Statistics notes: The normal distribution
Open accessAbstract
Multispectral fluorescence imaging (MSFI) is a rapidly growing field with broad applications in both preclinical and clinical settings. Application of this novel technology in small-animal imaging and microscopy produces enhanced sensitivity and reliable quantification and resolves multiple simultaneous signals. MSFI flow cytometry can quantify multiple fluorescent parameters with morphologic or subcellular spatial details on millions of cells. MSFI has the potential to improve the accuracy of disease detection or differentiation and intrasurgical metastatic diagnosis, guide neurosurgeries, and monitor treatment response.
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Means of random samples from any distribution will themselves have a normal distribution.
“and (c) means of random samples from any distribution will themselves have normal distribution (3).”
From Normality Tests for Statistical Analysis: A Guide for Non-Statisticians (2012) · cites this paper as [3]
The normal distribution (p. 1) says sample means “will themselves have a normal distribution,” but the same passage links this to increasing sample size and cautions that the sample size may need to be very large. The citing sentence omits that qualification and implies the result holds for random samples of any size. (LLM, conf=0.82)
Experimental — accuracy not yet measuredIn large samples (more than 30 or 40, or hundreds of observations), violation of the normality assumption does not cause major problems, and parametric procedures can be used even when the data are not normally distributed.
“With large enough sample sizes (> 30 or 40), the violation of the normality assumption should not cause major problems (4); this implies that we can use parametric procedures even when the data are not normally distributed (8).”
From Normality Tests for Statistical Analysis: A Guide for Non-Statisticians (2012) · cites this paper as [3]
In “The normal distribution” (p. 1), Altman and Bland say that methods including t tests need not have normally distributed observed data, but the sample should be compatible with a normal underlying population. This supports the cited point about non-normal observed data, not an unqualified claim that parametric procedures can be used whenever data are non-normal. The >30 or 40 threshold is attached to a different citation in the citing sentence. (LLM, conf=0.84)
Experimental — accuracy not yet measuredVisual inspection of the distribution for assessing normality is usually unreliable and does not guarantee that the distribution is normal.
“Visual inspection of the distribution may be used for assessing normality, although this approach is usually unreliable and does not guarantee that the distribution is normal (2, 3, 7).”
From Normality Tests for Statistical Analysis: A Guide for Non-Statisticians (2012) · cites this paper as [3]
The normal distribution (p. 1) illustrates observed data with a histogram and distinguishes the observed distribution from the underlying population distribution, supporting the caution that appearance alone does not guarantee population normality. Our copy does not say that visual inspection is usually unreliable. (LLM, conf=0.72)
Experimental — accuracy not yet measuredParametric statistical procedures, including correlation, regression, t tests, and analysis of variance, are based on the assumption that the data or populations are normally distributed, and their validity depends on this assumption.
“The assumption of normality needs to be checked for many statistical procedures, namely parametric tests, because their validity depends on it.”
From Normality Tests for Statistical Analysis: A Guide for Non-Statisticians (2012) · cites this paper as [3]
The assumption of normality needs to be checked for many statistical procedures, namely parametric tests.
“The assumption of normality needs to be checked for many statistical procedures, namely parametric tests, because their validity depends on it.”
From Normality Tests for Statistical Analysis: A Guide for Non-Statisticians (2012) · cites this paper as [3]
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Cites
Practical Statistics for Medical Research.
Walter, S., & Altman, D. G. (1992) · Biometrics · doi:10.2307/2532320 · Cited by 11,665 · see citing works
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Research works printed but not linked: 3
- BMJ: first published as 10.1136/bmj.310.6975.298 on 4 February 1995. Downloaded from http://www.bmj.com/ on 21 August 2023 by guest. Protected by copyright. size increases. normally distributed. We consider these topics future notes. will themselves have a normal distribution. As consequence, when we have samples of hundreds data. Nevertheless, because most clinical studies are distribution. sample size may have to be very large indeed. proportions) would have a normal distribution repeated samples.³
- 2 Gardner MJ, Altman DG. Calculating confidence intervals for proportions and their differences. In: Gardner MJ, Altman DG, eds. Statistics with confidence. London: British Medical Journal, 1989:28-33
- 3 Gardner MJ, Alunan DG, eds. Statistics with confidence. London: British Medical Journal, 1989:17.
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“If we have samples consisting of hundreds of observations, we can ignore the distribution of the data (3).”
InfluentialDescriptive statistics and normality tests for statistical data
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“Central limit theorem states that when sample size has 100 or more observations, violation of the normality is not a major issue.[5,8] Although for meaningful conclusions, assumption of the normality should be followed irrespective of the sample size.”
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- Authors
- Altman, D. G., & Bland, J. M.
- Affiliations
- St George's, University of London (GB)
- ORCID
- Altman, Douglas G
- Venue
- BMJ
- Publisher
- BMJ
- Published
- 1995-02-04
- Volume
- 310
- Issue
- 6975
- Pages
- 298
- ISSN
- 0007-1447 (ISSN-L)
- 0959-8138
- 1468-5833
- PMC
- PMC2548695
- OpenAlex
- W2008391847
- Cited by
- 549
- References
- 1
- Citations by year
- 2026: 36 · 2025: 53 · 2024: 53 · 2023: 41 · 2022: 46 · 2021: 39 · 2020: 32 · 2019: 23 · 2018: 20 · 2017: 27 · 2016: 27 · 2015: 13 · 2014: 21 · 2013: 12 · 2012: 13
- FWCI
- 7.01
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.bmj.com/company/legal-information/terms-conditions/legal-information/tdm-licencepolicy (tdm)
- Locations
- BMJ (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Probabilistic Statistics in Medicine
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Keywords
- normal distribution, statistics, multispectral fluorescence imaging, fluorescence flow cytometry, small animal imaging, treatment response monitoring
- MeSH terms
- Humans, Normal Distribution
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