scholarly journals W.S. Gosset and Some Neglected Concepts in Experimental Statistics: Guinnessometrics II

2011 ◽  
Vol 6 (2) ◽  
pp. 252-277 ◽  
Author(s):  
Stephen T. Ziliak
Keyword(s):  
Experimental Design ◽  
Sample Size ◽  
Large Scale ◽  
Statistical Significance ◽  
Small Sample ◽  
Small Samples ◽  
Significant Advance ◽  
Economic Approach ◽  
Barley Malt ◽  
Level Of Significance

AbstractStudent's exacting theory of errors, both random and real, marked a significant advance over ambiguous reports of plant life and fermentation asserted by chemists from Priestley and Lavoisier down to Pasteur and Johannsen, working at the Carlsberg Laboratory. One reason seems to be that William Sealy Gosset (1876–1937) aka “Student” – he of Student'st-table and test of statistical significance – rejected artificial rules about sample size, experimental design, and the level of significance, and took instead an economic approach to the logic of decisions made under uncertainty. In his job as Apprentice Brewer, Head Experimental Brewer, and finally Head Brewer of Guinness, Student produced small samples of experimental barley, malt, and hops, seeking guidance for industrial quality control and maximum expected profit at the large scale brewery. In the process Student invented or inspired half of modern statistics. This article draws on original archival evidence, shedding light on several core yet neglected aspects of Student's methods, that is, Guinnessometrics, not discussed by Ronald A. Fisher (1890–1962). The focus is on Student's small sample, economic approach to real error minimization, particularly in field and laboratory experiments he conducted on barley and malt, 1904 to 1937. Balanced designs of experiments, he found, are more efficient than random and have higher power to detect large and real treatment differences in a series of repeated and independent experiments. Student's world-class achievement poses a challenge to every science. Should statistical methods – such as the choice of sample size, experimental design, and level of significance – follow the purpose of the experiment, rather than the other way around? (JEL classification codes: C10, C90, C93, L66)

SMALL SAMPLE SIZE SCIENTIST

PEDIATRICS ◽  
1989 ◽  
Vol 83 (3) ◽  
pp. A72-A72
Author(s):  
Student
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Causal Explanation ◽  
Small Sample Size ◽  
Small Sample ◽  
Small Samples ◽  
High Expectations ◽  
Sampling Variation ◽  
The Law ◽  
The Stability

The believer in the law of small numbers practices science as follows: 1. He gambles his research hypotheses on small samples without realizing that the odds against him are unreasonably high. He overestimates power. 2. He has undue confidence in early trends (e.g., the data of the first few subjects) and in the stability of observed patterns (e.g., the number and identity of significant results). He overestimates significance. 3. In evaluating replications, his or others', he has unreasonably high expectations about the replicability of significant results. He underestimates the breadth of confidence intervals. 4. He rarely attributes a deviation of results from expectations to sampling variability, because he finds a causal "explanation" for any discrepancy. Thus, he has little opportunity to recognize sampling variation in action. His belief in the law of small numbers, therefore, will forever remain intact.

scholarly journals Coronavirus disease-2019 in cancer patients. A report of the first 25 cancer patients in a western country (Italy)

2020 ◽  
Vol 16 (20) ◽  
pp. 1425-1432 ◽  
Author(s):  
Elisa Maria Stroppa ◽  
Ilaria Toscani ◽  
Chiara Citterio ◽  
Elisa Anselmi ◽  
Elena Zaffignani ◽  
...  
Keyword(s):  
Sample Size ◽  
Antiviral Therapy ◽  
Cancer Patients ◽  
General Hospital ◽  
Small Sample Size ◽  
Statistical Significance ◽  
Western Country ◽  
Small Sample ◽  
Control Group ◽  
Worse Prognosis

