buy statistics essay

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The Role of Statistics in Decision-Making: A Comprehensive Analysis

1. Introduction to Statistics and its Importance

Among other things, statistics techniques are concerned with understanding and providing corrections for data collected from different information mechanisms. Each of these mechanisms has strengths and limitations that can impact the information collected and the degree of accuracy about the targeted population. Statistics tools are used to either gain a better understanding of the information collected or correct for the inherent challenges in moving from observed sample behaviors to making decisions about the wider population. The complex nature of these processes means that both responsively collecting information that is used to help make evidence-based decisions and understanding the resulting statistical analyses are critically important for truly informed decision making.

Statistics is a mathematical science that involves the use of quantitative methods to gather, describe, analyze, and make inferences from particular types of information. The results of these activities are well-established and widely used in making sound, evidence-based decisions. The scope of statistics includes collecting a wide range of information and correctly interpreting the described populations, using the observed sample behaviors. As such, these collective methods are critically important because they can be used to accurately and systematically summarize the observed data and, when combined with a particular decision-making process, also provide a degree of probability about the potential results of different alternative actions.

2. Descriptive Statistics: Understanding and Presenting Data

Descriptive statistics refers to methods used to summarize and describe data. These methods aid in reducing raw data into a manageable form, which facilitates the understanding of data. More importantly, an array of methods is used to communicate our observations accurately, efficiently, effectively, and convincingly. Pictorial presentations offer the most effective means for describing data structures, but data descriptions become more informative when summary measures are also used in communication. It is important to balance graphical presentations and summary measures because they collectively provide a more comprehensive representation of the data. Given both the potential and the risks associated with the use of information for decision making, analysts must be aware of the limitations and the trade-offs of different methods used for describing data structures. Indeed, we run the risk of making flawed decisions if we do not take the necessary time and care to construct the most accurate and reliable predictions.

This section introduces descriptive statistics as an essential tool used to understand phenomena and make effective decisions. The section examines how to use graphs, tables, proportions, and other measures to communicate data distributions more accurately than simply relying on the raw data. Moreover, the section explains how plotting data helps expose patterns, relationships, and inconsistencies. The presented material is essential, not only in understanding data, but also in making useful inferences. Consequently, the chapter offers opportunities for participants to apply their knowledge by working through examples. By extension, the instructors should invite participants to present or prepare examples for presentation during subsequent class sessions.

3. Inferential Statistics: Making Informed Decisions Based on Data

These types of tools can then help consumers of these results to understand the limitations of sample-based estimates and to make more informed decisions about the population from which the sample was drawn.

In settings like this one, inferential statistics provide research and decision-makers with the tools to measure and report the uncertainty concerning the sample-based information that is used to make population-based decisions. In the policy example, analysts usually don’t even attempt to measure and report all of the potential uncertainty in their estimates. Instead, they often report interval estimates, or ranges of values, within which the parameter of interest likely lies, on the basis of certain desired levels of confidence.

In this census example, the parameter population mean is the characteristic of interest. It is impossible to collect data from 100% of the members of the population; therefore, statistical inference is necessary. Instead, a sample taken from the population is used to infer information about the population mean.

For example, policymakers organize a census in order to obtain certain descriptive information on all members of a given population. They use that descriptive information to make decisions about how to provide for the public’s benefit by allocating tax revenues, passing laws, and using law enforcement measures.

Making informed decisions based on descriptive statistics often involves working with data that naturally comes in the form of statistical estimates. It is not practical for researchers and decision-makers to collect and analyze all the data, let alone to consider all of the data inputs and criteria for making each possible decision that may be important.

4. Advanced Statistical Techniques: Regression, ANOVA, and Hypothesis Testing

Data is usually in error with some probability. Many models assume that data errors have no structure, so there is no problem with these errors. In many situations, there is a correlation in the data errors within a sample or between responses on the same subject at different times, etc. This sort of complication in the error structure is the realm of heteroscedasticity in regression analysis. Statistics, for the most part, determines “group differences” through the application of hypothesis testing. In hypothesis testing, the model or characteristics of one group is compared with that of another group or with a population. If differences are found between specific models or characteristics, one would indicate that these groups are different and there are group differences.

In a simple correlation, one variable depends on the other single variable, and we try to identify whether this dependence is positive or negative by analyzing the correlation coefficients. In reality, there is rarely this sort of simple relation, and we need to control for other influential variables. This idea is called multiple regression analysis. Some businesses can encourage more purchases by women or offer discounts for married men, etc., and can leverage these results with respect to other costs and efforts to their existing market segments. Multiple regression begins with a single dependent variable and continues with two or more independent variables.

5. The Ethical Use of Statistics in Research and Decision-Making

The use of statistics is to be objective, meaningful, simple, and as inexpensive as possible on a particular project, without being ethically biased in reaching a solution from a meager sample of information. The intent should not be malicious, manipulative, or fraudulent, and the result should not materially or financially impact those concerned. Regarding each procedure, a decision maker should ask two questions: How does the data analysis work, and is the interpretation presented in context with the experimental research method? Is the analysis performed correctly? Additionally, the investigator should ask: Are the statistical parameters (mean, median, and boundaries) appropriate to bind the data, and are the descriptive statistics representative of the population of concern?

Many ethical and professional dilemmas for statisticians arise because users are not sure of what analytical statistical techniques or experimental design to apply. Moreover, what defines an ethical use of statistics — how one should certainly not “lie” with statistics — has been a topic of great discussion. Statistical ethicists have managed to isolate the basic principles of an ethical use of statistics for professionals. These professionals can be students, researchers, business persons, electronic or mechanical processes, or anyone who would normally use the subject as an objective way to guide a decision.