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ANALYSIS OF BIOLOGICAL DATA BIOL4062/5062 Hal Whitehead

ANALYSIS OF BIOLOGICAL DATA BIOL4062/5062 Hal Whitehead

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ANALYSIS OF BIOLOGICAL DATA

BIOL4062/5062

Hal Whitehead

• Introduction

• Assignments

• Tentative schedule

• Analysis of biological data

• Instructor: Hal Whitehead– LSC3076 (Ph 3723; email [email protected])– Best times: 8:00-9:00 a.m.

• Teaching Assistant: ?

• Other instructors– Dr David Lusseau

Why “Analysis of Biological Data”?

• Biologists– increasingly using quantitative techniques

– to analyze larger and larger data sets

– need skills in data analysis• especially in broad area of ecology

• BIOL4062/5062– introduce techniques for analysis of biological data

– emphasis will be on the practical use and abuse of techniques, not derivations or mathematical formulae

– in assignments students explore real and realistic data sets

Related classes

• Design of Biological Experiments (BIOL4061/5061)

– most useful for those who work with systems that can be manipulated

• Courses in Statistics– more emphasis on mathematical sides

Some books (on reserve)

• Legendre, L. and P. Legendre. Numerical Ecology (2nd edition). Elsevier (1998)

• Manly, B.F.J. Multivariate statistical methods: a primer (2nd edition). Chapman & Hall (1994)

• Other books:– Many, do not need to be right up to date

Computer programs

• MINITAB

• SPSS

• SYSTAT

• SAS

• MATLAB (Statistics toolbox)

• S-plus

• R

Good, comprehensivepackages, can do analyses for this class

More sophisticatedand powerful,harder to use

Computer programs• MINITAB * †• SPSS * †• SYSTAT †• SAS * †• MATLAB (Statistics toolbox)• S-plus (freely available at Dal.?)• R † (freely available on the web)* on GS.DAL.CA

† in Biology-Earth Sciences computer lab

Support from ?

Support from Hal

Assignments

• Type 1– artificial data sets for trying different

techniques

• Type 2– real data set to try a real analysis

Type 1 assignments

• Five assignments, sent by email (next few days)

• Each 10% final mark

• Artificial but realistic data sets– Different data sets to each student, but

structurally similar– More analyses expected for graduate students

(BIOL5062)

• Analyze using a computer statistical package

Type 1 assignments• Hand in a short write-up, explaining clearly:

– what you did– what you found– what you think the results might mean biologically

• Beware of:– Rubbish!

• Check the results against patterns in the original data to make sure they make sense.

– Over-interpreting the results– Not answering the questions posed

Type 1 assignments

• Five assignments:– Multiple regression 10%– Log-linear models 10%– Principal components analysis 10%– Discriminant function analysis 10%– Cluster analysis, multidimensional scaling,

network analysis 10%

Type 2 assignment

• Find a biological data set, and then analyze it

• The analysis should not be:– part of past, present, or future Honours, MSc or

PhD thesis, or used for another class:

self-plagiarism– that, or repeat that, done by someone else:

plagiarism

Type 2 assignment

• The analysis can– use same data as in thesis or another course, but

totally different analysis– use data collected by your supervisor, or someone

else, but you should ask them– use a data set that you find on the web, or somewhere

else, but you should check that it is OK– be submitted for publication, but you must check that

you have all necessary permissions

Type 2 assignment• Minimum sizes of data set (ask Hal for exceptions or in case

of uncertainty):– For undergraduates (BIOL4062):

• >50 units x >3 variables

– For graduates (BIOL5062)• >50 units x >5 variables• either, two types of variables

– e.g. “Dependent; Independent”; “Species; Environment”

• or, link two data sets with one at least as large as the undergraduate data set

• Must address at least 3 biological questions (BIOL4062), or 4 questions (BIOL5062)

