Data are everywhere around us. Making sense of the massive amounts of data for the purpose of improving the health of a population requires understanding statistical principles and developing skills in applying these concepts. In this first module, we start by looking at the different types of data we often encounter and what we can say about them in a basic sense using descriptive statistics. We will learn about different ways to present the data to highlight important messages and investigate designing studies to understand the practical applications of important statistical concepts. The type of data often determines what statistical tools we can use, so this module is crucial for upcoming materials in this course.

Resources in this module are quite diverse. The resources are not an exhaustive reference for tools for understanding and presenting descriptive statistics, but rather a starting point, covering the basic concepts.

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

• Explore the basic principles of statistics and some of its common uses
• Understand the basic principles of probability, descriptive statistics, and data analysis
• Understand how to generate descriptive statistics from data
• Understand the different types of variables, how they are used, and how to summarize the data
• Understand and identify the different types of plots and graphs
• Generate descriptive statistics from data, calculate descriptive statistics and standard deviations, and understand the methods of summarizing a single quantitative variable
• Summarize and describe the distribution of a categorical variable and understand the uses and implications of the normal distribution
• Understand the basic types of data, the main ways in which data are used, and important considerations when using data in analysis
• Identify the design of a study and explain how this impacts interpretation
• Apply knowledge and skills in working with different data types in a chosen public health setting

Module 1: Lesson 1: Introduction to Biostatistics

Student Learning Objectives:

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

• Explore the basic principles of statistics and some of its common uses.
• Understand the basic principles of probability, descriptive statistics, and data analysis.
• Understand how to generate descriptive statistics from data.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 1 hour.

Required Learning Resources and Activities

Module 1: Lesson 2:  Types of Variables, Plots, and Graphs

Student Learning Objectives:

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

• Understand the different types of variables, how they are used, and how to summarize the data.
• Understand and identify the different types of plots and graphs.

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

Required Learning Resources and Activities

Module 1: Lesson 3:  Descriptive Statistics and Distribution

Student Learning Objectives:

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

• Generate descriptive statistics from data, calculate descriptive statistics and standard deviations, and understand the methods of summarizing a single quantitative variable.
• Summarize and describe the distribution of a categorical variable, and understand the uses and implications of the normal distribution.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 1 hour.

Required Learning Resources and Activities

Module 1: Lesson 4: Data Analysis and Study Design

Student Learning Objectives:

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

• Understand the basic types of data, the main ways in which data are used, and important considerations when using data in analysis.
• Identify the design of a study and explain how this impacts interpretation.
• Apply knowledge and skills in working with different data types in a chosen public health setting.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 3 hours.

Required Learning Resources and Activities

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

In this short module, we build on the concept of sampling distributions to use samples to make inferences on the population. We will start by understanding inference and estimation, then learn to calculate confidence intervals. We will also look at factors and conditions that influence estimation.

In contrast to an orderly presentation such as in previous modules, most of the resources in this module cover the same key concepts in slightly different ways.

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

• Understand and be able to apply point estimation and confidence interval estimation
• Recognize inference on means versus inference on proportions
• Be able to calculate one-sided and two-sided confidence intervals for mean and proportion
• Understand the effect of sample size and other conditions on estimation, as well as understand and be able to calculate the sample size needed to achieve the desired confidence level

Module 3: Lesson 1:  Point and Confidence Interval Estimation

Student Learning Objectives:

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

• Understand and be able to apply point estimation and confidence interval estimation.
• Recognize inference on means versus inference on proportions.
• Be able to calculate one-sided and two-sided confidence intervals for mean and proportion.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 3 hours.

Required Learning Resources and Activities

Module 3: Lesson 2: Effect of Sample Size on Confidence Interval

Student Learning Objectives:

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

• Understand the effect of sample size and other conditions on estimation as well as understand and be able to calculate the sample size needed to achieve the desired confidence level.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 1 hour.

Required Learning Resources and Activities

Hypothesis testing is a cornerstone in science. In biostatistics, it is often used to assess anything from the effectiveness of an intervention, to changes in the distribution of a health outcome. But many tests are out there, so how do they work? When do you use which? How does hypothesis testing differ from estimation and from regression modeling? We will answer these questions in this module. The concept of hypothesis testing may appear counter-intuitive at first, but this is the common “frequentist” approach of statistics; other approaches exist that are beyond the scope of this course. Pictures can help a great deal in understanding ideas such as the null and alternate hypotheses, power, types of errors, etc.

These days most calculations for hypothesis testing, power, and sample size calculations are performed using statistical software. It is still very important that you understand the fundamental theory underlying these concepts and which quantities influence these values; however, there is less emphasis on your ability to do hand calculations.

What you should know:

• Write hypothesis statements
• Choose the appropriate test
• Interpret results of the hypothesis test

What software can do:

• Run the hypothesis test chosen by you (e.g., calculate test statistic, report p-value)
• Calculate sample size given other values (e.g., desired power, effect size)

Several resources in this module cover the same topics but with different approaches. Reading about different ways to explain the same complex concept may help you find what speaks to you best. Utilize as many resources as needed to understand key concepts in this module.

