# Statistical Reasoning and Thinking

## The Four Dimensions of Statistical Reasoning

The four dimensions are an interrogative cycle, types of thinking, investigative cycle, as well as dispositions. They contain specific and generic statistical thinking habits that operate simultaneously within the thinker. Five thinking types that are marked fundamental are consideration of variation, transnumeration, need for data recognition, integrating contextual with statistical reasoning, and reasoning with statistical models (Wild & Pfankuch, 1999). Many questions emerge when considering thinking and framework regarding teaching, learning, and curriculum. This paper explores the four dimensions of statistical reasoning, offers a specific example, and explains the importance of a representative sample.

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## Investigative Cycle

The investigative cycle is involved statistical problems and abstracts, and it depends on the Problem, Plan, Data, Analysis, Conclusion (PPDAC) model. The problem element attempts to define the situation and grasps system dynamics. Planning involves piloting and analysis, data management, measurement system, as well as sampling design (Wild & Pfankuch, 1999). Data element entails cleaning, management, and collection of information from different sources. Moreover, planning involves hypothesis generation, data exploration, and unplanned and planned analysis, while conclusions involve communication, new data, interpretation, and reviews.

## Types of Thinking

Statistical thinking involves decision-making and learning under certainty to enhance control, prediction, or explanation. General types of thinking include the application of techniques, modeling, strategy, and seeking explanations. Strategic thinking improves the awareness of practical constraints, anticipating problems, and planning. Diverse techniques are applied, such as problem-solving tools, following precedents, and the use of archetypes and recognition (Wild & Pfankuch, 1999). Statistical thinking supports transnumeration, reasoning with statistical models, consideration of variation, and integrating contextual and statistical factors such as conceptions, knowledge, and information.

## The Interrogative Cycle

The dimension applies highly detailed thinking levels and macro levels. It is based on generating, seeking, interpreting, criticizing, and judging model. The generating aspects tend to imagine possibilities for information requirements, explanations, plans of attack, and models. The seeking aspect offers ideas and information externally and internally. The interpret aspect connects, compares, translates, reads, sees, and internally summarizes (Wild & Pfankuch, 1999). The criticizing part involves checking against external and internal factors. Finally, the judging section explains decisions to discard, believe or entertain based on the situation.

## Dispositions

The dimension is applied in situations where authors extremely gain interest in a problem. It is also applied when authors have heightened awareness and sensitivity to a specific problem. People tend to become more observant when dealing with the most interesting issues. This means that engagement tends to increase dispositional elements and boost the desire to make the necessary changes (Wild & Pfankuch, 1999). The dimension involves perseverance, engagement, openness, imagination, skepticism, seeking deeper meaning, awareness, and curiosity. It encourages people to be more observant and challenge preconceptions.

## The Application of the Four Dimensions of Statistical Reasoning in a Managerial Decision-Making

Statistical reasoning helps provide the necessary information to attain desirable decisions and overcome uncertain situations. It enables managers to evaluate the environment and analyze the organization to determine what to do to realize success in key areas such as marketing research and financial and auditing analysis. Establishing numerical benchmarks facilitates the evaluation and monitoring of the progress of a program or policy (Wild & Pfankuch, 1999). This ensures that policies identify and meet initial objectives while suggesting areas requiring improvement.

Statistics reasoning is important as it gives clear and objective numerical data on different aspects of life. For instance, it gives an important source of evidence on areas such as population characteristics and growth, economic performance, health matters, as well as the condition of the immediate environment. The Australian Bureau of Statistics (ABS) is a good example as it provides data in assisting and encouraging informed decision-making, discussion, and research in the community and within the government (Wild & Pfankuch, 1999). It aids the decision-making process by enabling the establishment of numerical benchmarks and monitoring and evaluating the program or policy process. ABS is expected to offer data and support the making of informed decisions, discussions, and research within communities and governments. The ability to interpret and understand data effectively enhances the implementation of positive changes and addresses community needs. This ensures that available policies satisfy intended needs in the best way possible.

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The four dimensions of statistical reasoning help identify and understand the challenging issue. This enables policymakers to gain information on the existing economic, environmental, or social issues requiring a solution. For instance, the dimension can be applied to point out challenging issues such as rising inflation and an aging population. They support an improved understanding of the existing problem and create room for the establishment of desirable corrective measures. The four dimensions tend to provide valuable sources of evidence to enable the alteration and initiation of a policy. Statistics tend to explain the severity and relevance of an issue showing the importance of taking certain measures (Wild & Pfankuch, 1999). This support timely and effective response to address arising issues before they cause bigger problems.

## Importance of Having a Representative Sample instead of a Random Sample

Representative samples ensure the inclusion of all appropriate types of people according to demographic, behavioral, and attitudinal characteristics. This means that the characteristics of the individuals interviewed match those of the larger population. The lack of a representative sample leads to bias where certain groups become over-represented with their opinions taken more seriously while underrepresenting others. Sampling uses various criteria to ensure that items are not taken randomly from the larger population but as a form of a representative. Random sampling favors a certain group implying that there are higher chances of inaccuracy due to unbalanced and unrepresentative collection. Sample bias exists since it is not always possible to force people to take surveys (Udo & Grilo, 2019). There are different ways of evaluating representativeness based on gender, profession, socioeconomic status, education, and personality. Selecting a representative sample avoids sampling errors and improves the reliability of data. This involves considering all participants and giving them equal chances of being selected in the recruitment procedures. It is necessary to avoid recruiting members of a certain population subset while ignoring the others.

A representative sample tends to reduce the sample size while improving the accuracy and reliability of data. This helps simplify the plan and reduce the time required to analyze and present results. Since it entails a relatively small population, the cost of doing research is usually low (Udo & Grilo, 2019). Considering the representation of a survey is important since it facilitates the targeting of the intended audience. It ensures that all the characteristics of a population are captured during the analysis process. Equal attention is given to every aspect when balanced and representative samples are taken. This eliminates problems realized in random sampling, such as sample selection bias, cost, time-consuming, and challenges in accessing the full list of the entire population.

## References

Udo, T., & Grilo, C. M. (2019). Psychiatric and medical correlates of DSM‐5 eating disorders in a nationally representative sample of adults in the United States. International Journal of Eating Disorders, 52(1), 42-50. Web.

Wild, C. J., & Pfankuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-248.

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