Type 2 assignment (4 steps)• a) Short meeting with Hal or *** to discuss your proposed data

set and proposed analysis: feedback– bring draft of 2b assignment

• b) Description of data set and proposed analysis.– where it came from– its structure(s) (number of variables, units, names of variables, types

of variables, ...)– proposed biological questions– proposed analytical methods– possible problems

– Example on web

Type 2 assignment (4 steps)• c (i) Presentation of results to the class by graduate

students– biological questions being addressed– brief description of the data set– how you analyzed it– conclusions– Example in Class

• c(ii) Undergraduate students should go to graduate presentations and will be tested on general issues arising from them on last day

Type 2 assignment (4 steps)• d) Write-up of your analysis as for a scientific journal paper

– Max 5 pages (4062) or 7 pages (5062) single-spaced• excluding references, tables, figures

– Explain biological question, methods in sufficient detail for someone to replicate them, problems, and biological conclusions

– Show graphically, or in tables, the major effects• Do not just present summaries of ordinations or significance levels of hypotheses

tests

– Introduction and Discussion can be shorter and less detailed than in published paper

• sufficient to give a good feel for biological issue being examined and the potential biological significance of the results

Example on web

Type 2 assignment• Marks

• 2b Description of data set and proposed analysis 5%

• 2c 15%– (i) Presentation of results by graduate students

(BIOL5062)– (ii) Test on general principles from graduate student

presentations (BIOL4062)

• 2d Write-up of results 30%

SYSTATdemo.at end oflectures

DateTopic

Who ExamplesType 1 Assignments

6-Sep Thurs Introduction to data analysis and the course HW11-Sep Tues Modes of statistical analysis HW TREE13-Sep Thurs Plotting and tabulating data and results HW SYSTAT18-Sep Tues Introduction to S-plus and R (optional) S-Plus20-Sep Thurs Correlation HW SYSTAT25-Sep Tues Linear regression HW SYSTAT27-Sep Thurs Multiple linear regression, path analysis HW SYSTAT 1a give

2-Oct Thurs General linear models HW SYSTAT4-Oct Tues Introduction to likelihood HW SYSTAT9-Oct Thurs Logistic regression HW SYSTAT 1a due

11-Oct Tues Categorical data and log-linear models HW SYSTAT 1b give16-Oct Thurs Introduction to multivariate analysis and

multivariate distances HW SYSTAT18-Oct Tues Principal Components Analysis HW SYSTAT 1c give23-Oct Thurs Network analysis-1 DL 1e give25-Oct Tues Network analysis-2 DL 1b due30-Oct Thurs Discriminant Function Analysis and Canonical

Variate Analysis HW SYSTAT1d give

1-Nov Thurs Canonical Correlation Analysis, Redundancy Analysis and Canonical Correspondence Analysis HW SYSTAT

1c due

6-Nov Tues Principal Coordinate Analysis, Correspondence Analysis and Multidimensional Scaling HW SYSTAT

1e give

8-Nov ThursCluster analyses

HW SYSTAT1e give; 1d due

13-Nov Tues Bootstraps and Jackknives HW SYSTAT15-Nov Thurs Permutation tests, Mantel tests and matrix

correlations HW SYSTAT1e due

20-Nov Tues Graduate presentations HW22-Nov Thurs Graduate presentations HW27-Nov Tues Graduate presentations HW29-Nov Thurs Test for undergraduates (BIOL4062) on grad.

student projects HW

Analysis of Biological Data

• Types of biological data

• History (very abbreviated!)

• The process of biological data analysis– why garbage may come out

• Hypothesis testing and data analysis– assumptions– other issues

Types of biological data

• Morphometric• Community ecology

– organism distribution and environmental variation

• Genetic data for ecological and evolutionary questions

• Population data for management, conservation, evolutionary questions

• Behavioural, physiological, ...

