# A introduction to non-parametric tests

Assistant Professor, Community Medicine um Velammal Hospitals
25. Nov 2019
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### A introduction to non-parametric tests

• 1. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Non-parametric tests An introduction Dr. S. A. Rizwan, M.D., Public Health Specialist, Saudi Board of Preventive Medicine, Riyadh, Kingdom of Saudi Arabia. 1Nov 2019
• 2. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Outline • Some common terms • Difference between parametric and nonparametric tests • When to use NPT • Advantages & disadvantages • Commonly used NPT • Take home messages 2Nov 2019
• 3. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Introduction • Parametric methods – They are based in means, standard deviations or parameters of distributions • The Normal distribution is not always appropriate – To study variables with a few observations – Non-symmetrical distributions 3Nov 2019
• 4. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Parametric & nonparametric concept • Most of the statistical methods referred to as parametric require the use of interval- or ratio-scaled data. • Nonparametric methods are often the only way to analyze nominal or ordinal data and draw statistical conclusions. • Nonparametric methods require no assumptions about the population probability distributions. • Nonparametric methods are often called distribution-free methods. 4Nov 2019
• 5. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Parametric test procedures • Involve population parameters (mean) • Have stringent assumptions (normality) • Examples: Z test, t test 5Nov 2019
• 6. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Nonparametric test procedures • Do not involve population parameters • Data measured on any scale (ratio or interval, ordinal or nominal) • Example: Wilcoxon rank sum test 6Nov 2019
• 7. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Assumptions of t test • The sampling distribution is normally distributed – For N <30 if the sample data is normally distributed then the sampling distribution will also be normal • The data should come from an interval or ratio scale • In practice an ordinal scale with 5 or more levels is ok 7Nov 2019
• 8. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Examples of nonnormal distributions 8Nov 2019
• 9. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Assumptions of t test (contd.) • There should not be extreme scores or outliers, because these have a disproportionate influence on the mean and the variance • For the independent samples t test the variance in the two samples should be approximately equal – This assumption is more important if sample size < 30 and / or sample sizes are unequal – As a rule of thumb, if the variance of one group is 3 or more times greater than the variance of the other group, then use non-parametric 9Nov 2019
• 10. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What are nonparametric tests? • ‘Non-parametric’ tests were developed for these situations where fewer assumptions have to be made. • Sometimes called distribution-free tests. • NP tests can be applied to Normal data but parametric tests have greater power if assumptions are met. 10Nov 2019
• 11. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course How to check for normality of data? 1. Thumb rules a) Mean & Range & SD b) Skewness and kurtosis c) Compare mean, median & mode d) Trimmed mean e) Outliers 2. Graphs a) Histogram with theoretical normal curve b) QQ plot c) Box plot and outlier detection d) Stem and leaf plot 3. Formal statistical tests a) W/S test b) Jarque-Bera test c) Shapiro-Wilks test d) Kolmogorov-Smirnov test e) D’Agostino test f) Grubbs and Dixon test (for outliers) 4. Comparing non-parametric and parametric test results 11Nov 2019
• 12. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Distribution-free tests • Distribution-free tests are statistical tests that do not rely on any underlying assumptions about the probability distribution of the sampled population. • The branch of inferential statistics devoted to distribution-free tests is called nonparametrics. • Nonparametric statistics (or tests) based on the ranks of measurements are called rank statistics (or rank tests). 12Nov 2019
• 13. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Ranks • Practical differences between parametric and NP are that NP methods use the ranks of values rather than the actual values • E.g. – 1,2,3,4,5,7,13,22,38,45 - actual – 1,2,3,4,5,6,7,8,9,10 - rank 13Nov 2019
• 14. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Rules for NPT • In general, for a statistical method to be classified as nonparametric, it must satisfy at least one of the following conditions. – The method can be used with nominal data. – The method can be used with ordinal data. – The method can be used with interval or ratio data when no assumption can be made about the population probability distribution. 14Nov 2019
• 15. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Parametric / Nonparametric tests Parametric Tests Non-parametric Tests Single sample t-test Wilcoxon-signed rank test Paired sample t-test Paired Wilcoxon-signed rank 2 independent samples t-test Mann-Whitney test (Wilcoxon Rank Sum) One-way Analysis of Variance Kruskal-Wallis Pearson’s correlation Spearman Rank Repeated Measures Friedman … many more … many more 15Nov 2019
• 16. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Types of NPT 16Nov 2019
• 17. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Advantages of nonparametric tests • Used with all scales • Easier to compute, developed originally before wide computer use • Make fewer assumptions • Need not involve population parameters • Results may be as exact as parametric procedures 17Nov 2019
• 18. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Disadvantages of nonparametric tests • May waste information – Parametric model more efficient if data permit • Difficult to compute by hand for large samples • Tables not widely available • Used only to test hypotheses, not for estimation purposes 18Nov 2019
• 19. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Limitations of nonparametric methods • Converting ratio level data to ordinal ranked data entails a loss of information • This reduces the sensitivity of the non-parametric test compared to the parametric alternative in most circumstances – sensitivity is the power to reject the null hypothesis, given that it is false in the population – lower sensitivity gives a higher type 2 error rate • Many parametric tests have no non-parametric equivalent – e.g. Two way ANOVA, where two IV’s and their interaction are considered simultaneously 19Nov 2019
• 20. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Take home messages • Fewer assumptions than parametric tests • So useful when these assumptions not met • Often used when sample size is small and difficult to tell if normally distributed • Ragbag of tests developed over time with no consistent framework 20Nov 2019
• 21. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course THANK YOU Kindly email your queries to sarizwan1986@outlook.com 21Nov 2019