Reasoning With Data Chapter 2 2019 McGraw Hill Education

Reasoning With Datachapter 2 2019 Mcgraw Hill Education All Rights R

Reasoning with Data Chapter 2 © 2019 McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Learning Objectives Define reasoning. Execute deductive reasoning. Explain an empirically testable conclusion. Execute inductive reasoning. Differentiate between deductive and inductive reasoning. Explain how inductive reasoning can be used to evaluate an assumption. Describe selection bias in inductive reasoning.

What is Reasoning? Reasoning is the process of forming conclusions, judgments, or inferences from facts or data. Reasoning and logic are often used interchangeably. Logic is a description of the rules and/or steps behind the reasoning process.

Two Arguments: Argument 1: The company's profits are up more than 10% over the past year. An increase of 10% is the result of excellent management. You were the manager over the past year. Therefore, I conclude that you engaged in excellent management last year. Argument 2: Ten of your 300 employees came to me with complaints about your management. They indicated that you treated them unfairly by not giving them a deserved raise. Therefore, I conclude that all of your employees are disgruntled with your management.

Understanding Reasoning: In presenting these two arguments, the goal is not to make a definitive decision about which you believe. The goal is to think about and distinguish different lines of reasoning. By doing this, you will be able to establish why you believe or question the claims made in the two arguments.

Two Major Types of Reasoning: Reasoning includes deductive reasoning and inductive reasoning. Both play an important role in interpreting and drawing conclusions from data analysis.

Deductive Reasoning

Deductive reasoning goes from the general to the specific, also known as top-down logic. It seeks to prove statements of the form “If A, then B.” Deductive reasoning always implies three components: assumptions (“If A”), methods of proof (“then”), and conclusions (“B”).

The purest applications of deductive reasoning are in mathematics. Two common approaches are direct proofs and transposition. Direct proofs begin with assumptions, explain methods of proof, and state the conclusion(s). Transposition involves proving that “If A, then B” is equivalent to “If not B, then not A.”

Direct Proofs

Using the example: If X and Y are odd numbers, then their sum (X + Y) is even. If X=5 and Y=9, then X + Y=14, which is even. In mathematical terms, if X=2K+1 and Y=2M+1 (where K and M are integers), then X+Y=2(K+M+1), which is divisible by 2, hence even.

Common Sense Approach

For instance, “If McDonald's offers breakfast all day, their revenues will increase.” Since McDonald's offers breakfast all day, adding more options is likely to retain customers and attract new ones, increasing overall revenue.

Transposition

Transposition involves proving “If A, then B” by showing that “If not B, then not A.” For example, if McDonald’s does not see an increase in revenue when offering breakfast all day, it implies that either there is no increase or that the menu expansion is ineffective.

Mathematical Proof Using Transposition

Prove: If X² is even, then X is even. Assuming X is odd, X=2K+1. X²=4K²+4K+1. Since 4K²+4K is divisible by 2, X²=2(2K²+2K)+1, which is odd. Contradiction implies that if X² is even, X must be even.

Deductive Reasoning in Law and Disputes

Deductive reasoning is crucial in law, where conclusions depend on the validity of methods and assumptions. Disputes often arise from disagreements over these elements. Reliability of deductive conclusions depends on robustness (accuracy across assumptions) and consistency with data.

Empirically Testable Conclusions

An empirically testable conclusion can be validated through observable data. For instance, management's hypothesis that relocating a product will increase sales can be tested by collecting and analyzing sales data post-move. The decision to accept or reject conclusions is based on inductive reasoning.

Inductive Reasoning

Inductive reasoning moves from specific instances to broader generalizations. It involves analyzing data samples from the population, which is the entire set of potential observations. Business decisions often rely on inductive reasoning to infer characteristics of the population based on sample data.

The strength of an inductive argument is expressed as the degree of support, ranging from 50% (tentative) to 100% (certain). This degree of support can be subjective (opinion-based, lacking statistical foundation) or objective (statistically based, more credible).

Evaluating Assumptions with Inductive Reasoning

Proper evaluation involves collecting data, testing hypotheses against observed data, and deciding whether to reject or accept conclusions. This process depends on the quality of the data and statistical support. If the data contradicts the conclusion, the hypothesis is rejected; if it aligns, the hypothesis is supported.

Selection Bias in Inductive Reasoning

Selection bias occurs when conclusions about a population are derived from biased samples that do not accurately represent the entire population. Common types include collector selection bias, where the sample is systematically chosen; availability bias, based on readily available data; and member selection bias, where individuals self-select into or out of the sample.

Biases diminish the reliability of inductive reasoning, risking inaccurate conclusions. Awareness and control of biases are essential for valid inferences in data analysis.

Conclusion

Both deductive and inductive reasoning are indispensable tools for interpreting data and making informed decisions. While deductive reasoning provides certainty when rules and assumptions are correct, inductive reasoning offers probabilistic support based on data samples. Recognizing the potential for bias and understanding the differences between these reasoning types enhance analytical rigor in research and business contexts.

References

• Chalmers, A. F. (2013). What Is This Thing Called Science? Open University Press.
• Copi, I. M., Cohen, C., & Flage, D. (2016). Introduction to Logic (14th ed.). Routledge.
• Finkenstaedt, T., & Bock, H. (2019). The Psychology of Reasoning. Springer.
• Hastings, K. (2020). Business Data Analysis. Sage Publications.
• Johnson-Laird, P. N. (2013). Deduction. The Oxford Handbook of Thinking and Reasoning. Oxford University Press.
• Kahneman, D. (2011). Thinking, Fast and Slow. Farrar, Straus and Giroux.
• Rubin, D. B. (2008). For Objective Causal Inference. Journal of the American Statistical Association, 103(481), 268-278.
• Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Experimental and Quasi-Experimental Designs for Generalized Causal Inference. Houghton Mifflin.
• Stanley, J. (2019). Critical Thinking in Business. Routledge.
• Wason, P. C. (1968). Reasoning about a rule. The Quarterly Journal of Experimental Psychology, 20(3), 273-281.