Statistics for Ecologists           Presented by
by Schwarz, Inc
          Carl James Schwarz  
Fellow of the American Statistical Association
        Accredited Professional Statistician
           P.Stat. (Statistical Society of Canada),
           PStat® (American Statistical Association)

Course Notes for Intermediate Ecological Statistics

The course notes below illustrate methods of statistical analysis for ecologists using JMP, R, and SAS.
Instructions for installing R, JMP, SAS (and other softeware)..

Sample code used in the notes is available at: Stat-Ecology Datasets and code.

The suggested citation for a chapter of notes is:
      Schwarz, C. J. (2019). Chapter Name.
      In Course Notes for Intermediate Ecological Statistics.
      Available at Retrieved yyyy-mm-dd.

     Package Chapter and sections
     JMP R SAS 1 In the beginning...
           1.1 My favorite papers
           1.2 Introduction
           1.3 Effective note taking strategies
           1.4 It's all $\Gamma \rho \epsilon \epsilon \kappa $ to me
           1.5 Which computer package?
           1.6 FAQ - Frequently Asked Question
     JMP R SAS 2 Introduction to Statistics
           2.1 TRRGET - An overview of statistical inference
           2.2 Parameters, Statistics, Standard Deviations, and Standard Errors
           2.3 Confidence Intervals
           2.4 Hypothesis testing
           2.5 Meta-data
           2.6 Bias, Precision, Accuracy
           2.7 Types of missing data
           2.8 Transformations
           2.9 Standard deviations and standard errors revisited
           2.10 Other tidbits
     JMP R SAS 3 Sampling
           3.1 Introduction
           3.2 Overview of Sampling Methods
           3.3 Notation
           3.4 Simple Random Sampling Without Replacement (SRSWOR)
           3.5 Sample size determination for a simple random sample
           3.6 Systematic sampling
           3.7 Stratified simple random sampling
           3.8 Ratio estimation in SRS - improving precision with auxiliary information
           3.9 Additional ways to improve precision
           3.10 Cluster sampling
           3.11 Multi-stage sampling - a generalization of cluster sampling
           3.12 Analytical surveys - almost experimental design
           3.13 References
           3.14 Frequently Asked Questions (FAQ)
     JMP R SAS 4 Designed Experiments - Terminology and Introduction
           4.1 Terminology and Introduction
           4.2 Applying some General Principles of Experimental Design
           4.3 Some Case Studies
           4.4 Key Points in Design of Experiments
           4.5 A Road Map to What is Ahead
     JMP R SAS 5 Single Factor - Completely Randomized Designs (a.k.a. One-way design)
           5.1 Introduction
           5.2 Randomization
           5.3 Assumptions - the overlooked aspect of experimental design
           5.4 Two-sample $t$-test- Introduction
           5.5 Example - comparing mean heights of children - two-sample $t$-test
           5.6 Example - Fat content and mean tumor weights - two-sample $t$-test
           5.7 Example - Growth hormone and mean final weight of cattle - two-sample $t$-test
           5.8 Power and sample size
           5.9 Summary of two-sample $t$-tests
           5.10 ANOVA approach - Introduction
           5.11 Example - Comparing phosphorus content - single-factor CRD ANOVA
           5.12 Example - Comparing battery lifetimes - single-factor CRD ANOVA
           5.13 Example - Cuckoo eggs - single-factor CRD ANOVA
           5.14 Multiple comparisons following ANOVA
           5.15 Prospective Power and sample sizen - single-factor CRD ANOVA
           5.16 Pseudo-replication and sub-sampling
           5.17 Frequently Asked Questions (FAQ)
           5.18 Table: Sample size determination for a two sample $t$-test
           5.19 Table: Sample size determination for a single factor, fixed effects, CRD
           5.20 Scientific papers illustrating the methods of this chapter
           5.21 Summary of 1-factor CRD ANOVA
     JMP R SAS 6 Single factor - pairing and blocking
           6.1 Introduction
           6.2 Randomization protocol
           6.3 Assumptions
           6.4 Comparing two means in a paired design - the Paired $t$-test
           6.5 Example - effect of stream slope upon fish abundance
           6.6 Example - Quality check on two laboratories
           6.7 Example - Comparing two varieties of barley
