Statistics for Ecologists |
Presented by StatMathComp Consulting 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) |
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 | |||||
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 | R | NA | 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. | |||||
JMP | NA | 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 | |||||
JMP | NA | 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 |