In this module, we cover three major topics of the foundation of biostatistics: 1) probability of events, 2) random variables, and 3) sampling distributions. Probability can be a simple concept, but it is sometimes not intuitive and may require much thinking and practice to fully grasp. Once we model health phenomena as random variables, then we can use the principles of probability to help us learn about their distributions and understand what is likely to happen. The central limit theorem and the normal model are very important tools to allow us to understand the big picture from a small snapshot (i.e., the relationship between population parameters and sample statistics) and to help us arrive at a concrete numerical measure of likelihood.

The resources in this module try to achieve a balance between theory and practice. These concepts may seem very different at first, but they are very much connected. Please feel free to explore different ways of presenting the concepts, and go back and forth between theory and practice until you are confident in your understanding and in calculating event probabilities.

Upon completion of this module, students should be able to:

• Relate the probability of an event to the likelihood of this event occurring
• Understand how to interpret and generate proportions from data
• Explain how relative frequency can be used to estimate the probability of an event
• Understand the concepts of probability, conditional probability, and independence
• Understand the concept of random variables
• Distinguish between samples and population and identify different types of samples
• Understand sampling distribution, variance, and the central limit theorem
• Understand the implications and uses of normality and skewness
• Be able to calculate and correctly interpret probability data from a sampling distribution

Module 2: Lesson 1: Probability, Frequency, and the Concepts of Probability

Student Learning Objectives:

Upon completion of this lesson, you will be able to:

• Relate the probability of an event to the likelihood of this event occurring.
• Understand how to interpret and generate proportions from data.
• Explain how relative frequency can be used to estimate the probability of an event.
• Understand the concepts of probability, conditional probability, and independence.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 2 hours.

Required Learning Resources and Activities

Module 2: Lesson 2: Variables, Sampling, and Distribution

Student Learning Objectives:

Upon completion of this lesson, you will be able to:

• Understand the concept of random variables.
• Distinguish between samples and populations and identify different types of samples.
• Understand sampling distribution, variance, and the central limit theorem.
• Understand the implications and uses of normality and skewness.
• Be able to calculate and correctly interpret probability data from a sampling distribution.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 7 hours.

Required Learning Resources and Activities