Parametric test for non-normally distributed continuous data: For and against
Keywords:
Biostatistics, Data analyses, Non-parametric statistics, Normal distributionAbstract
Choosing between parametric and non-parametric statistical tests for analysis of non-normally distributed continuous data is a long-standing controversy. Conventionally, it is recommended to use non-parametric tests but few others suggest using the parametric test. This article evaluates the simulation studies comparing the parametric tests with non-parametric tests in analysing the non-normally distributed continuous data. Non-parametric tests are recommended only when data is highly skewed and log transformation technique cannot change it to normal distribution. However, in most other situations parametric tests are more powerful in analysing non-normally distributed continuous data.
References
Fagerland MW. t-tests, non-parametric tests, and large studies--a paradox of statistical practice? BMC MedRes Methodol. 2012 Jun 14;12:78. PubMed PMID: 22697476. PMCid: PMC3445820. DOI: 10.1186/1471-2288-12-782)Vickers AJ. Parametric versus non-parametric statistics in the analysis of randomized trials with non-normally distributed data. BMC Med Res Methodol. 2005 Nov 3;5:35. PubMed PMID: 16269081, PMCid:PMC1310536, DOI: 10.1186/1471-2288-5-353)Blair RC, Higgins JJ. A Comparison of the Power of Wilcoxon’s Rank-Sum Statistic to That of Student’s tStatistic under Various Nonnormal Distributions. J Educ Stat. 1980. 5[4]:309-335. DOI:10.3102/107699860050043094)Blair RC, Higgins JJ. Comparison of the Power of the Paired Samples T test to that of Wilcoxon’s Signed-Ranks Test Under Various Population Shapes. Psychol Bull. 1985. 97[1]:119-28. DOI: 10.1037/0033-2909.97.1.1195)Fay MP, Proschan MA. Wilcoxon-Mann-Whitney or t-test? On assumptionsfor hypothesis tests andmultiple interpretations of decision rules. Stat Surv. 2010;4:1-39. PMid: 20414472,PMCid: PMC2857732.DOI: 10.1214/09-SS0516)Sawilowsky SS, Hillman SB. Power of the independent samples t test under a prevalent psychometricmeasuredistribution. J Consult Clin Psychol. 1992 Apr;60[2]:240-3. PMID: 1592953. DOI: 10.1037/0022-006X.60.2.2407)Sawilowsky SS, Blair RC. A more realistic look at the robustness and Type II error properties of the t testto departures from population normality.Psychol Bull. 1992;111[2]:352-360. DOI: 10.1037/0033-2909.111.2.3528)Wadgave U, Khairnar MR. Parametric tests for Likert scale: For and against. Asian J Psychiatr.2016;24:67-68. PMID: 279319119)Ghasemi A, Zahediasl S. Normality tests for statistical analysis: A guide for non-statisticians. Int JEndocrinol Metab. 2012. 10[2]: 486–489. PMID: 23843808, PMCid: PMC3693611, DOI:10.5812/ijem.350510)Öztuna D, Elhan AH, Tüccar E. Investigation of four different normality tests in terms of type 1 error rateand powerunder different distributions. Turkish J Med Sci. 2006. 36 [3]: 171-176.11)Razali NM, Wah YB. Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors, andAnderson-Darling tests. J Stat Model Anal. 2011. 2:21-33.12)Skovlund E, Fenstad GU. Should wealways choose a nonparametric test when comparing two apparentlynonnormal distributions? J Clin Epidemiol. 2001 Jan;54[1]:86-92. PMID: 11165471, DOI: 10.1016/S0895-4356(00)00264-X13)Zimmerman DW. Invalidation of parametric and nonparametric statistical tests by concurrent violation oftwo assumptions. J Exp Educ. 1998. 67[1]:55-68. DOI: 10.1080/0022097980959834414)Zimmerman DW, Zumbo BD. Parametric Alternatives to the Student T Test under Violation of Normalityand Homogeneity of Variance. Percept Mot Skills.1992;74[3]:835. DOI: 10.2466/pms.1992.74.3.83515)Fagerland MW, Sandvik L, Mowinckel P. Parametric methods outperformed non-parametric methods incomparisons of discrete numerical variables. BMC Med Res Methodol. 2011 Apr 13;11:44. DOI:10.1186/1471-2288-11-4416)Bland JM, Altman DG. Statistics Notes: Analysis of continuous data from small samples. BMJ. 2009.338:a3166. DOI: 10.1136/bmj.a3166
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