Background: We describe cancer patients with coronavirus disease-2019 (COVID-19) infection treated at the Piacenza’s general hospital (north Italy). Materials & methods: 25 cancer patients infected by COVID-19 admitted at the Piacenza’s general hospital from 21 February to 18 March 2020. Outcome from the infection were compared with infected noncancer patients. Results: 20 patients (80%) were treated with antiviral therapy and hydroxychloroquine and five (20%) received hydroxychloroquine alone. Nine (36%) patients died, while 16 (64%) overcome the infection. In the control group the mortality was 16.13% and the overcome from infection was 83.87%. Conclusion: Mortality for COVID-19 was greater in cancer patients when compared with noncancer patients, worse prognosis for older age, women and patients treated with hydroxychloroquine alone. However, the comparisons did not reach statistical significance in most cases. This could be due to the small sample size that is the main limitation of the study.

scholarly journals Effects of sample size on estimation of rainfall extremes at high temperatures

2017 ◽  
Vol 17 (9) ◽  
pp. 1623-1629 ◽  
Author(s):  
Berry Boessenkool ◽  
Gerd Bürger ◽  
Maik Heistermann
Keyword(s):  
Sample Size ◽  
High Temperatures ◽  
Generalized Pareto Distribution ◽  
Small Sample ◽  
Small Samples ◽  
Climate Data ◽  
Rainfall Frequency ◽  
High Quantiles ◽  
Limited Moisture ◽  
Quantile Estimates

Abstract. High precipitation quantiles tend to rise with temperature, following the so-called Clausius–Clapeyron (CC) scaling. It is often reported that the CC-scaling relation breaks down and even reverts for very high temperatures. In our study, we investigate this reversal using observational climate data from 142 stations across Germany. One of the suggested meteorological explanations for the breakdown is limited moisture supply. Here we argue that, instead, it could simply originate from undersampling. As rainfall frequency generally decreases with higher temperatures, rainfall intensities as dictated by CC scaling are less likely to be recorded than for moderate temperatures. Empirical quantiles are conventionally estimated from order statistics via various forms of plotting position formulas. They have in common that their largest representable return period is given by the sample size. In small samples, high quantiles are underestimated accordingly. The small-sample effect is weaker, or disappears completely, when using parametric quantile estimates from a generalized Pareto distribution (GPD) fitted with L moments. For those, we obtain quantiles of rainfall intensities that continue to rise with temperature.

scholarly journals Influence of Pilot and Small Trials in Meta-Analyses of Behavioral Interventions: A Meta-epidemiological Study

2020 ◽  
Author(s):  
Michael W. Beets ◽  
R. Glenn Weaver ◽  
John P.A. Ioannidis ◽  
Alexis Jones ◽  
Lauren von Klinggraeff ◽  
...  
Keyword(s):  
Sample Size ◽  
Behavioral Interventions ◽  
Meta Analysis ◽  
Statistical Significance ◽  
Feasibility Studies ◽  
Small Sample ◽  
Effect Sizes ◽  
Absolute Difference ◽  
Meta Analyses ◽  
The Impact

