Non-Parametric Statistical Tests PDF

StatisticalWorkshop Series 2023 Workshop 4: Non-Parametric Statistical Tests Dr. Arass J. Noori Goals Data Normality Statistics Scale of Variables Distributions Test selection  A collective recording of observations...

StatisticalWorkshop Series 2023 Workshop 4: Non-Parametric Statistical Tests Dr. Arass J. Noori Goals Data Normality Statistics Scale of Variables Distributions Test selection  A collective recording of observations either numerical or categorical is called data. It is classified into: 1. Qualitative data: when data is collected on the basis of attributes like sex, malocclusion, color, etc. (Nominal and Ordinal) Data 2. Quantitative data: when the data is collected through measurement using calipers like arch length, arch width, fluoride concentration in water supply. a. Discrete: when the variable under observation take only fixed value like whole numbers as DMF. (1, 4, 5, 77, 102, …etc) b. Continuous: if the variable can take any value in a given range decimal or fractional like arch length, mesiodistal width of the erupted tooth surface. (1.33, 34.6, 11.11 … etc). Scale of measures The Normal distribution (The Gaussian distribution) Normality tests: Many statistical tests -including ANOVA, t-tests and regression- require the normality assumption: variables must be normally 1. Statistical - Kolmogrov-Smirnov test distributed in the population. Where to do - Shapiro-wilk test normality 2. Graphical tests ? - Q-Q probability plots - box plots Before doing parametric tests on continuous data. What are Nonparametric Tests? In statistics, nonparametric tests are methods of statistical analysis that do not require a distribution to meet the required assumptions to be analyzed (especially if the data is not normally distributed). Due to this reason, they are sometimes referred to as distribution-free tests. Non-Parametric Parametric  History ▪ John Arbuthnot, a Scottish mathematician and physician, was the first to introduce nonparametric analytical methods in 1710. He performed a statistical analysis similar to the sign test. ▪ Nonparametric analysis was not used for a while after that paper, until Jacob Wolfowitz used the term “nonparametric” again in 1942. ▪ Then, in 1945, Frank Wilcoxon introduced a nonparametric analysis method using rank, which is the most commonly used method today. In 1947, Henry Mann and his student Donald Ransom Whitney expanded on Wilcoxon’s technique to develop a technique for comparing two groups of different number of samples. In 1951, William Kruskal and Allen Wallis introduced a nonparametric test method to compare three or more groups using rank data. Non-parametric Test Methods The non-parametric tests are completely based on the ranks, which are assigned to the ordered data. Click on Transform > Rank Cases... in the top menu Ranking Data Applications of Non-Parametric Test When parametric tests are not satisfied. When testing the hypothesis, data does not have any distribution. For quick data analysis. When unscaled data is available. Advantages and Disadvantages of Non-Parametric Test Easily understandable Short calculations Assumption of distribution is not required Applicable to all types of data The disadvantages of the non-parametric test are: Less efficient as compared to parametric test The results may or may not provide an accurate answer because they are distribution free Parametric and Non-parametric tests Chi-square test Chi-square is a statistical test that examines the differences between categorical variables from a random sample in order to determine whether the expected and observed results are well-fitting. Sign Test The sign test is used to compare the continuous outcome in the paired samples or the two matches samples. Null hypothesis, H0: Median difference should be zero Decision Rule: Reject the null hypothesis if the smaller of number of the positive or the negative signs are less than or equal to the critical value from the table. Wilcoxon Signed-Rank Test Wilcoxon signed-rank test is used to compare the continuous outcome in the two matched samples or the paired samples. Null hypothesis, H0: Median difference should be zero. Decision Rule: Reject the null hypothesis if the test statistic, W is less than or equal to the critical value from the table. Mann Whitney U Test Mann Whitney U test is used to compare the continuous outcomes in the two independent samples. Null hypothesis, H0: The two populations should be equal. Decision Rule: Reject the null hypothesis if the test statistic, U is less than or equal to critical value from the table. Kruskal Wallis Test Kruskal Wallis test is used to compare the continuous outcome in greater than two independent samples. Null hypothesis, H0: K Population medians are equal. Decision Rule: Reject the null hypothesis H0 if H ≥ critical value Spearman's correlation In statistics, Spearman's rank correlation coefficient or Spearman's ρ(rho), named after Charles Spearman and often denoted by the letter rs, is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables). It assesses how well the relationship between two variables can be described using a monotonic function. Chi-square test Without With trauma Age trauma Gender Total X2 groups No. No. Male 1890 150 2040 X2= 12.338 d.f= 1 Total Female 1882 93 1975 P