Statistical Methods - A Overview

Statistics is the branch of mathematics concerned with collection, classification, analysis, and interpretation of numerical facts, for drawing inferences on the basis of their quantifiable likelihood (probability). Statistics can interpret aggregates of data too large to be intelligible by ordinary observation because such data unlike individual quantities tend to behave in regular, predictable manner. It is subdivided into descriptive statistics and inferential statistics. Statistical Procedures can be divided into two major categories: Applied Statistics and Theoretical Statistics.

Applied Statistics compromise both Descriptive statistics and the application of inferential statistics (a.k.a., predictive statistics)

Theoretical statistics concerns both the logical arguments underlying justification of approaches to statistical inference, as well encompassing mathematical statistics.

Before going into the details we must be familiar with two important concepts: Population and Sample. A population is the total set of individuals, groups, objects, or events that the researcher is studying. A sample is a relatively small subset of people, objects, groups, or events, that is selected from the population. In short a subset of the population is called sample. It is a proportion of the population, a slice of it, a part of it and all its characteristics. A sample is a scientifically drawn group that actually possesses the same characteristics as the population – if it is drawn randomly.(This may be hard for you to believe, but it is true!) .

Example: Like if you are cooking a pot of soup(population), and you take a spoon full(sample) to see how it tastes. So although you didn't eat the entire pot of soup, you have a general idea of how it tastes

Descriptive Statistics

Descriptive statistics includes statistical procedures that we use to describe the population we are studying. The data could be collected from either a sample or a population, but the results help us organize and describe data. Descriptive statistics can only be used to describe the group that is being studying. That is, the results cannot be generalized to any larger group. This is the statistical method that is used for summarizing or describing a collection of data.
Examples: Frequency distribution, Measures of central tendencies (mean, median, mode) and graphs like pie charts and bar charts that describes the data.

Inferential Statistics

This is the branch of statistics that is used to make inferences or predictions about the characteristics of a population based on analysis and observation of sample data. That is, we can take the results of an analysis of a sample and can generalize it to the larger population that the sample represents. In order to do this, however, it is imperative that the sample is representative of the group to which it is being generalized.

To address this issue of generalization, we have tests of significance. A Chi-square or T-test, for example, can tell us the probability that the results of our analysis on the sample are representative of the population that the sample represents.

Examples: Linear Regression Analysis, Logistic Regression Analysis, ANOVA, Correlation Analysis, Structural Equation Modelling and Survival Analysis to name a few.

Inference is a vital element of scientific advance, since it provides a means for drawing conclusions from data that are subject to random variation. To prove the propositions being investigated further, the conclusions are tested as well, as part of the scientific method.

Mathematical statistics includes not only the manipulation of probability distributions necessary for deriving results related to methods of estimation and inference, but also various aspects of computational statistics and the design of experiments