Statistics for Ecologists Presented by StatMathComp Consultingby 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 http://www.stat.sfu.ca/~cschwarz/CourseNotes. 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
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
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
5.18 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
6.20 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
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

## 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 (cschwarz@stat.sfu.ca)
© 2019 Carl James Schwarz Last updated 2019-11-30