Model Based Statistics in Biology

D. C. Schneider

Department of Biology

Memorial University

St. John's, NL, Canada

BIOLOGY 4605 BIOLOGY 7220 Fall Term 2005

Preface	Course Outline and Organization	Lecture 1A

PART I. QUANTITATIVE BACKGROUND

Chapter 1	Model-based Statistics in the Natural and Social Sciences

1.1	The Role of Statistics in Science	Lecture 1C

1.2	Model Based Statistics in Biology	Lecture 1B

Verbal Models (Guess the Process)	Lab 1

1.3	Quantitative Reasoning	Lecture 2

Chapter 2	Quantities

2.1	Definition	Lecture 2

2.2	Types of Measurement Scale	Lecture 2

2.3	Data Collection, Recording, Error Checking	Lecture 3

2.4	Graphical and Tabular Display of Measured Quantities	Lecture 3

Critique of Graphs and Tables	Lab 5

2.5	Ratio Scale Units	Lecture 4

2.6	Dimensions	Lecture 4

2.7	Review Questions

Chapter 3	Rescaling Measured Quantities

3.1	Logical Re-scaling	Lecture 5A

3.2	Operations on Ratio Scale Quantities	Lecture 5A

3.3	Descriptive Statistics and Rescaling	Lecture 5A

3.4	Unit Conversion and Rigid Re-scaling	Lecture 5A

3.5	Review Questions

Chapter 4	Equations (Formal Models)	Lecture 6

4.1	Uses	Lecture 6

4.2	Reading and Translating Formal Models	Lecture 6

4.3	Homogeneity of Units	Lecture 6

4.4	Dimensional Homogeneity	Lecture 6

Lab 2

4.5	Review Questions

PART II. QUANTIFYING UNCERTAINTY

Chapter 5	Data Equations

5.1	Introduction	Lecture 7A

5.2	Deviations from a Single Value Model	Lecture 7A

5.3	Deviations from the Mean	Lecture 7A

5.4	Deviations from a Linear Trend	Lecture 7A

5.5	Deviations from the Means of Two or More Groups	Lecture 7B

5.6	Review Questions

Chapter 6	Frequency Distributions	Lecture 8

6.1	Empirical Frequency Distributions	Lecture 8

6.2	Theoretical Frequency Distributions -Notation	Lecture 9

6.3	Comparing Observed to Theoretical Frequency Distributions	Lecture 9

Lab 3

6.4	Review Questions

Chapter 7	Statistical Inference	Lecture 10

7.1	The Logic of Hypothesis testing

7.2	Hypothesis Testing with an Empirical Distribution	Lecture 10

Lab4

7.3	Hypothesis Testing with Cumulative Distribution Functions	Lecture 11

7.4	Parameter Estimates	Lecture 12

Lab 11

7.5	Confidence Limits	Lecture 12

7.6	Review Questions (Chapter 7)

7.7	Review Questions (Parts I and II)

PART III. THE GENERAL LINEAR MODEL. SINGLE EXPLANATORY VARIABLE

Chapter 8	Statistical Inference with the General Linear Model. Introduction	Lecture 13