           6.8 Example - Comparing prep of mosaic virus
           6.9 Example - Comparing turbidity at two sites
           6.10 Power and sample size determination
           6.11 Summary of paired $t$-tests
           6.12 Single Factor - Randomized Complete Block (RCB) Design
           6.13 Example - Comparing effects of salinity in soil
           6.14 Example - Comparing different herbicides
           6.15 Example - Comparing turbidity at several sites
           6.16 Power and Sample Size in RCBs
           6.17 Example - BPK: Blood pressure at presyncope
           6.18 Final notes
           6.19 Frequently Asked Questions (FAQ)
           6.20 Summary of 1-factor RCB ANOVA
     JMP R SAS 7 Incomplete block designs
           7.1 Introduction
           7.2 Example: Investigate differences in water quality
     JMP R SAS 8 Estimating an overall mean with subsampling
           8.1 Average flagellum length
     JMP R SAS 9 Single Factor - Sub-sampling and pseudo-replication
           9.1 Introduction
           9.2 Example - Fat levels in fish - balanced data in a CRD
           9.3 Example - fat levels in fish - unbalanced data in a CRD
           9.4 Example - Effect of UV radiation - balanced data in RCB
           9.5 Example - Monitoring Fry Levels - unbalanced data with sampling over time
           9.6 Example - comparing mean flagella lengths
           9.7 Final Notes
     JMP R SAS 10 Two Factor Designs - Single-sized Experimental units - CR and RCB designs
           10.1 Introduction
           10.2 Example - Effect of photo-period and temperature on gonadosomatic index - CRD
           10.3 Example - Effect of sex and species upon chemical uptake - CRD
           10.4 Power and sample size for two-factor CRD
           10.5 Unbalanced data - Introduction
           10.6 Example - Stream residence time - Unbalanced data in a CRD
           10.7 Example - Energy consumption in pocket mice - Unbalanced data in a CRD
           10.8 Example: Use-Dependent Inactivation in Sodium Channel Beta Subunit Mutation - BPK
           10.9 Blocking in two-factor CRD designs
           10.10 FAQ
     JMP R SAS 11 Two-factor split-plot designs
           11.1 Introduction
           11.2 The three basic structures
           11.3 Data and labeling experimental units.
           11.4 Assumptions
           11.5 Example - Tensile strength of paper - main plots in CRD
           11.6 Example - Biomass of trees - main plots in an RCB
           11.7 Example - Tenderness of meat - main plots in an RCB
           11.8 Example - Fungi degrading organic solvents - a split-plot in time
           11.9 Example - Home range - an unbalanced split-site plot in time
           11.10 Example - Floral scents and learning - pseudo-replication
           11.11 Example - Pheromone effects upon wild type and anarchist colonies of bee
           11.12 Repeated Measure Designs analyzed as a Split-Plot Analysis
           11.13 Example - Holding your breath at different water temperatures - BPK
           11.14 Example - Systolic blood pressure before presyncope - BPK
           11.15 Final notes
           11.16 Frequently Asked Questions (FAQ)
     JMP R SAS 12 Analysis of BACI experiments
           12.1 Introduction
           12.2 Before-After Experiments - prelude to BACI designs
           12.3 Simple BACI - One year before/after; one site impact; one site control
           12.4 Example: Change in density in crabs near a power plant - one year before/after; one site impact; one site control
           12.5 Simple BACI design - limitations
           12.6 BACI with Multiple sites; One year before/after
           12.7 Example: Density of crabs - BACI with Multiple sites; One year before/after
           12.8 BACI with Multiple sites; Multiple years before/after
           12.9 Example: Counting fish - Multiple years before/after; One site impact; one site control
           12.10 Example: Counting chironomids - Paired BACI - Multiple-years B/A; One Site I/C
           12.11 Example: Fry monitoring - BACI with Multiple sites; Multiple years before/after
           12.12 A statistical diversion
           12.13 Closing remarks about the analysis of BACI designs
           12.14 BACI designs power analysis and sample size determination
     JMP R SAS 13 Comparing proportions - Chi-square ($\chi ^2$) tests
           13.1 Introduction
           13.2 Response variables vs. Frequency Variables