Statistics is a hands-on discipline. The learning activity in this module asks you to run through some hypothesis tests from beginning to end. You should be able to perform calculations by hand and arrive at a conclusion. For more complex tests, you will likely need the assistance of statistical packages to do the bulk of the work for you.

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

• Reinforce understanding of probability distributions in the context of hypothesis testing, especially in drawing conclusions and types of errors
• Distinguish types of explanatory and response variables
• Understand the relationship between confidence interval and hypothesis testing
• Understand and apply hypothesis tests for a single mean and a single proportion as well as for two means (independent and paired/matched samples), and understand chi-squared test and ANOVA
• Understand inference, estimation, and the basics of hypothesis testing
• Understand implications of multiple testing and Bonferroni correction
• Understand and be able to correctly interpret p-values
• Understand the importance and implications of Type I and Type II errors
• Understand factors that affect study power and sample size requirements, and how they impact study design
• Summarize and describe nonparametric tests and understand the conditions under which they are applied
• Be able (1) to apply appropriate hypothesis tests to variable types in order to explore relationships and (2) to draw conclusions based on such hypothesis testing and to interpret p-values

Module 4: Lesson 1: Principles of Hypothesis Testing

Student Learning Objectives:

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

• Reinforce understanding of probability distributions in the context of hypothesis testing, especially in drawing conclusions and types of errors.
• Distinguish types of explanatory and response variables.
• Understand the relationship between confidence intervals and hypothesis testing.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 1 hour.

Required Learning Resources and Activities

Module 4: Lesson 2:  Applications of Hypothesis Testing

Student Learning Objectives:

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

• Understand and apply hypothesis tests for a single mean and a single proportion as well as for two means (independent and paired/matched samples), and understand the chi-squared test and ANOVA.
• Understand inference, estimation, and the basics of hypothesis testing.
• Understand implications of multiple testing and Bonferroni correction.
• Understand and be able to correctly interpret p-values.
• Understand the importance and implications of Type I and Type II errors.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 5 hours.

Required Learning Resources and Activities

Module 4: Lesson 3:  Power and Sample Size

Student Learning Objectives:

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

• Understand factors that affect study power and sample size requirements, and how they impact study design.

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

Required Learning Resources and Activities

Module 4: Lesson 4:  Nonparametric Tests

Student Learning Objectives:

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

• Summarize and describe non-parametric tests and understand the conditions under which they are applied.
• Be able (1) to apply appropriate hypothesis tests to variable types in order to explore relationships and (2) to draw conclusions based on such hypothesis testing and to interpret p-values.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 1 hour.

Required Learning Resources and Activities

In the previous module, we learned methods we could use to decide whether to reject a null hypothesis based on the evidence we have. However, what if we want more than a simple yes/no answer and wish to precisely predict how the outcome changes as the predictors change? This is the reason we use regression models, as we will learn in this module. This module has four lessons, and the division is based on the nature of the outcome variable: if it is a continuous variable, we use simple or multiple linear regression; if it is a binary categorical variable, we use logistic regression. These represent some very common and basic statistical models; there are many more regression methods in the field, but learning the basic concepts well will help you quickly pick up other methods when you need to. You will notice that some concepts cross over from epidemiology, such as risk, odds, confounding, bias, etc. It is helpful to possess some prior knowledge in epidemiology, but if you don’t, these concepts will also be explained in this module.

Resources on regression can vary a great deal in their depth and complexity. Don’t let the math scare you. Focus on the main ideas to start, and add the mathematical details as you continue progressing in the topic.

The learning activity in this module asks you to go through some regression models. Even more so than hypothesis testing, the tedious calculation parts are done by the computer, but you will need to answer questions about the model and about using the model. These are essential skills that you will need in order to understand research literature and reports.

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

• Understand linear relationships, outliers, and the basics of correlation
• Understand the difference between correlation and simple linear regression, and when to apply one or the other
• Understand homoscedasticity and its applications to correlation and regression
• Understand linear regression and how it relates to prediction
• Understand multiple linear regression and its applications
• Understand simple logistic regression analysis
• Understand multiple logistic regression analysis and distinguish between adjusted and unadjusted regression coefficients
• Be able (1) to distinguish between risks, e.g., absolute and relative risks, as well as odds and odds ratios, and (2) to differentiate relative risks from odds ratios and know how to conduct both methods
• Be able (1) to distinguish between correlation, linear and multiple regression, and logistic regression, and (2) to understand the purpose and methods of linear (simple and multiple) and logistic regression, including when to use each of them
• Be able to specify regression models and interpret regression results

Module 5: Lesson 1: Simple Linear Regression Analysis

Student Learning Objectives:

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

• Understand linear relationships, outliers, and the basics of correlation.
• Understand the difference between correlation and simple linear regression, and when to apply one or the other.
• Understand homoscedasticity and its applications to correlation and regression.
• Understand linear regression and how it relates to prediction.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 5 hours.

