Assumptions of statistical tests

assumption-dataData analysis basically entails three key approaches: Parametric, non-parametric and resampling technique. Parametric statistical testing is pivoted around certain assumptions which must be fulfilled by data under analysis. Failure of data to meet these assumptions can compromise with reliability and validity of parametric test results.

However, non-parametric tests are assumption free and can be applied in situations where assumptions of parametric tests are grossly violated. The garden variety assumption underpinning most parametric tests is normality (or Gaussian) distribution of outcome data. There are myriad of ways and methods to test this assumption including Shapiro Wilks tests, Kolmogorov Smirnov test and quantile-quantile (Q-Q) plot. Normal distribution of residues (observed minus predicted value) is also vital assumption in most linear regression models. Violation of underlying assumptions in a given parametric test is likely to produce less robust and reproducible results.