The material below comprises excerpts from books by Dr. Johnathan Mun, our CEO and founder, such as Readings in Certified Quantitative Risk Management, 3rd Edition, and Quantitative Research Methods Using Risk Simulator and ROV BizStats Software Applying Econometrics, Multivariate Regression, Parametric and Nonparametric Hypothesis Testing, Monte Carlo Risk Simulation, Predictive Modeling, and Optimization, 4th Edition (https://www.amazon.com/author/johnathanmun). All screenshots and analytical models are run using the ROV Risk Simulator and ROV BizStats software applications. Statistical results shown are computed using Risk Simulator or BizStats. Online Training Videos are also available on these topics as well as the Certified in Quantitative Risk Management (CQRM) certification program. All materials are copyrighted as well as patent protected under international law, with all rights reserved.
The study of statistics refers to the collection, presentation, analysis, and utilization of numerical data to infer and make decisions in the face of uncertainty, where the actual population data is unknown. There are two branches in the study of statistics: descriptive statistics, where data is summarized and described, and inferential statistics, where the population is generalized through a small random sample, making it useful for making predictions or decisions when the population characteristics are unknown.
A sample can be defined as a subset of the population being measured, while the population can be defined as all possible observations of interest of a variable. For instance, if one is interested in the voting practices of all U.S. registered voters, the entire pool of a hundred million registered voters is considered the population while a small survey of one thousand registered voters taken from several small towns across the nation is the sample. The calculated characteristics of the sample (e.g., mean, median, standard deviation) are termed statistics, while parameters imply that the entire population has been surveyed and the results tabulated. Thus, in decision making, the statistic is of vital importance considering that sometimes the entire population is yet unknown (e.g., who are all your customers, what is the total market share, and so forth) or it is very difficult to obtain all relevant information on the population because it would be too time- or resource-consuming.
In inferential statistics, the following are the usual steps in conducting research:
- Designing the experiment—this phase includes designing the ways to collect all possible and relevant data.
- Collection of sample data—data is gathered and tabulated
- Analysis of data—statistical analysis performed
- Estimation or prediction—inferences are made based on the statistics obtained
- Hypothesis testing—decisions are tested against the data to see the outcomes
- Determining goodness-of-fit—actual data is compared to historical data to see how accurate, valid, and reliable the inference may be.
- Decision making—decisions are made based on the outcome of the inference.