           13.3 Overview
           13.4 Single sample surveys - comparing to a known standard
           13.5 Comparing sets of proportions - single factor CRD designs
           13.6 Pseudo-replication
           13.7 Simpson's Paradox - Combining tables
           13.8 More complex designs
           13.9 Final notes
           13.10 Appendix - how the test statistic is computed
           13.11 Fisher's Exact Test
           13.12 Summary of 1-factor CRD chi-square tests
     JMP R SAS 14 Correlation and simple linear regression
           14.1 Introduction
           14.2 Graphical displays
           14.3 Correlation
           14.4 Single-variable regression
           14.5 A no-intercept model: Fulton's Condition Factor $K$
           14.6 Frequent Asked Questions - FAQ
           14.7 Summary of simple linear regression
     JMP R SAS 15 Detecting trends over time
           15.1 Introduction
           15.2 Simple Linear Regression
           15.3 Transformations
           15.4 Pseudo-replication
           15.5 Introduction
           15.6 Power/Sample Size
           15.7 Power/sample size examples
           15.8 Testing for common trend - ANCOVA
           15.9 Example: Degradation of dioxin - multiple locations
           15.10 Example: Change in yearly average temperature with regime shifts
           15.11 Dealing with Autocorrelation
           15.12 Dealing with seasonality
           15.13 Seasonality and Autocorrelation
           15.14 Non-parametric detection of trend
           15.15 Summary
     JMP R SAS 16 Regression with pseudo-replication
           16.1 Introduction
           16.2 Example: Selenium concentration in fish tissue
           16.3 Pseudo-replication when regression is over time
           16.4 Comparing slopes after environmental impact
     JMP R SAS 17 Regression - hockey sticks, broken sticks, piecewise, change points
           17.1 Hockey-stick, piecewise, or broken-stick regression
           17.2 Searching for the change point
           17.3 What is the first time that a treatment mean differ from a control mean
     JMP R SAS 18 Analysis of Covariance - ANCOVA
           18.1 Introduction
           18.2 Assumptions
           18.3 Comparing individual regression lines
           18.4 Comparing means after covariate adjustments
           18.5 Power and sample size
           18.6 Example: Degradation of dioxin - multiple locations
           18.7 Example: Change in yearly average temperature with regime shifts
           18.8 Example - More refined analysis of stream-slope example
           18.9 Example: Comparing Fulton's Condition Factor $K$ among groups
           18.10 Final Notes
     JMP RNA 19 Multiple linear regression
           19.1 Introduction
           19.2 Example: Blood pressure vs.\ age, weight, and stress
           19.3 Regression problems and diagnostics
           19.4 Polynomial, product, and interaction terms
           19.5 The general linear test
           19.6 Indicator variables
           19.7 Example: Degradation of dioxin - multiple locations
           19.8 Example - More refined analysis of stream-slope example
           19.9 Example: Predicting PM10 levels
           19.10 Model selection methods
     JMP R SAS 20 Logistic Regression
           20.1 Introduction
           20.2 Data Structures
           20.3 Assumptions made in logistic regression
           20.4 Example: Space Shuttle - Single continuous predictor
           20.5 Example: Predicting Sex from physical measurements - Multiple continuous predictors
           20.6 Retrospect and Prospective odds-ratio
           20.7 Example: Parental and student usage of recreational drugs - $2 \times 2$ table.
           20.8 Example: Effect of selenium on tadpoles deformities - $2 \times k$ table.
           20.9 Example: Pet fish survival - Multiple categorical predictors
           20.10 Example: Horseshoe crabs - Continuous and categorical predictors.
           20.11 Assessing goodness of fit
           20.12 Complete Separation in Logistic Regression
           20.13 Final Words
           20.14 Summary of simple logistic regression and logistic ANOVA
     JMP R SAS 21 Logistic Regression - Advanced Topics
           21.1 Introduction
           21.2 Sacrificial pseudo-replication
           21.3 Example: Fox-proofing mice colonies - dealing with sacrificial pseudo replication
           21.4 Example: Over-dispersed Seed Germination Data