Abstract Background: Pilot/feasibility or studies with small sample sizes may be associated with inflated effects. This study explores the vibration of effect sizes (VoE) in meta-analyses when considering different inclusion criteria based upon sample size or pilot/feasibility status. Methods: Searches were conducted for meta-analyses of behavioral interventions on topics related to the prevention/treatment of childhood obesity from 01-2016 to 10-2019. The computed summary effect sizes (ES) were extracted from each meta-analysis. Individual studies included in the meta-analyses were classified into one of the following four categories: self-identified pilot/feasibility studies or based upon sample size (N≤100, N>100, and N>370 the upper 75th of sample size). The VoE was defined as the absolute difference (ABS) between the re-estimations of summary ES restricted to study classifications compared to the originally reported summary ES. Concordance (kappa) of statistical significance between summary ES was assessed. Fixed and random effects models and meta-regressions were estimated. Three case studies are presented to illustrate the impact of including pilot/feasibility and N≤100 studies on the estimated summary ES.Results: A total of 1,602 effect sizes, representing 145 reported summary ES, were extracted from 48 meta-analyses containing 603 unique studies (avg. 22 avg. meta-analysis, range 2-108) and included 227,217 participants. Pilot/feasibility and N≤100 studies comprised 22% (0-58%) and 21% (0-83%) of studies. Meta-regression indicated the ABS between the re-estimated and original summary ES where summary ES were comprised of ≥40% of N≤100 studies was 0.29. The ABS ES was 0.46 when summary ES comprised of >80% of both pilot/feasibility and N≤100 studies. Where ≤40% of the studies comprising a summary ES had N>370, the ABS ES ranged from 0.20-0.30. Concordance was low when removing both pilot/feasibility and N≤100 studies (kappa=0.53) and restricting analyses only to the largest studies (N>370, kappa=0.35), with 20% and 26% of the originally reported statistically significant ES rendered non-significant. Reanalysis of the three case study meta-analyses resulted in the re-estimated ES rendered either non-significant or half of the originally reported ES. Conclusions: When meta-analyses of behavioral interventions include a substantial proportion of both pilot/feasibility and N≤100 studies, summary ES can be affected markedly and should be interpreted with caution.

scholarly journals Quantifying prehistoric physiological stress using the TCA method:

2019 ◽  
Vol 46 ◽  
pp. 284-295
Author(s):  
Kristina Penezić ◽  
Marko Porčić ◽  
Jelena Jovanović ◽  
Petra Kathrin Urban ◽  
Ursula Wittwer-Backofen ◽  
...  
Keyword(s):  
Sample Size ◽  
Calcium Metabolism ◽  
Physiological Stress ◽  
Small Sample Size ◽  
Statistical Significance ◽  
Small Sample ◽  
Way Of Life

The Neolithic way of life was accompanied by an increase in various forms of physiological stress (e.g. disease, malnutrition). Here we use the method of tooth cementum annulation (TCA) analysis in order to detect physiological stress that is probably related to calcium metabolism. The TCA method is applied to a sample of teeth from three Mesolithic and five Neolithic individuals from the Central Balkans. The average number of physiological stress episodes is higher in the Neolithic group – but the statistical significance of this result cannot be evaluated due to the small sample size, therefore these results should be taken as preliminary.

scholarly journals Pattern of Coronary Artery Stenosis among Ischaemic Heart Disease Cases in Chittagong

2017 ◽  
Vol 28 (1) ◽  
pp. 30-31
Author(s):  
Abu Tarek Iqbal ◽  
Jalal Uddin ◽  
Dhiman Banik ◽  
Salehuddin ◽  
Hasan Mamun ◽  
...  
Keyword(s):  
Coronary Artery ◽  
Sample Size ◽  
Large Scale ◽  
Resource Constraints ◽  
Coronary Artery Stenosis ◽  
Small Sample Size ◽  
Sampling Technique ◽  
Small Sample ◽  
Artery Stenosis ◽  
Study Results

Many studies were conducted on the topic over the whole world but there is none in Chittagong, Bangladesh. To know the pattern of coronary artery stenosis in Chittagong we have conducted the study because it is important for effective case management. It was an observational study. Convenient sampling technique was used and sample size was fixed to 110 considering resource constraints. All the cases were diagnosed on the basis of history, clinical features and laboratory investigations. Coronary artery angiogram was methodically conducted. All relevant data had been recorded and were managed manually. The findings were validated statistically. Discussion was made with updated literature review and finally conclusion was drawn. Total 110 cases were studied. Stenosis was found in 77(70%) cases. Among them 83% were male and 17% were female. Age range was 30-80 years but 76% cases were of 40-60 years age group. Among the stenosed cases SVD 29%, DVD 20% and TVD 20% only. Only 01% was LMCA. Commonest stenosed vessel was LAD 71%. RCA 60%, LCX 58% and LMCA 6%. 47% of stenosed cases were found with normal ECG. Ejection fraction of 57% stenosed cases was >55%. Study results are not significantly apart from studies in home and abroad. The limitation is small sample size. So, a multicenter study on a large scale cases is hereby advocated for a conclusive opinionMedicine Today 2016 Vol.28(1): 30-31

