A method of statistical analysis in the field of sports science when assumptions of parametric tests are not violated

Elżbieta Sandurska, Aleksandra Szulc

Abstract


Introduction: Application of statistical software typically does not require extensive statistical knowledge, allowing to easily perform even complex analyses. Consequently, test selection criteria and important assumptions may be easily overlooked or given insufficient consideration. In such cases, the results may likely lead to wrong conclusions.

Aim: To discuss issues related to assumption violations in the case of Student's t-test and one-way ANOVA, two parametric tests frequently used in the field of sports science, and to recommend solutions.

Description of the state of knowledge: Student's t-test and ANOVA are parametric tests, and therefore some of the assumptions that need to be satisfied include normal distribution of the data and homogeneity of variances in groups. If the assumptions are violated, the original design of the test is impaired, and the test may then be compromised giving spurious results. A simple method to normalize the data and to stabilize the variance is to use transformations. If such approach fails, a good alternative to consider is a nonparametric test, such as Mann-Whitney, the Kruskal-Wallis or Wilcoxon signed-rank tests.

Summary: Thorough verification of the parametric tests assumptions allows for correct selection of statistical tools, which is the basis of well-grounded statistical analysis. With a few simple rules, testing patterns in the data characteristic for the study of sports science comes down to a straightforward procedure.


Keywords


t-test, analysis of variance, mathematical transformations, statistics as topic, nonparamentric test

Full Text:

PDF

References


Bartlett MS. The use of transformations. Biometrics. 1947; 3(1), 39-52.

Boneau CA. The effects of violations of assumptions underlying the t test. Psychological bulletin. 1960; 57(1), 49.

Chmielewska K., Chmielewski J., Szulc A. Statistical prediction methods in public health. Acta Universitatis Matthiae Belii Physical Education and Sport, 2014, Vol. 6 (2), 15-26

Cleophas TJ. Zwinderman AH. Non-parametric tests. Cleophas TJ. Zwinderman AH. Statitical Analysis of Clinical Data on a Pocket Calculator. Springer Netherlands, 2011

Fay MP, Proschan MA. Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules. Statistics surveys. 2010; 4, 1.

Feir-Walsh BJ, Toothaker LE. An empirical comparison of the ANOVA F-test, normal scores test and Kruskal-Wallis test under violation of assumptions. Educational and Psychological Measurement. 1974; 34(4), 789-799.

Ferguson GA, Takane Y. Analiza statystyczna w psychologii i pedagogice. PWN. Warszawa; 1997.

Flanagan E. The Reactive Strength Index Revisited. (https://www.trainwithpush.com/blog/reactive-strength-index-revisited. 26.12. 2016).

Flanagan, E.P. and Comyns, T.M., 2008. The use of contact time and the reactive strength index to optimize fast stretch-shortening cycle training. Strength & Conditioning Journal, 30(5), 32-38.

Good PI, Hardin JW. Common errors in statistics (and how to avoid them). John Wiley & Sons; 2012.

Jankowicz-Szymańska A, Wojtanowski W, Chronowski M, Ridan T. Porównanie motoryczności dzieci pełnosprawnych, niesłyszących i niepełnosprawnych intelektualnie w stopniu lekkim. Instytut Rozwoju Służb Społecznych. 2011.

Jankowska D, Majka A. Zastosowanie alternatywnych metod rozstrzygania o istnieniu różnic pomiędzy średnimi w badaniach rolniczych. Annales Universitatis Mariae Curie-Skłodowska. Sectio E, Agricultura. 2009; 64(3), 50-57.

Keppel G, Wickens TD. Design and Analysis: A researcher’s handbook. Upper Saddle River, NJ: Pearson Prentice Hall. 2004.

Lindman HR. Analysis of variance in complex experimental designs. WH Freeman & Co. 1974.

Lindman HR. Analysis of variance in experimental design. Springer, New York. 1991.