Development of biological data analysis• >~1850 Displays• >~1900 ANOVA's, regression, correlation

– without computers

• >~1930 Non-parametric methods• >~1970 Multiple regression and multivariate analysis

– matrix algebra using computers

• >~1980 Robust methods: bootstraps, jackknives, permutations– need powerful computers

Real Biological System

Stochastic error Measurement error

Data Model+Assumptions

Data Analysis

Inferences about Biological System

Sampling process

Garbage in => Garbage out• Good data + Errors => Garbage

in => Garbage out– Check data entry

• Good data + Errors in routine => Garbage out– Check results, run routines on data

with known answer,– run on 2 routines

• Good data + Wrong model => Garbage out– Think about, read about and

discuss model

Real Biological System

Stochastic error Measurement error

Data Model+Assumptions

Data Analysis

Inferences about Biological System

Sampling process

Hypothesis Testing Data AnalysisHypothesis

Experimental Design

Experiment

Analysis

Conclusion

[ANOVA, T-test]Agriculture

Experimental ecology

Physiology

Animal behaviour

Data Collection

Data Analysis

Hypothesis

[scatter plots, box plots, most multivariate analyses]

Fisheries

Community ecology

Paleontology

Some assumptions• Normality

– can only be properly examined on large data sets– mainly a problem on small ones– an important issue for hypothesis testing– normality desirable in data analysis

• Linearity– makes hypothesis testing easier– makes data analysis easier

• Independence– major problem for hypothesis testing– no problem, or advantage, in data analysis

Transformdataor usenon-linear ornon-parametricmethods

Other issues in data analysis

• Missing data– Often present in ecological data

• Outliers– What do we do with apparent outliers?– Remove them?

• Multiple comparisons– Major issue with hypothesis testing– Not an issue with data analysis

• although: Patterns appear in random data

Next class:

• Inference in ecology and evolution:– Null hypothesis statistical tests– Effect size statistics– Bayesian statistics– Information theoretic model comparisons

DateTopic

Who ExamplesType 1 Assignments

6-Sep Thurs Introduction to data analysis and the course HW11-Sep Tues Modes of statistical analysis HW TREE13-Sep Thurs Plotting and tabulating data and results HW SYSTAT18-Sep Tues Introduction to S-plus and R (optional) S-Plus20-Sep Thurs Correlation HW SYSTAT25-Sep Tues Linear regression HW SYSTAT27-Sep Thurs Multiple linear regression, path analysis HW SYSTAT 1a give

2-Oct Thurs General linear models HW SYSTAT4-Oct Tues Introduction to likelihood HW SYSTAT9-Oct Thurs Logistic regression HW SYSTAT 1a due

11-Oct Tues Categorical data and log-linear models HW SYSTAT 1b give16-Oct Thurs Introduction to multivariate analysis and

multivariate distances HW SYSTAT18-Oct Tues Principal Components Analysis HW SYSTAT 1c give23-Oct Thurs Network analysis-1 DL 1e give25-Oct Tues Network analysis-2 DL 1b due30-Oct Thurs Discriminant Function Analysis and Canonical

Variate Analysis HW SYSTAT1d give

1-Nov Thurs Canonical Correlation Analysis, Redundancy Analysis and Canonical Correspondence Analysis HW SYSTAT

1c due

6-Nov Tues Principal Coordinate Analysis, Correspondence Analysis and Multidimensional Scaling HW SYSTAT

1e give

8-Nov ThursCluster analyses

HW SYSTAT1e give; 1d due

13-Nov Tues Bootstraps and Jackknives HW SYSTAT15-Nov Thurs Permutation tests, Mantel tests and matrix

correlations HW SYSTAT1e due

20-Nov Tues Graduate presentations HW22-Nov Thurs Graduate presentations HW27-Nov Tues Graduate presentations HW29-Nov Thurs Test for undergraduates (BIOL4062) on grad.

student projects HW

Performance in BIOL4062/5062

• Graduate students (BIOL5062)– some do well with rather little effort– some do well with a lot of effort

• Undergraduate students (BIOL4062)– most do well with some effort

• adequate statistical background

– some do poorly• inadequate statistical background or effort