Review Questions

Chapter 9	GLM Regression

9.1	Explanatory Variable Fixed by Experiment	Lecture 14A

Lab 6

9.2	Explanatory Variable Fixed into Classes	Lecture 14B

9.3	Explanatory Variable Measured with Error	Lecture 14C

9.4	Exponential Functions	new

9.5	Power Laws	Lecture 14D

9.6	Model Revision	new

9.7	Review Questions

Chapter 10	GLM. ANOVA

10.1	Single Sample t-test

10.2	Two Sample t-test	Lecture 15A

Lab 7

10.3	One way ANOVA, Fixed Effects	Lecture 15C

Lab 7

10.4	One way ANOVA, Random Effects	Lecture 15B

10.5	Review Questions

Chapter 11	Review of GLM, single explanatory variable.	Lecture 15D

11.1	Model Based versus Voodoo Statistics	Lecture 15D

11.2	Review of Concepts	Lecture 15D

11.3	Commentary on the Generic Recipe	Lecture 15D

11.4	Review Questions

PART IV. THE GENERAL LINEAR MODEL. MULTIPLE EXPLANATORY VARIABLES

Chapter 12	Multiple Regression

12.1	Two Explanatory Variables	Lecture 19

12.2	Three or More Explanatory Variables	new

12.3	Review Questions

Chapter 13	GLM. ANOVA. Multiple Factors

13.1	Fixed Effects without Interaction	Lecture 16A

13.2	Fixed Effects with Interaction	new

13.3	Fixed and Random Effects (Paired t-test)	new

Lab 8

13.4	Fixed and Random Effects (Randomized Block)	Lecture 16B

13.5	Fixed and Random Effects (Repeated Measures)	Lecture 16C

13.6	Nested Random Effects (Hierarchical ANOVA)	Lecture 17

13.7	More Than Two Factors	to be written

13.8	Review Questions

Chapter 14	GLM ANCOVA

14.1	Comparing Regression Lines	Lecture 18A

14.2	Statistical Control	Lecture 18B

14.3	Model Revision	Lecture 18C

Lab 8

14.4	More Than Two Explanatory Variables (to be written)	Lecture 18D

14.5	Review Questions

Chapter 15	Review of the General Linear Model	Lecture 20

Lab 9 / 10

Review Questions (Parts III and IV)

PART V. THE GENERALIZED LINEAR MODEL (GzLM).

Chapter 16	Analysis of Deviance

16.1	Goodness of Fit and Analysis of Deviance.	Lecture 22a

16.2	Analysis of Deviance for Normal Errors	Lecture 22b

16.3	Review Questions

Chapter 17	Poisson Response Variables

17.1	Poisson Regression	Lecture 23A

17.2	Single Categorical Explanatory Variable (Log-linear Model)	Lecture 23B

17.3	Single Categorical Explanatory Variable (Power of Test)	Lecture 23D

17.4	Two or More Categorical Explanatory Variables	Lecture 23C

17.5	Row by Column Contingency Test	Lecture 24C

17.6	Poisson ANCOVA	Lecture 23E

17.7	Model Revision	Lecture 23F

17.8	Review Questions

Chapter 18	Binomial Response Variables.

18.1	Logistic Regression (Dose - Response)	Lecture 24A

18.2	Single Factor. Prospective Analysis	Lecture 24B

18.3	Single Factor. Retrospective Analysis	Lecture 24B

18.4	Single Random Factor.	Lecture 24C

18.5	Two Categorical Explanatory Variables	Lecture 24D

18.6	Logistic ANCOVA	Lecture 24E

18.7	Review Questions

PART VI. EXTENSIONS OF THE GENERAL LINEAR MODEL

Chapter 19	Exploratory Data Analysis (EDA)

19.1	Introduction	Lecture 26A

19.2	Model Revision	Lecture 26B

19.3	Dropping Variables	Lecture 27A

19.4	Adding Variables	Lecture 27B

19.5	Review Questions

Chapter 20	Multivariate Analysis

20.1	Correlation	Lecture 28A

20.2	Correlation - Model Revision	Lecture 28B

20.3	Autocorrelation	Lecture 28

20.4	Canonical Analysis	Lecture 29

20.5	Review Questions

Chapter 21	Estimating Population Size	Lecture 30

Chapter 22	Review

Review of Numerical Methods in Biology	Lecture 31

Review of Statistical Inference

Review of the GLM	Lecture 32

Review Questions

How to use these lecture notes.

These lecture notes were first put on reserve in Fall term of 1997, at the request of several students taking the course. Usage was sufficient that the notes were again placed on reserved in Fall terms of 1998 and 2000. The notes were placed on a website in Fall of 2000.

The material covered in class (and hence in the lecture notes) is standard in content. However, the presentation of this material is unique in its emphasis on the model based approach to statistical analysis. This approach differs from that in undergraduate texts. Consequently the material covered in class (and hence in these notes) will be complementary to text presentations, rather than repeating the text approach.

These lecture notes contain detailed information used in class presentations.

These notes also contain more examples of concepts presented during class--usually only one example is presented for each concept in class.

You are responsible for concepts that are covered in class, rather than all of the concepts covered in these lecture notes.

So how should you use these notes ?

These lecture notes were put on reserve and on a website so they could be used in reviewing material presented in class. They were made available so that you could check detailed information, especially calculations, and graphical material presented in class. You should use them to check your own notes, and to review relative to your own notes, rather than as a substitute for taking notes.

Some students print copies and bring them to class, so they can highlight the points covered in class.

You can also use these notes as a source of more examples of concepts presented in class.

If you have questions about the concepts in these notes, be sure to see the instructor or one of the demonstrators.