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Communications to the Editor |

On Some Analyses FREE TO VIEW

Arthur D. Tsakok, MSc
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Mathematical Centre, London, UK

Correspondence to: A.D. Tsakok, Mathematical Centre, 46 Leighton Gdn, London NW10 3PT, UK; e-mail: adtsakok@hotmail.com



Chest. 2005;128(3):1888. doi:10.1378/chest.128.3.1888-a
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To the Editor:

There are methodological errors being made in statistical analyses, resulting in flawed results. Examples are in the studies by Hiasa et al1and Oudiz et al.2The problem is the authors’ use of two-sample t tests, analysis of variance, or analysis of covariance to compare means, which assumes the normality and equality of unknown variances in the groups considered. The Central Limit Theorem justifies normality for mean inferences, but unknown variances need not be equal, making these methods not generally applicable to comparing means. This problem is not removed by futilely3 testing for the equality of variances.

Avoiding normality and nuisance variances with rank tests such as the Wilcoxon test2 means that, if significant, they do not specifically say anything about the mean, median, mode, or any specific moment of the distributions, being a comparison of distributions. Moreover, these rank tests are biased4 to one side in a two-sided test. This is irrespective of deaths, the reason given.2

Table 2 ,2 judging by the labels used, the confidence intervals for mean differences, and the ensuing discussion, clearly shows an interest in means. The confidence intervals are meaningless because the statistic used was not given.

The problem of comparing the means of normal populations exactly with unknown variances is the Behrens-Fisher problem, which was solved by Tsakok5in its generalized form. The Tsakok solution is more effective in detecting significant mean differences, even with unknown equal variances. Its exposition6 is available elsewhere.

A statistical software package (GSP; London, UK) implements the Tsakok technique. Some results from Table 11and Table 22 are given. These appear to have been overlooked. After taking care to obtain the data, they deserve correct analysis.

The article by Tsakok7on exact, unconditional, uniformly most powerful unbiased tests extends the Tsakok technique to the nonparametric problem of comparing distributions, superseding rank tests or the Fisher exact test (which is neither exact nor unconditional). An extension to dependent samples8is indicated. The Tsakok articles are reprinted9 with further results.

Table Graphic Jump Location
Table 2. Some Results of Mean Comparisons From Table 2*2
* 

PAPm = mean pulmonary arterial pressure. See Table 1 for abbreviation not used in the text.

Table Graphic Jump Location
Table 1. Some Results of Mean Comparisons From Table 2*1
* 

S = significant difference between means at 0.02 (one significant figure) significance level; RV5 = voltage of R wave in lead V5; SV1 = voltage of S wave in lead V1; LVDd = left ventricular end-systolic dimension; MIBG = metaiodobenzylguadine; H/M =heart/mediastinum ratio.

Hiasa, G, Hamada, M, Saeki, A, et al (2004) Cardiac sympathetic nerve activity can detect congestive heart failure sensitively in patients with hypertrophic cardiomyopathy.Chest126,679-686
 
Oudiz, RJ, Schilz, RJ, Barst, RJ, et al Treprostinil, a prostacyclin analogue in pulmonary arterial hypertension associated with connective tissue disease.Chest2004;126,420-427
 
Kendall, MG, Stuart, A The advanced theory of statistics1973;vol 2,484 Charles Griffin and Co. London, UK:
 
Lehmann, E.L. Testing statistical hypotheses1959,187 John Wiley and Sons. New York, NY:
 
Tsakok, AD A solution to the generalized Behrens-Fisher problem. Metron. 1978;;36 ,.:79
 
Tsakok, AD Comment on visual acuity. Ophthalmic Epidemiol. 2002;;9 ,.:347
 
Tsakok, AD A test of fit satisfying some optimality criteria non-asymptotically. Metron. 1978;;36 ,.:105
 
Tsakok, AD A generalization of the Borel-Cantelli lemma. Metron. 1995;;53 ,.:25
 
Tsakok, AD. Statistics and the unified field. 1987; Mathematical Centre. London, UK:.
 

Figures

Tables

Table Graphic Jump Location
Table 2. Some Results of Mean Comparisons From Table 2*2
* 

PAPm = mean pulmonary arterial pressure. See Table 1 for abbreviation not used in the text.

Table Graphic Jump Location
Table 1. Some Results of Mean Comparisons From Table 2*1
* 

S = significant difference between means at 0.02 (one significant figure) significance level; RV5 = voltage of R wave in lead V5; SV1 = voltage of S wave in lead V1; LVDd = left ventricular end-systolic dimension; MIBG = metaiodobenzylguadine; H/M =heart/mediastinum ratio.

References

Hiasa, G, Hamada, M, Saeki, A, et al (2004) Cardiac sympathetic nerve activity can detect congestive heart failure sensitively in patients with hypertrophic cardiomyopathy.Chest126,679-686
 
Oudiz, RJ, Schilz, RJ, Barst, RJ, et al Treprostinil, a prostacyclin analogue in pulmonary arterial hypertension associated with connective tissue disease.Chest2004;126,420-427
 
Kendall, MG, Stuart, A The advanced theory of statistics1973;vol 2,484 Charles Griffin and Co. London, UK:
 
Lehmann, E.L. Testing statistical hypotheses1959,187 John Wiley and Sons. New York, NY:
 
Tsakok, AD A solution to the generalized Behrens-Fisher problem. Metron. 1978;;36 ,.:79
 
Tsakok, AD Comment on visual acuity. Ophthalmic Epidemiol. 2002;;9 ,.:347
 
Tsakok, AD A test of fit satisfying some optimality criteria non-asymptotically. Metron. 1978;;36 ,.:105
 
Tsakok, AD A generalization of the Borel-Cantelli lemma. Metron. 1995;;53 ,.:25
 
Tsakok, AD. Statistics and the unified field. 1987; Mathematical Centre. London, UK:.
 
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