Łopatka M, Guzik-Kopyto A, Michnik R, Rycerski W. Badania antropometryczne kończyny górnej oraz pomiar siły ścisku dłoni i kciuka. Aktualne Problemy Biomechaniki. 2012.

McGill R, Tukey JW, Larsen WA. Variations of box plots. The American Statistician, 1978, 32.1: 12-16.

Michnik R, Jurkojć J, Czapla K. Biomechaniczna ocena zdolności siłowych siatkarek. Modelowanie Inżynierskie. 2012; 13(44), 217-222.

Moder K. Alternatives to F-test in one way ANOVA in case of heterogeneity of variances (a simulation study). Psychological Test and Assessment Modeling. 2010; 52(4), 343-353.

Reinhart A. Statistics Done Wrong: The Woefully Complete Guide. No Starch Press. 2015.

Scariano SM, Davenport JM. The effects of violations of independence assumptions in the one-way ANOVA. The American Statistician. 1987; 41(2), 123-129.

Sheskin DJ. Handbook of parametric and nonparametric statistical procedures. crc Press, 2003.

Sobczyk M. Statystyka. Wydawnictwo Naukowe PWN. 1996.

Sokołowski A. O niewłaściwym stosowaniu metod statystycznych. Materiały szkoleniowe. StatSoft Polska [online], 2004.

Stanisz A. Podstawy statystyki dla prowadzących badania naukowe. Odcinek 10: Testy istotności różnic dla prób zależnych. Medycyna Praktyczna. 1999, 7-8: 207-209.

Stanisz A. Przystępny kurs statystyki: z zastosowaniem STATISTICA PL na przykładach z medycyny. Statystyki podstawowe. StatSoft, 2006.

Stanisz A. Przystępny kurs statystyki z zastosowaniem STATISTICA PL na przykładach z medycyny: Modele liniowe i nieliniowe. StatSoft, 2007.

StatSoft, Inc. (2014). STATISTICA (data analysis software system), version 12. www.statsoft.com.

Szreder M. O weryfikacji i falsyfikacji hipotez. Przegląd Statystyczny, 2010, 57.2-3: 82-88.

Szulc A. Biofizyczne i środowiskowe podstawy analizy składu ciała metodą BIA. Journal of Health Sciences - 2013, Vol. 3 (13), 410-427

Walesiak M. Strategie postępowania w badaniach statystycznych w przypadku zbioru zmiennych mierzonych na skalach różnego typu. 1993.

Watała C, Różalski M, Boncler M, Kaźmierczak P. Badania i publikacje w naukach biomedycznych: tom 1. Planowanie i prowadzenie badań, tom 2. Przygotowywanie publikacji; alfa-Medica Press, Bielsko-Biała. 2011.

Watała C, Zakład Zaburzeń Krzepnięcia Krwi KDL. Jak skutecznie wykorzystywać metody statystyczne w planowaniu i przeprowadzaniu eksperymentu naukowego? Statystyka i data mining w badaniach naukowych, StatSoft, Warszawa. 2005.

Wieczorek M. Rozwój fizyczny i sprawność fizyczna dzieci głuchych jako pozytywny miernik ich zdrowia fizycznego. Prob. Hig. Epidemiol. 2011; 92(2), 304-310.




DOI: http://dx.doi.org/10.5281/zenodo.293761

Refbacks

  • There are currently no refbacks.




Copyright (c) 2016 © The Author (s)

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Journal of Education, Health and Sport formerly Journal of Health Sciences

Declaration on the original version.

Editors indicates that the main version of the magazine is to issue a "electronic".

The journal has had 5 points in Ministry of Science and Higher Education parametric evaluation. § 8. 2) and § 12. 1. 2) 22.02.2019.

