Using the Student’s t-test with extremely small sample sizes
01 Aug 2013-Practical Assessment, Research and Evaluation (Center for Educational Assessment. 813 North Pleasant Street, Amherst, MA 01002. e-mail: pare@umass.edu; Tel: 413-577-2180; Web site: https://scholarworks.umass.edu/pare)-Vol. 18, Iss: 10, pp 10
TL;DR: In this article, a simulation study was conducted to compare the performance of the one-and two-sample t-test for normal distributed populations and for various distortions such as unequal sample sizes, unequal variances, and the combination of unequal sample size and unequal variance, and a lognormal population distribution.
Abstract: Researchers occasionally have to work with an extremely small sample size, defined herein as N ≤ 5. Some methodologists have cautioned against using the t-test when the sample size is extremely small, whereas others have suggested that using the t-test is feasible in such a case. The present simulation study estimated the Type I error rate and statistical power of the one- and two-sample t-tests for normally distributed populations and for various distortions such as unequal sample sizes, unequal variances, the combination of unequal sample sizes and unequal variances, and a lognormal population distribution. Ns per group were varied between 2 and 5. Results show that the t-test provides Type I error rates close to the 5% nominal value in most of the cases, and that acceptable power (i.e., 80%) is reached only if the effect size is very large. This study also investigated the behavior of the Welch test and a rank-transformation prior to conducting the t-test (t-testR). Compared to the regular t-test, the Welch test tends to reduce statistical power and the t-testR yields false positive rates that deviate from 5%. This study further shows that a paired t-test is feasible with extremely small Ns if the within-pair correlation is high. It is concluded that there are no principal objections to using a t-test with Ns as small as 2. A final cautionary note is made on the credibility of research findings when sample sizes are small.
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TL;DR: Impaired muscle function in seven different mouse models of human osteolytic bone metastases is found, implicating a role for the tumor-bone microenvironment in cancer-associated muscle weakness.
Abstract: Cancer-associated muscle weakness is a poorly understood phenomenon, and there is no effective treatment. Here we find that seven different mouse models of human osteolytic bone metastases-representing breast, lung and prostate cancers, as well as multiple myeloma-exhibited impaired muscle function, implicating a role for the tumor-bone microenvironment in cancer-associated muscle weakness. We found that transforming growth factor (TGF)-β, released from the bone surface as a result of metastasis-induced bone destruction, upregulated NADPH oxidase 4 (Nox4), resulting in elevated oxidization of skeletal muscle proteins, including the ryanodine receptor and calcium (Ca(2+)) release channel (RyR1). The oxidized RyR1 channels leaked Ca(2+), resulting in lower intracellular signaling, which is required for proper muscle contraction. We found that inhibiting RyR1 leakage, TGF-β signaling, TGF-β release from bone or Nox4 activity improved muscle function in mice with MDA-MB-231 bone metastases. Humans with breast- or lung cancer-associated bone metastases also had oxidized skeletal muscle RyR1 that is not seen in normal muscle. Similarly, skeletal muscle weakness, increased Nox4 binding to RyR1 and oxidation of RyR1 were present in a mouse model of Camurati-Engelmann disease, a nonmalignant metabolic bone disorder associated with increased TGF-β activity. Thus, pathological TGF-β release from bone contributes to muscle weakness by decreasing Ca(2+)-induced muscle force production.
282 citations
National and Kapodistrian University of Athens1, Academy of Athens2, University of Copenhagen3, University of Dundee4, University of Zurich5, Boston Children's Hospital6, University of South Carolina7, University of Southampton8, Catalan Institution for Research and Advanced Studies9, Manchester Academic Health Science Centre10, Science for Life Laboratory11, Palacký University, Olomouc12
TL;DR: The data reveal the tumour-promoting ability of p21 through deregulation of DNA replication licensing machinery—an unorthodox role to be considered in cancer treatment, since p21 responds to various stimuli including some chemotherapy drugs.
Abstract: The cyclin-dependent kinase inhibitor p21(WAF1/CIP1) (p21) is a cell-cycle checkpoint effector and inducer of senescence, regulated by p53. Yet, evidence suggests that p21 could also be oncogenic, through a mechanism that has so far remained obscure. We report that a subset of atypical cancerous cells strongly expressing p21 showed proliferation features. This occurred predominantly in p53-mutant human cancers, suggesting p53-independent upregulation of p21 selectively in more aggressive tumour cells. Multifaceted phenotypic and genomic analyses of p21-inducible, p53-null, cancerous and near-normal cellular models showed that after an initial senescence-like phase, a subpopulation of p21-expressing proliferating cells emerged, featuring increased genomic instability, aggressiveness and chemoresistance. Mechanistically, sustained p21 accumulation inhibited mainly the CRL4-CDT2 ubiquitin ligase, leading to deregulated origin licensing and replication stress. Collectively, our data reveal the tumour-promoting ability of p21 through deregulation of DNA replication licensing machinery-an unorthodox role to be considered in cancer treatment, since p21 responds to various stimuli including some chemotherapy drugs.
