Course: Statistical Reasoning I

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Syllabus

Course Description

Statistical Reasoning in Public Health provides a broad overview of biostatistical methods and concepts used in the public health sciences, emphasizing interpretation and concepts rather than calculations or mathematical details. It develops ability to read the scientific literature to critically evaluate study designs and methods of data analysis, and it introduces basic concepts of statistical inference, including hypothesis testing, p-values, and confidence intervals. Topics include comparisons of means and proportions; the normal distribution; regression and correlation; confounding; concepts of study design, including randomization, sample size, and power considerations; logistic regression; and an overview of some methods in survival analysis. The course draws examples of the use and abuse of statistical methods from the current biomedical literature.

Course Objectives

Upon completion of this course, you will be able to do the following:
  • Understand and give examples of different types of data arising in public health studies.
  • Interpret differences in data distributions via visual displays.
  • Calculate standard normal scores and resulting probabilities.
  • Calculate and interpret confidence intervals for population means and proportions.
  • Interpret and explain a p-value.
  • Perform a two-sample t-test and interpret the results; calculate a 95% confidence interval for the difference in population means.
  • Use Stata to perform two sample comparisons of means and create confidence intervals for the population mean differences.
  • Select an appropriate test for comparing two populations on a continuous measure, when the two sample t-test is not appropriate.
  • Understand and interpret results from Analysis of Variance (ANOVA), a technique used to compare means amongst more than two independent populations.
  • Choose an appropriate method for comparing proportions between two groups; construct a 95% confidence interval for the difference in population proportions.
  • Use Stata to compare proportions amongst two independent populations.
  • Understand and interpret relative risks and odds ratios when comparing two populations.
  • Understand why survival (timed to event) data requires its own type of analysis techniques.
  • Construct a Kaplan-Meier estimate of the survival function that describes the "survival experience" of a cohort of subjects.
  • Interpret the result of a log-rank test in the context of comparing the "survival experience" of multiple cohorts.
  • Interpret output from the statistical software package Stata related to the various estimation and hypothesis testing procedures covered in the course.

Readings

There is no required textbook for this course.

Students are also required to have access to Small Stata, a version of Stata that is less powerful (in terms of the amount of data it can store and process, not in terms of functionality) than regular Intercooled Stata, and costs significantly less. Small Stata carries a one-year users license. However, if you intend to further your study of statistics beyond this course, you may wish to purchase a copy of Intercooled Stata 8.

Other useful, but optional, references include the following:

  • Freedman, D., Pisani, R., Purves, R. Statistics
  • Moore, D., McCabe, G. Introduction to the Practice of Statistics
  • Altman, D.G. (1991). Practical Statistics for Medical Research. London: Chapman and Hall

Course Topics

  • Lecture 1: Describing Data, Part 1
  • Lecture 2: Describing Data, Part 2
  • Lecture 3: Sampling Variability and Confidence Intervals
  • Special Lecture: Some Useful Stata Information
  • Lecture 4: An Introduction to Hypothesis Testing: The Paired t-test
  • Lecture 5: Comparing Means Among Two (or More) Independent Populations
  • Lecture 6: Comparing Proportions Between Two Independent Populations
  • Lecture 7: When Time Is of Interest: The Case for Survival Analysis

Course Format

The content of this course is divided into four separate modules. All the required course work can be accessed from the Lecture Materials page. The lecture sections are presented sequentially and should be completed in that order. Each of these sections combines audio presentation and slides - just like attending lectures in class. You may return to any previous section at any point and review its contents at your convenience.