Biometry Course

Lesson 1 • Organising and Displaying Data

Raw biological data must be structured before analysis. Frequency tables, histograms, and stem-and-leaf plots reveal distributional patterns.

Lesson 2 • Types of Biological Data

Biological variables are classified by measurement scale and structure. Understanding data types determines which statistical methods are appropriate.

Lesson 3 • Measurement and Sampling Concepts

Accurate measurement and representative sampling underpin valid biological inference. This section introduces error sources and sampling logic.

Lesson 1 • Exploratory Data Analysis Techniques

Box-and-whisker plots, scatter plots, and summary tables support rapid pattern detection. EDA precedes formal inference and reveals outliers and grouping effects.

Lesson 2 • Measures of Central Tendency

Mean, median, and mode each capture a different aspect of a distribution's centre. Choosing the right measure depends on data type and skewness.

Lesson 3 • Measures of Dispersion

Variance, standard deviation, and range quantify variability in biological measurements. Dispersion measures complement central tendency for full data description.

Lesson 1 • Sampling Distributions and the Central Limit Theorem

The sampling distribution of the mean enables inference from samples to populations. The central limit theorem justifies normal-based methods for large samples.

Lesson 2 • Discrete Probability Distributions

Binomial, Poisson, and negative binomial models describe count data in biology. Each distribution's assumptions and parameters are linked to biological processes.

Lesson 3 • Continuous Probability Distributions

Normal, log-normal, and exponential distributions model continuous biological traits. Parameter estimation and probability calculations are practised with biological examples.

Lesson 1 • One-Sample and Two-Sample Tests

Z-tests and t-tests compare sample statistics to reference values or between groups. Assumptions of normality and equal variance are verified before application.

Lesson 2 • Nonparametric Alternatives

When normality assumptions fail, rank-based tests provide valid inference. Mann-Whitney, Wilcoxon, and Kruskal-Wallis tests are applied to biological data.

Lesson 3 • Logic of Hypothesis Testing

Null and alternative hypotheses frame biological questions as testable claims. Type I and Type II errors define the cost of incorrect decisions.

Lesson 1 • One-Way ANOVA

One-way ANOVA tests equality of means across three or more groups simultaneously. The F-ratio partitions total variation into between-group and within-group components.

Lesson 2 • Two-Way and Factorial ANOVA

Two-way ANOVA evaluates main effects and interactions between two factors. Interaction plots reveal whether factor effects depend on each other.

Lesson 3 • Experimental Design Principles

Randomisation, replication, and blocking reduce bias and increase precision. Common designs—CRD, RCB, and Latin square—are matched to biological scenarios.

Lesson 4 • Multiple Comparison Procedures

Post-hoc tests identify which group pairs differ after a significant ANOVA result. Familywise error rate control is essential when making multiple comparisons.

Lesson 1 • Correlation Analysis

Pearson and Spearman coefficients measure the strength and direction of bivariate associations. Correlation does not imply causation, a distinction critical in biology.

Lesson 2 • Nonlinear and Polynomial Regression

Biological growth, dose-response, and enzyme kinetics often follow nonlinear patterns. Polynomial and intrinsically nonlinear models capture these curved relationships.

Lesson 3 • Multiple Linear Regression

Multiple predictors are combined to explain biological variation more completely. Model selection, multicollinearity, and adjusted R-squared guide variable inclusion.

Lesson 4 • Regression Model Validation

Cross-validation and influence diagnostics ensure models generalise beyond the training data. Cook's distance and leverage statistics identify influential observations.

Lesson 1 • Logistic Regression for Binary Outcomes

Logistic regression models the probability of a binary biological event as a function of predictors. Odds ratios from logistic models quantify predictor effects.

Lesson 2 • Goodness-of-Fit Tests

Goodness-of-fit tests compare observed frequencies to theoretically expected distributions. Applications include testing Mendelian ratios and Hardy-Weinberg equilibrium.

Lesson 3 • Contingency Tables and Chi-Square Tests

Contingency tables cross-classify two or more categorical variables. Chi-square tests assess independence between biological traits or treatment outcomes.

Lesson 1 • Ordination and Community Analysis

NMDS and canonical correspondence analysis reveal ecological gradients in species data. These methods connect multivariate patterns to environmental predictors.

Lesson 2 • Discriminant Analysis

Linear discriminant analysis classifies biological specimens into predefined groups. Cross-validated error rates assess classification accuracy for new observations.

Lesson 3 • Cluster Analysis

Hierarchical and k-means clustering group biological specimens by multivariate similarity. Dendrograms and silhouette plots evaluate cluster quality and biological meaning.

Lesson 4 • Multivariate Analysis of Variance

MANOVA tests simultaneous group differences across multiple response variables. Pillai's trace and Wilks' lambda are the primary test statistics used.