Reflection on Different Statistical Techniques

Reflection
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Reflection
Probability
In almost every decision there is to be made, an entity acknowledges the inherent uncertainty. Probability theory comes to the fore as it enables the articulation of a decision through the analysis of risks and minimization of the prevailing gamble in the decision-making process (Orga & Ogbo, 2012). Unsurprisingly, gambling games are the first places where the theory of probability was applied. The conception of probability arose from two primary perspectives: a statistical and an epistemic side (Batanero et al., 2016). The former is predicated upon objective mathematical rules, while the latter is quite subjective because it is dependent on the person’s or entity’s degree of conviction on the information available. Both are fundamental given that the entity in question may lack credible data on the statistical side, paving the way for qualitative injunctions. Nevertheless, the great thing about probability theory is that it considers various dimensions of events, including mutually exclusive, collectively exhaustive, independent, complementary, and joint ones.
Probability is applicable in several circumstances in the modern workplace. As portrayed earlier, probably could come in handy in risk evaluation and more so in those moments when a business intends to expand their operations. In this case, the objective probability will be vital in calculating the expected value of various alternatives. Besides risk evaluation, probability is equally important in determining sales forecasting with the input of scenario analysis. Although predicting precise future sales is practically impossible, a business has to articulate a feasible plan for this purpose. To this end, a scenario analysis stipulates the best-case and worst-case scenarios that await a business.
Distribution
There are dozens of distributions that elicit different statistical properties. Such distributions include binomial, Poisson, geometric, hypergeometric, and discrete uniform distributions. In the case of data and distribution, beginning with raw data and consequently answering primal questions about it could come in handy in the process of characterization. First, it has to be determined whether the data is discrete or continuous. Secondly, the entity will look at the symmetry or asymmetry of the data. The third aspect is to determine the existence of the upper or lower limits and, finally, observing the likelihood of extreme values.
Checking the continuity of data is fundamental besides being the most obvious categorization of data. In most cases, a firm’s inputs towards a typical project and, more importantly, the estimates here are continuous. Excellent examples include profit margins, market share, and market size, which are all continuous variables. On the other hand, risk factors such as threats from terrorist attacks and regulatory actions take on discrete forms. Normal distribution appears to be the most popular symmetric distribution because of its two parameters, which are standard deviation and mean. Limits provide insight into specific business situations such as the company’s market value, revenues, and profits. All these aspects conjure to provide the management with better scenario analysis of situations that face them. A probability distribution is vital in scenario analysis because they are crucial in creating many theoretical distinct possibilities that are likely to be the outcomes of certain events or course of action. A probability distribution is also influential in risk evaluation. For instance, it can curate a near-possible number in the decline of an organization’s sales forecast.
Uncertainty
There is no doubt as to the impact that uncertainty has on the decision-making process justifying its increased attention from scholars, academicians, and economic players as well. Sniazhko (2019) defines uncertainty “as the lack of knowledge about the probabilities of the future state of events” (p. 2). Uncertainty affects an organization’s level of commitment, entry mode choices, internationalization paths, and expansion plans. Since the decision-maker is unable to eliminate uncertainty, the decision-making becomes ineffective, and thus, they are required to measures that are influential in reducing or coping with the underlying uncertainties.
One of the most obvious approaches in nullifying or mitigating against the degree of uncertainty is data gathering. Brothers et al. (2008) assert that information gathered is relatively sufficient to achieve analytical comprehensiveness of the environment. Information gathering facilitates the scanning of the external environments, which in most circumstances is the reason most businesses exit the marketplace. On the other hand, proactive collaboration (cooperation) can come in handy in a testing environment where there the uncertainty is high. Ultimately, the entities involved have a better understanding of the environment and, thus, can curate or make predictions of the condition thereof (Simangunsong, Hendry, & Stevenson, 2012). Finally, a company can reduce uncertainty through networking. In this case, the interested party will collect information via its social relationships and through the reinforcement of existing networks. This position enables them to control the input, demand, and competition to a certain degree.
Sampling
Data sampling is another technique often used in statistics. It is “used to analyze patterns and trends in a subset of data that is representative of a larger data set being examined” (Calvello, 2020). In essence, sampling will dictate how much data should be collected and how often this is done. This method of statistical analysis must be conducted proficiently. Otherwise, it could go wrong, meaning that solid research is fundamental before the process begins. Data sampling is crucial because conclusions about populations are drawn from samples. Having decided to proceed with the data sampling process, an organization will first be tasked with identifying and defining the population that is to be subjected to this analysis. Several ways can be used to achieve this end, including interviews, questionnaires, focus groups, various observations, opinion polls, and surveys. One could also refer to this process as data collection, and in this case, necessary parameters need to be established.
The second step is selecting the sampling frame, which encapsulates the list of items or individuals that form the population from which the sample is to be taken. Next, the sampling method will be articulated, which could either be a probability or non-probability sampling. The former is used quantitative research, while the latter is applied in qualitative research (Lopez & Whitehead, 2013). The next step, which is the fourth, involves the determination of the sample size to analyze. In this case, the sample size represents the precise number of samples whose measurements will be fundamental for the observations to be made. The final step is collecting data from the sample. From there, the firm can make an appropriate actionable plan, conclusion, or decision concerning the data thereof.
Statistical Inference
There is a four-step process: data production, exploratory data analysis, probability, and inference encompasses statistics. The first three are vital in the successful accomplishment of the last one. This relationship leads to the definition of statistical inferences as “claims made using probability models of data generating processes, intended to characterize unknown features of the populations or processes form which data are thought to be assembled” (Tong, 2019, p. 246). In essence, inferential statistics take information derived from the sample and generalizes it to the larger population. This notion is different from differential statistics, where data is only described. The statistical inference made is highly predicated upon the sample size, variability in the sample, and the size of the observed differences.
Several types of statistical inferences are applied in making conclusions. Some of these types include chi-square statistics, multivariate regression, bivariate regression, Pearson correlation, confidence interval, and one-sample hypothesis testing. The inference is highly applicable in the decision-making process, with the more familiar situations being those where choice has to be made between two actions concerning the result of a hypothesis test. Nevertheless, the most primal question is where statistical inference is applied in contemporary society. Retrospectively, statistical inference is applied in different fields to facilitate future predictions for various observations. These fields include but are not limited to the pharmaceutical sector, share market, machine learning, fraud detection, financial analysis, artificial intelligence, and business analysis.
Regression Analysis
Regression analysis (RA) is another highly used statistical technique. It is “used to ...