The Derivation and Choice of Appropriate Test Statistic (Z, t, F and Chi-Square Test) in Research Methodology
Mathematics Letters
Volume 5, Issue 3, September 2019, Pages: 33-40
Received: Apr. 18, 2019; Accepted: Jul. 16, 2019; Published: Jan. 7, 2020
Views 484      Downloads 282
Teshome Hailemeskel Abebe, Department of Economics, Ambo University, Ambo, Ethiopia
Article Tools
Follow on us
The main objective of this paper is to choose an appropriate test statistic for research methodology. Specifically, this article tries to explore the concept of statistical hypothesis test, derivation of the test statistic and its role on research methodology. It also try to show the basic formulating and testing of hypothesis using test statistic since choosing appropriate test statistic is the most important tool of research. To test a hypothesis various statistical test like Z-test, Student’s t-test, F test (like ANOVA), Chi square test were identified. In testing the mean of a population or comparing the means from two continuous populations, the z-test and t-test were used, while the F test is used for comparing more than two means and equality of variance. The chi-square test was used for testing independence, goodness of fit and population variance of single sample in categorical data. Therefore, choosing an appropriate test statistic gives valid results about hypothesis testing.
Test Statistic, Z-test, Student’s t-test, F Test (Like ANOVA), Chi Square Test, Research Methodology
To cite this article
Teshome Hailemeskel Abebe, The Derivation and Choice of Appropriate Test Statistic (Z, t, F and Chi-Square Test) in Research Methodology, Mathematics Letters. Vol. 5, No. 3, 2019, pp. 33-40. doi: 10.11648/
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Alena Košťálová. (2013). Proceedings of the 10th International Conference “Reliability and Statistics in Transportation and Communication” (RelStat’10), 20–23 October 2010, Riga, Latvia, p. 163-171. ISBN 978-9984-818-34-4 Transport and Telecommunication Institute, Lomonosova 1, LV-1019, Riga, Latvia.
Banda Gerald. (2018). A Brief Review of Independent, Dependent and One Sample t-test. International Journal of Applied Mathematics and Theoretical Physics. 4 (2), pp. 50-54. doi: 10.11648/j.ijamtp.20180402.13.
David, J. Pittenger. (2001). Hypothesis Testing as a Moral Choice. Ethics & Behavior, 11 (2), 151-162, DOI: 10.1207/S15327019EB1102_3.
DOWNWARD, L. B., LUKENS, W. W. & BRIDGES, F. (2006). A Variation of the F-test for Determining Statistical Relevance of Particular Parameters in EXAFS Fits. 13th International Conference on X-ray Absorption Fine Structure, 129-131.
J. P. Verma. (2013). Data Analysis in Management with SPSS Software, DOI 10.1007/978-81-322-0786-3_7, Springer, India.
Joginder Kaur. (2013). Techniques Used in Hypothesis Testing in Research Methodology A Review. International Journal of Science and Research (IJSR) ISSN (Online): 2319-7064 Index Copernicus Value: 6.14 | Impact Factor: 4.438.
Kousar, J. B. and Azeez Ahmed. (2015). The Importance of Statistical Tools in Research Work. International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Volume 3, Issue 12, PP 50-58 ISSN 2347-307X (Print) & ISSN 2347-3142 (Online).
Liang, J. (2011). Testing the Mean for Business Data: Should One Use the Z-Test, T-Test, F-Test, The Chi-Square Test, Or The P-Value Method? Journal of College Teaching and Learning, 3 (7), doi: 10.19030/tlc.v3i7.1704.
LING, M. (2009b). Compendium of Distributions: Beta, Binomial, Chi-Square, F, Gamma, Geometric, Poisson, Student's t, and Uniform. The Python Papers Source Codes 1:4.
MCDONALD, J. H. (2008). Handbook of Biological Statistics. Baltimore, Sparky House Publishing.
Pallant, J. (2007). SPSS Survival Manual: A Step by Step to Data Analysis Using SPSS for Windows (Version 15). Sydney: Allen and Unwin.
Pearson, K. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables that arisen from random sampling. Philos. Mag. 1900, 50, 157-175. Reprinted in K. Pearson (1956), pp. 339-357.
Philip, E. Crewson.(2014). Applied Statistics, First Edition. United States Department of Justice.
Sorana, D. B., Lorentz, J., Adriana, F. S., Radu, E. S. and Doru, C. P. (2011). Pearson-Fisher Chi-Square Statistic Revisited. Journal of Information; 2, 528-545; doi: 10.3390/info2030528; ISSN 2078-2489,
Sureiman Onchiri.(2013). Conceptual model on application of chi-square test in education and social sciences. Academic Journals, Educational Research and Reviews; 8 (15); 1231-1241; DOI: 10.5897/ERR11.0305; ISSN 1990-3839.
Tae Kyun Kim. (2015). T test as a parametric statistic. Korean Society of Anesthesiologists. pISSN 2005-6419, eISSN 2005-7563.
Vinay Pandit. (2015). A Study on Statistical Z Test to Analyses Behavioral Finance Using Psychological Theories, Journal of Research in Applied Mathematics Volume 2~ Issue 1, pp: 01-07 ISSN (Online), 2394-0743 ISSN (Print): 2394-0735.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186