Effectiveness of online versus live multi-family psychoeducation group therapy for children and adolescents with mood or anxiety disorders: a pilot study

2016 ◽  
Vol 30 (4) ◽  
Author(s):  
Iman Sapru ◽  
Sarosh Khalid-Khan ◽  
Elaine Choi ◽  
Nazanin Alavi ◽  
Archana Patel ◽  
...  
Keyword(s):  
Anxiety Disorder ◽  
Group Therapy ◽  
Anxiety Disorders ◽  
Sample Size ◽  
Small Sample Size ◽  
Statistical Significance ◽  
Relative Effectiveness ◽  
Small Sample ◽  
Rank Test ◽  
Family Psychoeducation

Abstract Objective: [1] To highlight the effectiveness of multi-family psychoeducation group therapy (MFPGT) in children with mood or anxiety disorders; [2] to measure change in knowledge and awareness of mood and anxiety disorders in families and children; and [3] to compare the relative effectiveness of online compared to live MFPGT. Method: Participants included families of children (12 years or younger) referred with a mood or anxiety disorder to the Division of Child and Adolescent Psychiatry at Queen’s University (n=16) who were on a waitlist to see a psychiatrist. Change was measured through questionnaires for all parents before and after the program. Using SPSS v22, comparisons between the online (n=6) and live (n=10) groups were made using the Mann-Whitney U test and within group comparisons were made using Wilcoxon signed-rank test. Results: The online and live education groups showed similar overall improvements in knowledge acquisition and expressed emotion in participating families. However, statistical significance must be interpreted with caution due to the small sample size. Conclusions: Online MFPGT may be an effective way to increase knowledge, provide resources and support and build on skills thus giving individuals more control and confidence when dealing with a mood or anxiety disorder while on a waitlist. MFPGT showed equal efficacy in live and online groups, indicating that the online program has the potential to be a more convenient and accessible program for families. More research is needed with a greater sample size.

Current practice for social workers on planning contact for special guardianship children

2019 ◽  
Vol 14 (4) ◽  
pp. 251-265
Author(s):  
Nicholas Thompson
Keyword(s):  
Focus Groups ◽  
Sample Size ◽  
Social Workers ◽  
Current Practice ◽  
Local Authority ◽  
Statistical Significance ◽  
Small Sample ◽  
Content Type ◽  
Contact Frequency ◽  
The Subject

