What are the basic statistical techniques in research methodology

What are the basic statistical techniques in research methodology and describe their uses.

Ans.

Statistics is a branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation. In applying statistics to, for example, a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as “all people living in a country” or “every atom composing a crystal”. Statistics deals with all aspects of data, including the planning of data collection in terms of the design of surveys and experiments.

Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution’s central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.

A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a “false positive”) and Type II errors(null hypothesis fails to be rejected and an actual difference between populations is missed giving a “false negative”). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.

Statistical techniques are used in a wide range of types of scientific and social research, including: biostatistics, computational biology, computational sociology, network biology, social science, sociology and social research. Some fields of inquiry use applied statistics so extensively that they have specialized terminology. These disciplines include:

Actuarial science (assesses risk in the insurance and finance industries)
Applied information economics
Astrostatistics (statistical evaluation of astronomical data)
Biostatistics
Business statistics
Chemometrics (for analysis of data from chemistry)
Data mining (applying statistics and pattern recognition to discover knowledge from data)
Data science
Demography (statistical study of populations)
Econometrics (statistical analysis of economic data)
Energy statistics
Engineering statistics
Epidemiology (statistical analysis of disease)
Geography and geographic information systems, specifically in spatial analysis
Image processing
Medical statistics
Political science
Psychological statistics
Reliability engineering
Social statistics
Statistical mechanics

In addition, there are particular types of statistical analysis that have also developed their own specialised terminology and methodology:

Bootstrap/Jackknife re-sampling
Multivariate statistics
Statistical classification
Structured data analysis (statistics)
Structural equation modelling
Survey methodology
Survival analysis
Statistics in various sports, particularly baseball – known as Sabermetrics and cricket

Statistics form a key basis tool in business and manufacturing as well. It is used to understand measurement systems variability, control processes (as in statistical process control or SPC), for summarizing data, and to make data-driven decisions. In these roles, it is a key tool, and perhaps the only reliable tool.