To be parametric or non-parametric, that is the question: Parametric and non-parametric statistical tests

Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...

Nonparametric statistics offer a powerful alternative to traditional parametric methods, useful when assumptions about the population distribution cannot be made. Unlike parametric tests, which require data to follow a specific distribution with well-defined parameters (such as the mean and standard deviation), nonparametric tests do not require such constraints. This makes them particularly valuable when dealing with small sample sizes, skewed data, or ordinal and categorical variables.
One of...

In parametric statistics, two fundamental tests stand out for their utility and wide application: the Student's t-test and goodness-of-fit tests. These tests provide researchers with a robust method for drawing insights from data, testing hypotheses, and making informed decisions based on their findings.
The Student's t-test is a statistical test that examines if there is a statistically significant difference between the means of two groups. This test is instrumental when dealing with...

Analysis of Variance, or ANOVA, is a powerful statistical technique used to analyze parametric data, primarily in research and experimental studies. It's designed to compare the means of two or more groups, assisting researchers in identifying any significant differences between these group means. There are two main types of ANOVA based on the complexity of the analysis: one-way and two-way.
One-way ANOVA is applied when a single independent variable or factor is scrutinized. It compares...

The Anderson-Darling test is a statistical method used to determine whether a data sample is likely drawn from a specific theoretical distribution. Unlike parametric tests, it does not require assumptions about specific parameters of the distribution. Instead, it compares the sample's empirical cumulative distribution function (ECDF) with the cumulative distribution function (CDF) of the hypothesized distribution. Critical values for the test are specific to the chosen distribution rather...

The Kruskal-Wallis test, also known as the Kruskal-Wallis H test, serves as a nonparametric alternative to the one-way ANOVA, offering a solution for analyzing the differences across three or more independent groups based on a single, ordinal-dependent variable. This statistical test is particularly valuable in scenarios where the data does not meet the normal distribution assumption required by its parametric counterparts. Kruskal-Wallis test is designed typically to handle ordinal data or...