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### Quantitative Methods

An introduction to the FHS course

An introduction to the FHS course

The course text

OUP, £22.99

http://www.oup.co.uk/best.textbooks/biology/grafenhails/

An introduction to the FHS course

Preliminaries

An introduction to the FHS course

Preliminaries

STN 12noon

Caroline.Antlett

Elizabeth.Bossom

Adrian.Briggs

Adrian.deFroment

Sarah.Docherty

Stuart.Douglas

James.Gawne

Phillip.Hyett

Rebecca.Jeffree

Mhairi.Lathe

Thomas.Ross

Raj.Singh

Kate.Stone

Andrew.Watson

Louisa.Winkler

STN 2pm

Claire.Bernard

Louise.Bradley

Katie.Bulpin

Victoria.Carter

Peter.Collins

Emma.Dawes

Nicholas.Dias

Katharine.Drinkwater

Jocelyn.Elmes

Phillipa.Gillingham

Nicholas.Harding

Adam.Hunter

Matthew.Jones

Christopher.Shelmerdine

Martin.Walker

STN 11am

Jessica.Burt

Christopher.Chappell

Henry.Gill

Henry.Hammerbeck

Sally.Hogbin

Sarah.Knowles

Andrew.Lancaster

Robert.Moreton

Guy.Negretti

Olga.Papadopoulos

Olivia.Rakotomalala

Madeleine.Ryan

Robert.Steel

Harriet.Stevens

John.Walton

An introduction to the FHS course

Preliminaries

CTO 12noon

John.Coles

Claire.Foggon

Nicola.Frost

Thomas.Gardner

Neal.Haddaway

Georgina.Mallows

Mariana.Morales

Daniel.Morgan

Alison.Murray

Anna.Pearson

Laura.Procter

Mark.Twinning

Briony.Webb

jennifer.williams1

Mellissa.Wong

CTO 2pm

Daniel.Crabtree

Mark.Diffenthal

James.Donald

Edmund.Donovan

Anisa.Fradley

Jasper.Green

Katy.Jordan

William.Leonard

Victoria.Marsh

Jennifer.Robertson

Sarah.Russell

Joanna.Scott

Adam.Willman

CTO 11am

Elizabeth.Aitken

Shanta.Barley

Claire.Chantry

Harriet.Douthwaite

Michael.Dowell

Sean.Frisby

Louise.Graver

Ian.Grieve

Victoria.Harding

Timothy.Harris

Ellen.James

Patrick.Mellor

Daniel.Plimmer

Anna.Prior

Merryn.Thomas

An introduction to the FHS course

Preliminaries

- Read the chapter in the book, and think about how to do the exercises
- Attend the lecture
- Attend the practical, and do the exercises
- Write up the practical later, and hand in
- Retrieve the write-up the following week

An introduction to the FHS course

Preliminaries

Basic themes

- Model formulae - learn the language of statistics
- Geometry - pictures are nice, nicer than algebra
- Computers - do the donkey work

Together, these allow you to learn the statistics you need to operate as a biologist.

An introduction to the FHS course

Preliminaries

This Term - the GLM toolbox

§1 An introduction to the FHS course and analysis of variance

§2 Regression

§3 Models, parameters and GLMs

§4 Using more than one x-variable

§5 Designing experiments

§6 Combining continuous and categorical variables

An introduction to the FHS course

What is an Analysis of Variance?

An introduction to the FHS course

What is an Analysis of Variance?

An introduction to the FHS course

What is an Analysis of Variance?

An introduction to the FHS course

What is an Analysis of Variance?

An introduction to the FHS course

What is an Analysis of Variance?

An introduction to the FHS course

What is an Analysis of Variance?

An introduction to the FHS course

What is an Analysis of Variance?

An introduction to the FHS course

What is an Analysis of Variance?

An introduction to the FHS course

What is an Analysis of Variance?

An introduction to the FHS course

What is an Analysis of Variance?

An introduction to the FHS course

What is an Analysis of Variance?

SSY = Total sum of squares

SSE = Error sum of squares

SSF = Fertiliser sum of squares

(SSY = SSF + SSE)

EMS = SSE / 27

FMS = SSF / 2

Under H0, EMS and FMS are approximately equal

F = EMS/FMS should be about 1

An introduction to the FHS course

What is an Analysis of Variance?

SSY = Total sum of squares

SSE = Error sum of squares

SSF = Fertiliser sum of squares

(SSY = SSF + SSE)

EMS = SSE / 27

FMS = SSF / 2

Under H0, EMS and FMS are approximately equal

F = EMS/FMS should be about 1

An introduction to the FHS course

Analysis of Variance in Minitab

An introduction to the FHS course

Analysis of Variance in Minitab

- from Minitab supplement

- availability

- SAS and SPSS

An introduction to the FHS course

Analysis of Variance in Minitab

An introduction to the FHS course

Analysis of Variance in Minitab

An introduction to the FHS course

Analysis of Variance in Minitab

An introduction to the FHS course

Analysis of Variance in Minitab

An introduction to the FHS course

Geometry and Analysis of Variance

An introduction to the FHS course

Geometry and Analysis of Variance

An introduction to the FHS course

Geometry and Analysis of Variance

An introduction to the FHS course

Geometry and Analysis of Variance

An introduction to the FHS course

Geometry and Analysis of Variance

An introduction to the FHS course

Geometry and Analysis of Variance

An introduction to the FHS course

Geometry and Analysis of Variance

An introduction to the FHS course

Geometry and Analysis of Variance

An introduction to the FHS course

Geometry and Analysis of Variance

An introduction to the FHS course

Geometry and Analysis of Variance

An introduction to the FHS course

Geometry and Analysis of Variance

(30)

deviations of plot values from grand mean

FY

MY

[27]

[29]

deviations of plot values from group means

F

M

MF

(3)

(1)

[2]

deviations of group means

from grand mean

An introduction to the FHS course

Geometry and Analysis of Variance

3 partitions: MY = MF + FY (vector or data addition)Sums of squares add (Pythagoras)Degrees of Freedom add (dimensions)

An introduction to the FHS course

Geometry and Analysis of Variance

An introduction to the FHS course

Last words…

- statistics is not maths and is not too hard
- learn it while you’ve got all the help around you
- isn’t it exciting that a sum of squares is a sum of squares?

Next week: Regression

Read Chapter 2

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