Non-Parametric Test (2023) PDF

By: Dr. Hanif Farhan Mohd Rasdi  Normal distribution is the bell-shaped distribution that describes how so many natural, machine-made, or human performance outcomes are distributed.  Parameter = population characteristics  Statistics = sample characteristics ...

By: Dr. Hanif Farhan Mohd Rasdi  Normal distribution is the bell-shaped distribution that describes how so many natural, machine-made, or human performance outcomes are distributed.  Parameter = population characteristics  Statistics = sample characteristics  mean mean Inference population sample mean Inference? sample population https://andymath.com/parameter-vs-statistic/  Parameters i.e., μ (population mean) and σ2 (population variance) are usually unknown.  Therefore, the mean & variance are then estimated using the sample mean and sample variance.  This method requires normal distribution to fit the distribution of the population.  What happens if the data are not normally distributed?  Non-parametric test!  Distribution-free tests: ◦ statistical tests that do not rely on the probability distribution of the sampled population.  Rank tests. ◦ Nonparametric tests that are based on the ranks of measurements Raw exam marks Ordering Rank (N=13) 35 31 1 43 35 2 48 38 3.5 (Corrected for ties) 31 38 3.5 (Corrected for ties) 38 39 5 42 40 6 50 41 7 41 42 8 62 43 9 38 48 10 54 50 11 39 54 12 40 62 13  Exam marks Exam marks Rank Rank (group A: n=6) (group B: n=7) 35 2 50 11 43 9 41 7 48 10 62 13 3.5 (corrected 31 1 38 for ties) 3.5 (corrected 38 for ties) 54 12 42 8 39 5 40 6 Sum A 33.5 Sum B 57.5 Mean rank A 33.5/6 = 5.58 Mean rank B 57.5/7 =8.21  Advantage ◦ Fewer assumptions ◦ Use median (stable measure for skewed distribution) ◦ Valid when data are non-normal ◦ Can analyze ordinal data, ranked data, and outliers  Disadvantage ◦ May waste information (original vs. ranked data) ◦ Less statistical power compared to parametric test ◦ Table for critical values is not commonly available Parametric Test Non Parametric test One Sample Wilcoxon Signed Rank One Sample t test test Mann Whitney U test (also called Independent t test Wilcoxon Rank Sum test) Paired Sample Wilcoxon Signed Rank Paired t test test One Way Independent ANOVA Kruskal Wallis H test One Way Repeated Measures Friedman’s test ANOVA Spearman rho (another option is Pearson Correlation Kendall’s tau)  Option A Option B (legacy of older versions)  ONE SAMPLE WILCOXON SIGNED RANK TEST  Non-parametric equivalent to one-sample t test.  Aim: To compare median/average rank with a specified value.  Assumptions: 1. Independence 2. Scale of measurement: at least ordinal  Store Songket sold Store Songket sold 1 302 11 352 2 321 12 323 3 309 13 321 4 352 14 307 5 302 15 322 6 307 16 323 7 322 17 314 8 298 18 302 9 307 19 309 10 307 20 314 Tests of Normality Kolmogorov-Smirnov Shapiro-Wilk Statistic df Sig. Statistic df Sig. Songket.211 20.020.828 20.002 Sold Move ‘Songket Sold’ into Test Field  1 2 3 z=3.927, p20, report U & z (standardized test score) U=185.50, z = -2.55, p < 0.05 KRUSKAL WALLIS H TEST  Non-parametric equivalent to one-way independent ANOVA  Compare three or more independent samples of: ◦ ordinal (ranked) data (or) ◦ continuous (interval/ratio) data with non-normal distribution  Assumptions: 1. Independence 2. Scale of measurement: at least ordinal  EXCELLENT POOR CONTROL ID GRADE ID GRADE ID GRADE 1 2 11 4 21 5 2 1 12 3 22 1 1= A 3 2 13 3 23 3 2= B 4 3 14 5 24 3 3= C 4= D 5 2 15 5 25 1 5= E 6 3 16 2 26 2 7 3 17 2 27 4 8 1 18 3 28 4 9 1 19 4 29 2 10 3 20 4 30 3  Dependent variable (i.e. grade) Independent variable (i.e. condition)  1 2 3 H= 6.518, p