These source materials provide an introductory overview of descriptive statistics and probability within the life sciences, emphasizing the systematic handling of biological variation. The lesson details fundamental statistical vocabulary, the classification of qualitative and quantitative dataacross different measurement scales, and the organization of raw information into frequency distribution tables. Furthermore, it outlines the practical application of various graphical methods, including histograms, frequency polygons, pie charts, and scatter plots, to accurately visualize and interpret data sets.

This chapter provides a comprehensive overview of descriptive statistics, focusing on how to effectively summarize, analyze, and interpret complex data sets, particularly in biological contexts. This chapter breaks down data description into three core components: center, spread, and shape. It explores various measures of central tendency like the mean, median, and mode, detailing their specific applications and limitations. Additionally, the material covers measures of dispersion such as variance, standard deviation, and standard error, explaining how to quantify variability within sample groups. Finally, the chapter examine the shape of distributions through the concepts of skewness and kurtosis, teaching researchers how to identify data asymmetry, handle outliers, and choose appropriate analytical methods for skewed biological variables.

This chapter explains the transition from descriptive statistics to statistical inference, emphasizing the use of sample data to draw conclusions about broader populations. Key topics include fundamental sampling definitions, probability and non-probability sampling techniques, and the mechanics of the Central Limit Theorem to understand how sample means behave. The chapter also detail the construction and interpretation of confidence intervals, highlighting how to accurately estimate unknown population parameters while accounting for sample size and uncertainty. Ultimately, the it offers a comprehensive foundation for calculating standard errors, identifying sampling biases, and applying estimation formulas in practical biological and data-driven scenarios.

This chapter details the fundamental principles of hypothesis testing, establishing how researchers evaluate population claims using sample data. It explains the mechanics of formulating null and alternative hypotheses, computing test statistics, and utilizing p-values alongside significance levels to decide whether to reject or fail to reject the default assumption. Additionally, the chapter addresses the inevitability of Type I and Type II errors, outlines the concept of statistical power, and compares the applications of one-tailed versus two-tailed tests in scientific research.

This chapter explores descriptive statistics and probability distributions, focusing on how mathematical models represent both discrete counts and continuous measurements in biological contexts. It details three primary distributions—the Binomial, Poisson, and Normal—outlining their unique parameters, formulas, properties, and specific applications. Furthermore, the chapter explains how these different models relate to one another through mathematical approximations, such as using the central limit theorem and scaling rates. Finally, it provides practical guidance on choosing the correct statistical model based on experimental conditions, recognizing common calculation mistakes, and interpreting biological data.

This chapter provide a comprehensive guide to inferential statistics and biological applications, focusing primarily on hypothesis testing for means. Students learn how to execute and interpret Z-tests when population standard deviations are known, as well as Student's t-tests and Welch's t-tests for smaller or more variable samples. The material emphasizes matching specific statistical methods to experimental designs, such as utilizing paired-sample tests for before-and-after studies to eliminate subject-to-subject variation. Additionally, the chapter underscores the importance of checking assumptions, constructing confidence intervals alongside p-values, and understanding effect sizes rather than relying solely on automated software.

This chapter provides a comprehensive understanding to inferential statistics, focusing specifically on Analysis of Variance (ANOVA) and subsequent post-hoc testing methods used in biological research. It explains the statistical logic behind comparing multiple group means by analyzing underlying variances, detailing both one-way and two-way factorial designs to handle single or multiple explanatory variables simultaneously. It outlines the necessary mathematical formulas, core assumptions such as normality and homoscedasticity, and common analytical mistakes to avoid during data interpretation. Furthermore, the sources emphasize the importance of Tukey's Honestly Significant Difference (HSD) test for managing familywise error rates when identifying specific pairs of differing means following a significant overall test.

This chapter explores inferential statistics, distinguishing between parametric methods that require normal distributions and non-parametric alternatives like the Mann-Whitney U, sign, and Kruskal-Wallis tests, which rely on ranks and are ideal for skewed data or small samples. It also covers chi-square tests, detailing goodness-of-fit applications to determine if observed counts match theoretical genetic ratios, as well as tests of independence using contingency tables to evaluate the association between categorical variables. Furthermore, the chapter addresses assumptions, degrees of freedom, expected frequencies, and effect sizes such as Phi and Cramér's V. Finally, it provides practical biological examples, worked problems, and common analytical mistakes to help researchers correctly select and interpret these statistical tools.

This chapter outlines inferential statistics methods used to analyze quantitative data and biological relationships. Correlation analysis is explored through Pearson and Spearman coefficients to measure the strength and direction of linear and monotonic associations between variables. Simple linear regression provides a framework for predicting a response variable from a single predictor using the method of least squares and evaluating goodness of fit. Finally, multiple regression expands upon these concepts by incorporating multiple predictors to isolate specific effects, manage confounding variables, and address potential challenges like multicollinearity and overfitting.

This chapter outlines advanced statistical applications in ecology and epidemiology, focusing on quantifying biological communities and evaluating health risks. The first section of the chapter details biodiversity indices, such as the Shannon–Wiener and Simpson's indices, which measure species richness, evenness, and community similarity. The second section of the chapter explains population estimation techniques, highlighting the mark–recapture method and the Chapman estimator for calculating wildlife abundance and density. Finally, the third section of the chapter explores epidemiological measures like relative risk and odds ratios, demonstrating how researchers use cohort and case-control studies to analyze the association between exposures and diseases.