1223 Journal of Education, Health and Sport eISSN 2391-8306 7

ISSN 2391-8306 formerly ISSN: 1429-9623 / 2300-665X

Archives 2011 - 2014

PBN 2011 - 2014

https://pbn.nauka.gov.pl/sedno-webapp/search?search&searchCategory=WORK&filter.inJournal=36616

POL-index 2011 - 2014

https://pbn.nauka.gov.pl/polindex-webapp/browse/journal/journal-32a319c5-a850-4f44-ba70-1418a6087655

BASE 2011 - 2014

https://www.base-search.net/Search/Results?lookfor=Journal+of+Health+Sciences+%28Radom%29&type=all&oaboost=1&ling=1&name=&thes=&refid=dcrespl&newsearch=1

http://elibrary.ru/contents.asp?titleid=37467

http://journal.rsw.edu.pl/index.php/JHS/issue/archive

Indexed in Bases, Bazy indeksacyjne: ERIH Plus, Worldcat, PBN/POL-Index, ICI Journals Master List, Directory of Open Access Journals (DOAJ), ZBD, Ulrich's periodicals, Google Scholar, Polska Bibliografia Lekarska

US NLM = 101679844

101679844 - NLM Catalog Result - NCBI

https://www.ncbi.nlm.nih.gov/nlmcatalog/101679844

Find a library that holds this journal: http://worldcat.org/issn/23918306

Journal Language(s): English 

PBN Poland

https://pbn.nauka.gov.pl/sedno-webapp/journals/49068

POL-index

https://pbn.nauka.gov.pl/polindex-webapp/browse/journal/journal-c39c8169-88d2-45db-9e7f-d948ce9981c4

BASE

https://www.base-search.net/Search/Results?join=AND&bool0[]=AND&lookfor0[]=2391-8306&type0[]=all&page=11&l=pl&oaboost=1&refid=dcpagepl

Redaction, Publisher and Editorial Office

Instytut Kultury Fizycznej Uniwersytet Kazimierza Wielkiego w Bydgoszczy, Institute of Physical Education Kazimierz Wielki University in Bydgoszcz, Poland 85-091 Bydgoszcz ul. Sportowa 2  www.ukw.edu.pl Copyright by Instytut Kultury Fizycznej UKW w Bydgoszczy http://ojs.ukw.edu.pl/index.php/johs  Open Access ISSN 2391-8306 formerly ISSN: 1429-9623 / 2300-665X

The journal has been approved for inclusion in ERIH PLUS.

The ERIH PLUS listing of the journal is available at https://dbh.nsd.uib.no/publiseringskanaler/erihplus/periodical/info?id=485984

SIC Science citation index (calculated on the basis of TCI and Page Rank) 0

Russian Impact factor 0.16

Indexed in Index Copernicus Journals Master List.

http://journals.indexcopernicus.com/Journal+of+Education+Health+and+Sport,p24782242,3.html

ICV 2018 = 95.95 ICV 2017 = 91.30 ICV 2016 = 84.69 ICV 2015 = 93.34 ICV 2014 = 89.51 Standardized Value: 8.27 ICV 2013: 7.32 ICV 2012: 6.41 ICV 20115.48

The InfoBase Index IBI Factor for the year 2015 is 3.56 in InfoBase Index.com.

Website: www.infobaseindex.com

Universal Impact Factor 1.78 for year 2012. (http://www.uifactor.org/AppliedJournals.aspx)

Indexed in Polish Scholarly Bibliography (PBN) (PBN Polska Bibliografia Naukowa) (https://pbn.nauka.gov.pl/journals/36616)

is a portal of the Polish Ministry of Science and Higher Education, collecting information on publications of Polish scientists and on Polish and foreign scholarly journals. Polish Scholarly Bibliograhpy is a part of POL-on - System of Information on Higher Education. It is operated by the Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw.

Indexed in Russian Sciences Index Российский индекс научного цитирования (РИНЦ) http://elibrary.ru/contents.asp?titleid=37467

Indexed in Arianta Polish scientific and professional electronic journals Aneta Drabek i Arkadiusz Pulikowski

(http://www1.bg.us.edu.pl/bazy/czasopisma/czasop_full.asp?id=3595)