Required Learning Resources and Activities

Module 5: Lesson 2:  Multiple Linear Regression Analysis

Student Learning Objectives:

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

• Understand multiple linear regression and its applications.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 1 hour.

Required Learning Resources and Activities

Module 5: Lesson 3:  Logistic Regression Analysis

Student Learning Objectives:

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

• Understand simple logistic regression analysis.
• Understand multiple logistic regression analysis and distinguish between adjusted and unadjusted regression coefficients.
• Be able (1) to distinguish between risks, e.g., absolute and relative risks, as well as odds and odds ratios, and (2) to differentiate relative risks from odds ratios and know how to conduct both methods.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 4 hours.

Required Learning Resources and Activities

Module 5: Lesson 4: Overview of Correlation and Regression Analysis

Student Learning Objectives:

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

• Be able (1) to distinguish between correlation, linear and multiple regression, and logistic regression, and (2) to understand the purpose and methods of linear (simple and multiple) and logistic regression, including when to use each of them.
• Be able to specify regression models and interpret regression results.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 1 hour.

Required Learning Resources and Activities

Health phenomena are complex. Often there are variables that interact with the variables in our primary relationship of interest. In order to understand how these other variables influence the primary association and to be sure that the effect we find actually reflects the relationship we are interested in, we can use some statistical tools to help us. This short module offers an introductory look at how to use biostatistics to identify the nature and extent of these influences. These tools are best used in conjunction with domain expertise; therefore, it is important that you also understand the context of a particular research question or a relationship.

The learning activity in this module is a mentored activity that ties together several aspects of statistical analysis in the context of a research project. We hope that through discussions with your mentor, you can further your understanding of these tools and see them in action.

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

• Know the definition of a confounder and understand the concepts of adjustment and stratification, as well as the concepts of confounding and effect modification
• Identify the statistical techniques for dealing with confounding and effect modification and their strengths and limitations
• Be able to comment on the validity of study conclusions with respect to confounding and alternative explanations and appreciate that association neither means causation nor indicates the directionality of potential cause and effect
• Identify potential confounders in a relationship from a theoretical perspective and understand the consequences of using faulty reasoning and improper methods in studies
• Apply analytical statistics in the context of a research project and be able to think critically about practical application of statistical concepts

Module 6: Lesson 1: Confounding and Effect Modification

Student Learning Objectives:

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

• Know the definition of a confounder and understand the concepts of adjustment and stratification, as well as the concepts of confounding and effect modification.
• Identify the statistical techniques for dealing with confounding and effect modification and their strengths and limitations.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 3 hours.

Required Learning Resources and Activities

Module 6: Lesson 2: Confounders and their Impact on Study Conclusions

Student Learning Objectives:

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

• Be able to comment on the validity of study conclusions with respect to confounding and alternative explanations and appreciate that association neither means causation nor indicates the directionality of potential cause and effect.
• Identify potential confounders in a relationship from a theoretical perspective and understand the consequences of using faulty reasoning and improper methods in studies.
• Apply analytical statistics in the context of a research project and be able to think critically about the practical application of statistical concepts.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 1 hour.

Required Learning Resources and Activities

As we come to the end of this course, it is time to review the major concepts in the context of public health research and practice. In this module, we will look at the importance of evidence-based decision-making, along with some tips and advice on how to read public health literature to spot misleading claims and inappropriate methods. Finally, we will look at two examples of how biostatistics is used in public health initiatives that benefit the population.

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

• Understand and explain the relative strengths and limitations of biostatistics as it applies in various settings in public health
• Be able to detect misleading claims and inappropriate methods in research papers as well as appreciate that a statistically significant result may not be clinically significant
• Appreciate that many interests may influence researchers towards favorable interpretation and presentation of their findings
• Understand that public health programs rely on biostatistics principles and methodologies to collect, analyze, use, and present data
• Relate specific public health contributions to biostatistics concepts learned in this course

Module 7: Lesson 1: Limitations and Misinterpretations of Biostatistics

Student Learning Objectives:

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

• Understand and explain the relative strengths and limitations of biostatistics as it applies in various settings in public health.
• Be able to detect misleading claims and inappropriate methods in research papers as well as appreciate that a statistically significant result may not be clinically significant.
• Appreciate that many interests may influence researchers towards favorable interpretation and presentation of their findings.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 3 hours.

Required Learning Resources and Activities

Module 7: Lesson 2: Biostatistics in Public Health Programs

Student Learning Objectives:

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

• Understand that public health programs rely on biostatistics principles and methodologies to collect, analyze, use, and present data.
• Relate specific public health contributions to biostatistics concepts learned in this course.

Approximate time required to complete the readings (at 144 words/minute) and assignments for this module: 1 hour.

Required Learning Resources and Activities