What is Statistics

Definition

Statistics is a branch of Mathematics that deals with data. It may be pure Mathematics, probability, or applied Mathematics in which case it is used to organize data (Descriptive Statistics) or make predictions as to the occurrence of an event (Inferential Statistics).

Descriptive Statistics

Descriptive Statistics employs methods and simple arithmetic that allows us to organize our data, for example making graphs or calculating an average.

Inferential Statistics

Inferential Statistics uses methods and more complex mathematical calculations that allow us to make inferences, predictions. Examples of inferential statistics are statistical tests like the t-test or Analysis of Variance (ANOVA).

In several fields, including experimental science, prediction take the form of a probability statement regarding the occurrence of a chance event, the chance event being the finding of an experiment. If the probability of that the finding or result of research is a chance event, and not the result of the experimental manipulation is small, then we conclude that the finding of our research is reliable, i.e. it is significant.

Statistics may be further categorized into Parametric and Non-parametric

Parametric Statistics

Parametric tests are chosen to analyze data in those instances in which we know that the characteristic we are measuring is normally distributed in the population (for example nose length) and our measurement is ratio scale of measurement or interval scale of measurement. Read the print book. Examples of parametric tests are the t-test and analysis of variance

Non-parametric Statistics

We choose non-parametric tests when our data are at the nominal scale of measurement or ordinal scale of measurement.

A list of non-parametric tests

chi-square test
sign test
Wilcoxon Signed Rank test
Friedman test
Kruskal-Wallis test
Mann-Whitney test
Mood’s Median test
Spearman Rank Correlation