Introduction to Statistical Reasoning (Fall 2023 Primary Instructor)

Primary Instructor

As a primary instructor, I gave lectures and led discussions, created course syllabus, developed and designed lecture notes in LaTex, provided handouts, problem sets, posted weekly summaries, wrote exams (2), and quizzes. In addition, I set up and managed a Canvas site for the course. I made myself available to students by holding in-person office hours, holding tutoring ceters (2 hours per week), staying after each class to answer questions, and conducting review sessions (2) and providing study guides (2) before each exam (2). I was also involved in grading homework assignments (10), exams(2), and workbook problems (21). Two projects were assigned during the semester. Throughout the semester, I closely monitored each student’s progress and was quick to respond to their emails.

Textbooks

• Required Textbook:
  • William S. Rayens, “The workbook: Beyond the Numbers: Student-Centered Activities for Learning Statistical Reasoning”

Course Description

The goal of this course is to help students develop or refine their statistical literacy skills. Both the informal activity of human inference arising from statistical constructs, as well as the more formal perspectives on statistical inference found in confidence intervals and hypothesis tests are studied. Throughout, the emphasis is on understanding what distinguishes good and bad inferential reasoning in the practical world around us.

Student Learning Outcomes

The primary goals of this course are:

• Human Inference: the primary intent of this module is to help students begin to absorb common statistical information appropriately and to form associated human inferences carefully. The focus will be on tables, charts and summaries in the media, but some time will be spent on the psychology of inference as well.
  • Identify categorically good or bad statistical summaries, charts and graphs and sexplain the reasons they are so categorized.
  • Identify categorically good or bad statistical arguments based on statistical summaries, charts, and graphs, and explain the reasons they are so catregorized.
  • Compute basic statistical summaries and create simple graphs.
  • Define and apply basic experimental design vocabulary.
  • Identify confounding variables and evaluate their effects on experimental results.
  • Explain the role of randomization in simple experimental design.
  • Explain in non-mathematical terms the concept of statistical significance.
  • Identify and assess associations seen in scatterplots and two-way tables.
  • Distinguish the concepts of association and causation, and explain how they offer different types of evidence.
  • Compute, apply, and interpret the correlation coefficient.
• Confidence Intervals: the primary intent of this module is to develop a deeper sense of what statistical confidence means and doesn’t mean by exploring sampling variability and encountering some of the important theory behind repeated sampling. The focus will be largely on polls and social surveys.
  • Define and demonstrate simple random sampling.
  • Identify and analyze alternative sampling methods.
  • Explain the difference between randomness and representativeness.
  • Define sampling variability, and explain the role it plays in the construction of a confidence interval.
  • Define sampling distribution, and explain the role it plays in the construction of the marigin of error.
  • Compute and interpret confidence intervals for a proportion or mean.
  • Define and apply the empirical rule to solve provavility problems.
  • Identify categorically good or bad surveys, and explain the reasons they are so categorized.
  • Explain the difference between sampling variability and non-sampling variability.
  • Identify and evaluate strategies for addressing non-sampling variability.
• Formal Inference: the primary intent of this module is to encounter the concepts and language of hypothesis testing by way of the more common ideas of sensitivity and specificity. Discussion will revolve around field sobriety tests and home pregnancy tests.
  • Define and compute senstivity and specificity.
  • Explain the effect on sensitivity and specificity of changes to the testing criteria.
  • Identify and demonstrate the difference between probabilities of conditional and unconditional events.
  • Define Type I eror and explain how to view hypothesis tesing as a screen test.
  • Explain the difference between a Type I error and a p-value.
  • Define the meaning of the phrase statistical significance.
  • Analyze the use of the phrase statistically significant in media reports.
  • Explain the difference between statistical significance and practical significance.
  • Execute the steps needed to test simple hypothesis.
  • Compute and demonstrate the use of p-value when testing a hypothesis.

Course Schedule

Rough Outline:

• Sampling
• Sampleing - Confidence Intervals
• Sampleing - When MOE Doesn’t Apply
• Sensitivity and Specificity
• Confounding and the Language of Experimentation
• Correlation and Causatrion
• Hypothesis Testing - As a Diagnostics
• Hypothesis Testing - Computations
• Number Sense - Basic Numeracy

Covered Chapters are:

• Chapter 1: Number sense: basic numeracy
• Chapter 2: Number sense: basic computational skills and benchmarks
• Chapter 4: Sampling: purpose and challenges
• Chapter 5: Confidence intervals: what they re and how we use them
• Chapter 6: Confidence intervals: where they come from
• Chapter 7: Sampling: when probability isn’t enough
• Chapter 3: Statistical experiments and the problem of confounding
• Chapter 12: More than one variable: association and correlation
• Chapter 8: The language of decision making
• Chapter 9: Hypothesis testing: concepts and consumption
• Chapter 10: Hypothesis testing: computations
• Chapter 11: Hypothesis testing: importance of clinical significance

Software

StatKey and/or Excel.