sodium chloride excretion.

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Extended Tables of the Wilcoxon Matched Pair Signed Rank Statistic

Cited by 33 publications

References 0 publications

Normal Approximations to the Distributions of the Wilcoxon Statistics: Accurate to What N ? Graphical Insights

Normal Approximations to the Distributions of the Wilcoxon Statistics: Accurate to What N ? Graphical Insights

Role of Sensory Nerves in the Cardiovascular and Respiratory Changes with Isometric Forearm Exercise in Man

Effect of angiotensin II and captopril on renal tubular function in man.

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