by Raluca Balan (University of Ottawa, Canada) & Gilles Lamothe (University of Ottawa, Canada)

Chapter 3: Axioms of Probability (231k)
Chapter 5: Independence (86k)
Chapter 11: Hypothesis Testing (362k)

Data Sets

Statistical reasoning and modeling are of critical importance to modern biology. This textbook introduces fundamental concepts from probability and statistics which will pave the way for the student of biology to become a well-rounded scientist. No previous study of probability or statistics is assumed. Calculus topics are not used extensively in this book, though some integration and differentiation are expected. The calculus prerequisite is primarily intended to assure a certain level of mathematical maturity.

This book puts emphasis on examples, which are presented to motivate the theory. The presentation style is concise and self-contained, briefly including the mathematical elements that are needed for studying probability and statistics. The examples are relevant to students in the life sciences with interests in genetics, biology, ecology, health, etc.

We believe that aspects of probability theory are of biological interest and that probability underlies the theory of inferential statistics. Thus, we place an equal emphasis on probability and statistics which are both essential for solving and understanding many types of biological problems.

• Probability:
  • Introduction to Probability
    • Interpreting Probabilities
  • Elementary Genetics and Probability
    • Tree Diagrams and Punnett Squares
    • Computation Methods
    • Problems
  • Axioms of Probability
    • Venn Diagrams
    • Addition Rule
    • Problems
  • Conditional Probability
    • Definition
    • Multiplication Rule
    • Bayes' Rule
    • Problems
  • Independence
    • Statistical Independence
    • Problems
  • Discrete Random Variables
    • Definition
    • Binomial Distribution
    • Poisson Distribution
    • Problems
  • Continuous Random Variables
    • Definition
    • Normal Distribution
    • Problems
  • Supplementary Problems (Probability)
• Statistics:
  • Introduction to Statistics
    • Random Sampling and Data Description
    • Sampling Distributions and Point Estimation
    • Assessing Normality
    • Problems
  • Confidence Intervals
    • Confidence Intervals for the Mean: σ² Known
    • Confidence Intervals for the Mean: σ² Unknown
    • Confidence Intervals for the Proportion
    • Problems
  • Hypothesis Testing
    • Hypothesis Testing for the Mean: σ² Known
    • Hypothesis Testing for the Mean: σ² Unknown
    • Hypothesis Testing for the Proportion
    • Problems
  • Comparison of Two Independent Samples
    • Study/Experimental Design
    • Confidence Intervals and Tests for Means
    • Confidence Intervals and Tests for Proportions
    • Problems
  • Paired Samples
    • Confidence Intervals for μ_D
    • Hypothesis Testing for μ_D
    • Problems
  • Categorical Data
    • Test of Independence
    • Test of Homogeneity
    • Problems
  • Regression and Correlation
    • Least Squares Line
    • Regression Model
    • Correlation
    • Problems
  • Supplementary Problems (Statistics)