216 citations
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Book•
30 Sep 2018TL;DR: The book as mentioned in this paper gives step-by-step guidance through the process of statistical analysis and provides multiple examples of how statistical techniques can be used to analyse and visualise linguistic data It also includes a useful selection of discussion questions and exercises which you can use to check your understanding.
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References
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Book•
01 Jan 1956
TL;DR: This is the revision of the classic text in the field, adding two new chapters and thoroughly updating all others as discussed by the authors, and the original structure is retained, and the book continues to serve as a combined text/reference.
Abstract: This is the revision of the classic text in the field, adding two new chapters and thoroughly updating all others. The original structure is retained, and the book continues to serve as a combined text/reference.
35,552 citations
15 Aug 2006
TL;DR: In this paper, the authors discuss the implications of these problems for the conduct and interpretation of research and suggest that claimed research findings may often be simply accurate measures of the prevailing bias.
Abstract: There is increasing concern that most current published research findings are false. The probability that a research claim is true may depend on study power and bias, the number of other studies on the same question, and, importantly, the ratio of true to no relationships among the relationships probed in each scientific field. In this framework, a research finding is less likely to be true when the studies conducted in a field are smaller; when effect sizes are smaller; when there is a greater number and lesser pre-selection of tested relationships; where there is greater flexibility in designs, definitions, outcomes, and analytical modes; when there is greater financial and other interest and prejudice; and when more teams are involved in a scientific field in chase of statistical significance. Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true. Moreover, for many current scientific fields, claimed research findings may often be simply accurate measures of the prevailing bias. In this essay, I discuss the implications of these problems for the conduct and interpretation of research.
5,003 citations
TL;DR: In this paper, the authors discuss the implications of these problems for the conduct and interpretation of research and conclude that the probability that a research claim is true may depend on study power and bias, the number of other studies on the same question, and the ratio of true to no relationships among the relationships probed in each scientifi c fi eld.
Abstract: Summary There is increasing concern that most current published research fi ndings are false. The probability that a research claim is true may depend on study power and bias, the number of other studies on the same question, and, importantly, the ratio of true to no relationships among the relationships probed in each scientifi c fi eld. In this framework, a research fi nding is less likely to be true when the studies conducted in a fi eld are smaller; when effect sizes are smaller; when there is a greater number and lesser preselection of tested relationships; where there is greater fl exibility in designs, defi nitions, outcomes, and analytical modes; when there is greater fi nancial and other interest and prejudice; and when more teams are involved in a scientifi c fi eld in chase of statistical signifi cance. Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true. Moreover, for many current scientifi c fi elds, claimed research fi ndings may often be simply accurate measures of the prevailing bias. In this essay, I discuss the implications of these problems for the conduct and interpretation of research. It can be proven that most claimed research fi ndings are false.
4,999 citations
Journal Article•
TL;DR: The On-Line Encyclopedia of Integer Sequences (OEIS) as mentioned in this paper is a database of 13,000 number sequences and is freely available on the Web (http://www.att.com/~njas/sequences/) and is widely used.
Abstract: The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences. It is freely available on the Web (http://www.research.att.com/~njas/sequences/) and is widely used.
There are several ways in which it benefits research: 1 It serves as a dictionary, to tell the user what is known about a particular sequence. There are hundreds of papers which thank the OEIS for assistance in this way.
1 The associated Sequence Fans mailing list is a worldwide network which has evolved into a powerful machine for tackling new problems.
1 As a direct source of new theorems, when a sequence arises in two different contexts.
1 As a source of new research, when one sees a sequence in the OEIS that cries out to be analyzed.
The 40-year history of the OEIS recapitulates the story of modern computing, from punched cards to the internet.
The talk will be illustrated with numerous examples, emphasizing new sequences that have arrived in the past few months. Many open problems will be mentioned.
Because of the profusion of books and journals, volunteers play an important role in maintaining the database. If you come across an interesting number sequence in a book, journal or web site, please send it and the reference to the OEIS. (You do not need to be the author of the sequence to do this.) There is a web site for sending in "Comments" or "New sequences".
Several new features have been added to the OEIS in the past year. Thanks to the work of Russ Cox, searches are now performed at high speed, and thanks to the work of Debby Swayne, there is a button which displays plots of each sequence. Finally, a "listen" button enables one to hear the sequence played on a musical instrument (try Recamaan's sequence A005132!).
4,548 citations
Book•
01 Jan 1978
TL;DR: In this paper, applied nonparametric statistics are applied to the problem of applied non-parametric statistical data collection in the context of the application of applied NN statistics, including:
Abstract: Applied nonparametric statistics , Applied nonparametric statistics , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
4,248 citations