           21.5 Example: Are mosquitos choosy? A preference experiment.
           21.6 Example: Reprise: Are mosquitos choosy? A preference experiment with complete blocks.
           21.7 Example: Reprise: Are mosquitos choosy? A preference experiment with INCOMPLETE blocks.
     JMPNA NA 22 Poisson Regression
           22.1 Introduction
           22.2 Experimental design
           22.3 Data structure
           22.4 Single continuous $X$ variable
           22.5 Single continuous $X$ variable - dealing with overdispersion
           22.6 Single Continuous $X$ variable with an OFFSET
           22.7 ANCOVA models
           22.8 Categorical $X$ variables - a designed experiment
           22.9 Log-linear models for multi-dimensional contingency tables
           22.10 Variable selection methods
           22.11 Summary
     JMP R SAS 23 A short primer on residual plots
           23.1 Linear Regression
           23.2 ANOVA residual plots
           23.3 Logistic Regression residual plots - Part I
           23.4 Logistic Regression residual plots - Part II
           23.5 Poisson Regression residual plots - Part I
           23.6 Poisson Regression residual plots - Part II
     JMPNA NA 24 Time Series - a VERY brief introduction
           24.1 Introduction
           24.2 Fundamental material
           24.3 White noise and autocorrelation in regression
           24.4 Detrending, Differencing and Integration
           24.5 Autoregressive Models on stationary series
           24.6 Moving Average Models on stationary series
           24.7 Combining Moving Average and Autoregressive Models - \ensuremath {\textit {ARIMA
           24.8 Model Selection - I
           24.9 Estimation
           24.10 Model Selection - II - AIC
           24.11 Model checking
           24.12 Forecasting
           24.13 Summary
     JMP R SAS 25 Tables
           25.1 A table of uniform random digits
           25.2 Selected {\bf Binomial
           25.3 Selected {\bf Poisson
           25.4 Cumulative probability for the {\bf Standard Normal Distribution
           25.5 Selected percentiles from the {\bf $t$-distribution
           25.6 Selected percentiles from the {\bf chi-squared-distribution
           25.7 Sample size determination for a two sample $t$-test
           25.8 Power determination for a two sample $t$-test
           25.9 Sample size determination for a single factor, fixed effects, CRD
           25.10 Power determination for a single factor, fixed effects, CRD
     JMP R SAS 26 THE END!
           26.1 Statisfaction - with apologies to Jagger/Richards
           26.2 ANOVA Man with apologies to Lennon/McCartney
     JMP R SAS 27 An overview of environmental field studies
           27.1 Introduction
           27.2 Analytical surveys
           27.3 Impact Studies
           27.4 Conclusion
           27.5 References
           27.6 Selected journal articles
           27.7 Examples of studies for discussion - good exam questions!
     JMP R SAS 28 Case Studies
           28.1 Case Study - Can bees learn?
           28.2 Case Study - Effect of dissolved gas upon fish behavior
           28.3 Case Study - Excessive post-exercise oxygen consumption (EPOC) of fish following exposure to rotenone
           28.4 Case Study - Gas Monitoring in Kelowna
           28.5 Case Study - lichen growth
           28.6 Case Study - Swimming performance of fish following exposure to rotenone
           28.7 Case Study - Effect of an exploration camp upon wolverine behavior

Reanalysis of data from published papers

Material not yet integrated into the above notes

Short courses that are available - send me an email for details.

These are typically 3 days in length and can be offered as a block of 3 days, or spread over several weeks (e.g. 1/2 day per week over 6 weeks). Many of these have been offered via the
Columbia Mountains Institute of Applied Ecology. I can also give these short courses at your own site. Unfortunately, SFU's Distance Education faculty has shown NO interest in offering these through SFU.

Additional Teaching materials - past exams; sample mid-terms; assignments, etc. These materials are graduatlly being merged into my general course notes

  • StatVillage - a clickable map using real census data
  • On-line experimental design - a system for generating computer experiments
    Email comments or suggestions to Carl Schwarz (
    © 2019 Carl James Schwarz Last updated 2019-11-30