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Website http://www.mun.ca/biology/quant/

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Websitehttp://www.mun.ca/biology/quant/

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Welcome to Biology 4605 / 7220Model Based Statistics in Biology

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Cookie Experiment

Was there a preference?Chocolate chip Cinnamon Rolls

Are they different?Use statistics – Binomial Test!

= =

χ2 = p-value =

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Are we feeding you a bunch of lies?

Leonard Henry Courtney(1832-1918)

• Do statisticians use a bunch of fancy tests to bolster weak arguments?

• Are stats misused and misinterpreted?

There are three kinds of lies; lies, damned lies and statistics.- Journal of the Royal Statistical

Society, No. 59 (1896)

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• Problems:– Rare events– Zero-inflated– Mean is inappropriate

• Hypothetical example: Less than one endangered species was observed per transect (mean: 0.57 ind./transect). Proceed with development!

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Statistics are Balderdash!

Ernest Rutherford (1871-1937)

If your experiment needs statistics, you ought to have

done a better experiment

• Fair Enough….• Balance is important• What about field studies?

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No! Hypothesis testing is inevitable

Every experiment may be said to exist only in order to give the facts a chance of

disproving the null hypothesis R.A. Fisher

(1890-1962)

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Hypothesis testing is statistical flotsam

Everyone will have his own pet assortment of flotsam; mine include most of the

theory of significance testing, including multiple comparison tests, and non

parametric statistics.

John Nelder(1949-2010)

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The trouble with significance testingElementary statistics courses for biologists tend to lead to the use of a stereotyped set of tests:1. Without critical attention to the underlying model involved;2. Without due regard to the precise distribution of sampling

errors;3. With little concern for the scale of measurement;4. Careless of dimensional homogeneity;5. Without considering the ideal transformation;6. Without any attempt at model simplification;7. With too much emphasis on hypothesis testing and too little

emphasis on parameter estimation.- M.J. Crawley 1993

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So how should we analyse our data?!1. Use Model Based Statistics2. Don’t let significance testing do the

thinking for you

You are always better off thinking about why a model could generate your data and then testing that model- L. Wilkinson et al. 1992

Model

Plant height

Tim

e in

sun

light

Data

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Classic approach

• Identify a test by name.• Check its assumptions.• Use automated routines

provided in a package.• Sort through the output for

a p-value.• Report whether p was less

than 5%.

Model Based approach

• What is the response variable?

• What are the explanatory variables?

• Write the model.• Check the residuals. Model

appropriate? Error structure correct?

• Take corrective action. • Report the model,

parameter values, and standard errors.X

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In short:Write the model* and discard the search for tests

Plant height

Tim

e in

sun

light

Data = Model + Residual Y = mX + b + Residual

(Regression)

*Don’t panic…writing a model is easy

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How to conceptualise a modelQuick example

Data

Verbal

Graphical Formal

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Data

Verbal

Graphical Formal

R M1 0

1 25

2 0

2 50

3 25

4 0

4 25

4 50

5 0

5 25

5 75

5 100

5 150

5 175

5 200

6 25

6 50

6 75

6 125

6 150

6 175

7 0

7 25

8 0

8 50

9 25

10 0

10 25

Continued…

M = Catch of scallops (kg)R = Seabed roughness (acoustic values)

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Data

Verbal

Graphical Formal

R M1 0

1 25

2 0

2 50

3 25

4 0

4 25

4 50

5 0

5 25

5 75

5 100

5 150

5 175

5 200

6 25

6 50

6 75

6 125

6 150

6 175

7 0

7 25

8 0

8 50

9 25

10 0

10 25

Continued…

M = Catch of scallops (kg)R = Seabed roughness (acoustic values)

Grab samples:5&6 = Gravel1-4 = Sand7-10 = Cobble

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Data

Verbal

Graphical Formal

Catch is higher in gravel thanin finer (sand) or coarser(cobble) substrates

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Data

Verbal

Graphical Formal

Catch is higher in gravel thanin finer (sand) or coarser(cobble) substrates

• No obvious linear trend

• Simplify– Two means model

(gravel vs. other)

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Data

Verbal

Graphical Formal

Catch is higher in gravel thanin finer (sand) or coarser(cobble) substrates

Two mean modelM = K1 if R = 5 or 6 (gravel)M = K2 if R not equal 5 or 6

Data = Model + Residual M = [K1 ,K2] + Residuals

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The General Linear Model

Data = Model + Normal Residual

Data = [Two means] + Normal residual } t-test

Data = [Several means] + Normal residual } Oneway ANOVA

Data = [Two factors] + Normal residual } twoway ANOVA

Data = [Line] + Normal residual } Regression

Data = [Line + factors] + Normal residual } ANCOVA

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Reasons for the model based approach

1. Statistics is modelling

2. Carryover: biological models statistics

3. Model approach leads to learning of concepts and principles

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Testing modelsLet computers do the work

Excel Minitab SPSS SAS RSpreadsheet visible LPull down menus LEasily graph data Basic stats functions Randomise data General Linear Model ? Residual analysis Logistic regression Generalized Linear Model Easy to learn FREE

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Course Goals

1. Introduce you to effective ways of thinking quantitatively about biological phenomena

2. Increase your skill and confidence in the application of quantitative methods

3. Develop your critical capacity, both for your own work and that of others

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