Purpose An integral feature of Special Guardianship Orders (SGO) is that the children should have some contact with their parents after the order is granted. Local authority social workers have a duty to plan and recommend levels and types of contact. But there is no policy guidance provided on how to undertake these duties, and little is known about the process that practitioners undertake. The purpose of this paper is to investigate the recommending of contact in special guardianship cases, and to provide data on what contact social workers are recommending the factors they take into consideration and the reasons for their decisions. Design/methodology/approach The research involved a mixed-methods approach comprising of a questionnaire and focus groups. This part of the study comprised of an online questionnaire that was completed by 102 local authority social workers. Responses were downloaded into SPSS Statistics v22 for data analysis and a content analysis was conducted. Findings Quantitative results from the questionnaire are reported in this paper. Respondents provided comprehensive details on what they include in their recommendations, including levels of contact frequency and specific directions. Practitioners rated the factors they considered in reaching their decisions, and gave their general views on special guardianship contact. Results indicated that practitioners are recommending less contact for fathers than for mothers, and may feel less positively about paternal contact. Bivariate analysis suggests that some older and more experienced social workers are recommending lower levels of contact. Research limitations/implications The statistical significance of the results was limited by the relatively small sample size. It was therefore decided to limit bivariate analyses to consideration of just three independent variables: the social worker’s age and number of years in practice, and the age of the child at the time of their SGO, against dependent variables concerning the levels of contact that had been recommended for mothers and fathers and how positive these were considered to be. Because of the limited sample size, most of the results were above this level, and so were not statistically significant. Practical implications Special guardianship has been in place for 12 years now, but apart from Jim Wade’s 2014 study there has been no major research to guide and inform practice. Such major changes in child welfare require substantiating research, and this study is an attempt to begin filling that gap. The questionnaire part of this study has for the first time provided data on the views, motivations and practice of social workers across the country making recommendations on special guardianship contact. Social implications The study provides a picture of the type of contact being recommended for birth parents. This information will be useful for practitioners, who might otherwise not know what their colleagues in other local authorities are recommending, and it is hoped that this will encourage further debate on the subject. Originality/value Special guardianship has so far been poorly served by research. To the author’s knowledge, apart from Wade’s study there is very little research on the subject, and no significant research at all on special guardianship contact. This questionnaire, alongside the four focus groups that formed the second part of the study, provides the first picture of current practice across the country.

Test Method with Small Samples of Electro-Explosive Devices Based on Information Equivalence Principle

2011 ◽  
Vol 65 ◽  
pp. 291-294
Author(s):  
Yao Hua Wang ◽  
Liang Wang ◽  
Hai Shan Yang ◽  
Bao Guo Zhu
Keyword(s):  
Sample Size ◽  
Equivalence Principle ◽  
Small Sample ◽  
Test Method ◽  
Small Samples ◽  
Reliability Test ◽  
Ignition Probability ◽  
Sample Test ◽  
Definition Of Information ◽  
Explosive Devices

In order to solve the problem which generally exists in assessing high explosive ignition reliability of electro-explosive devices (EED), a new test method, based on information equivalence principle, is proposed on the condition of a relatively smaller sample size for instead. According to the definition of information principle, the method measures the reliability test information by the negative logarithm of ignition probability of EED and converts the test by GJB376-1987 at a larger amount of stimulation with a big sample size to a small one. We adopt this method to assess the ignition reliability of EED used in the emergency opening system. The result is that we just need 29 sample size on the confidence of not less than 95% and the ignition reliability greater than 0.999. Compared with the 2996 sample size in GJB376-1987, the method reduces the sample usage greatly. Tests shows that the small sample test method based on information equivalence principle for the ignition reliability test of EED is accurate, feasible and can meet the objective of experimental design

scholarly journals Taking population stratification into account by local permutations in rare-variant association studies on small samples

2020 ◽  
Author(s):  
J. Mullaert ◽  
M. Bouaziz ◽  
Y. Seeleuthner ◽  
B. Bigio ◽  
J-L. Casanova ◽  
...  
Keyword(s):  
Sample Size ◽  
Rare Variant ◽  
Population Stratification ◽  
Type I Error ◽  
Small Sample Size ◽  
Association Studies ◽  
Small Sample ◽  
Small Samples ◽  
Type I ◽  
Rare Variant Association

AbstractMany methods for rare variant association studies require permutations to assess the significance of tests. Standard permutations assume that all individuals are exchangeable and do not take population stratification (PS), a known confounding factor in genetic studies, into account. We propose a novel strategy, LocPerm, in which individuals are permuted only with their closest ancestry-based neighbors. We performed a simulation study, focusing on small samples, to evaluate and compare LocPerm with standard permutations and classical adjustment on first principal components. Under the null hypothesis, LocPerm was the only method providing an acceptable type I error, regardless of sample size and level of stratification. The power of LocPerm was similar to that of standard permutation in the absence of PS, and remained stable in different PS scenarios. We conclude that LocPerm is a method of choice for taking PS and/or small sample size into account in rare variant association studies.

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