Nonparametric Statistics

Nonparametric Statistics 

Use: When data violates assumptions of parametric tests. Data transformations do not solve problems. Analyses are performed on the ranks of the data (not original or raw data). 

Nonparametric alternatives: 

Mann-Whitney U test: 

Used instead of Two Independent Sample Student’s t-test 

Wilcoxon signed rank: (paired samples or matched pairs) test: 

Used instead of Two Dependent Sample Student’s t test 

Kuruksal- Wallis H test: 

Used instead of ANOVA 

Data Problems and Transformations

Data Problems and Transformations: 

Use: When data violates assumptions of parametric tests. It is used to correct violations. It involves transforming original variables into new variables. There are three main types for different types of data and problems. 

Types: 

Logarithmic (log 10) transformations 

Conditions: 

·     Standard Deviations are proportional to the mean 

·     Controlled variables are constant and equal 

·     Means are positively correlated with the variance 

·     Standard Deviation increases with increasing size of measurement. 

·     Variances are not equal (heterogeneity of variances) 

·     Data is positively skewed 

Types: 

Square Root Transformations 

Conditions: 

·     Data is likely to confirm to a Poisson (non-normal) distribution 

·     Count (integer) data 

·     Mean is positively correlated with the variance 

·     Variance increases with increasing mean 

Types: 

Arcsine transformations 

Conditions: 

·     Data are percentages or proportions 

·     Data tend to fit a binomial distribution