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Quantitative Methods
An introduction to the FHS course
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An introduction to the FHS course
The course text
OUP, £22.99
http://www.oup.co.uk/best.textbooks/biology/grafenhails/
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An introduction to the FHS course
Preliminaries
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An introduction to the FHS course
Preliminaries
STN 11am
Jessica.BurtChristopher.ChappellHenry.GillHenry.HammerbeckSally.HogbinSarah.KnowlesAndrew.LancasterRobert.MoretonGuy.NegrettiOlga.PapadopoulosOlivia.RakotomalalaMadeleine.RyanRobert.SteelHarriet.StevensJohn.Walton
STN 12noon
Caroline.AntlettElizabeth.BossomAdrian.BriggsAdrian.deFromentSarah.DochertyStuart.DouglasJames.GawnePhillip.HyettRebecca.JeffreeMhairi.LatheThomas.RossRaj.SinghKate.StoneAndrew.WatsonLouisa.Winkler
STN 2pm
Claire.BernardLouise.BradleyKatie.BulpinVictoria.CarterPeter.CollinsEmma.DawesNicholas.DiasKatharine.DrinkwaterJocelyn.ElmesPhillipa.GillinghamNicholas.HardingAdam.HunterMatthew.JonesChristopher.ShelmerdineMartin.Walker
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An introduction to the FHS course
Preliminaries
CTO 11am
Elizabeth.AitkenShanta.BarleyClaire.ChantryHarriet.DouthwaiteMichael.DowellSean.FrisbyLouise.GraverIan.GrieveVictoria.HardingTimothy.HarrisEllen.JamesPatrick.MellorDaniel.PlimmerAnna.PriorMerryn.Thomas
CTO 12noon
John.ColesClaire.FoggonNicola.FrostThomas.GardnerNeal.HaddawayGeorgina.MallowsMariana.MoralesDaniel.MorganAlison.MurrayAnna.PearsonLaura.ProcterMark.TwinningBriony.Webbjennifer.williams1Mellissa.Wong
CTO 2pm
Daniel.CrabtreeMark.DiffenthalJames.DonaldEdmund.DonovanAnisa.FradleyJasper.GreenKaty.JordanWilliam.LeonardVictoria.MarshJennifer.RobertsonSarah.RussellJoanna.ScottAdam.Willman
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• 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
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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.
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An introduction to the FHS course
Preliminaries
§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
This Term - the GLM toolbox
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An introduction to the FHS course
What is an Analysis of Variance?
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An introduction to the FHS course
What is an Analysis of Variance?
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An introduction to the FHS course
What is an Analysis of Variance?
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An introduction to the FHS course
What is an Analysis of Variance?
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An introduction to the FHS course
What is an Analysis of Variance?
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An introduction to the FHS course
What is an Analysis of Variance?
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An introduction to the FHS course
What is an Analysis of Variance?
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An introduction to the FHS course
What is an Analysis of Variance?
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An introduction to the FHS course
What is an Analysis of Variance?
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An introduction to the FHS course
What is an Analysis of Variance?
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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
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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
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An introduction to the FHS course
Analysis of Variance in Minitab
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An introduction to the FHS course
Analysis of Variance in Minitab
- from Minitab supplement
- availability
- SAS and SPSS
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An introduction to the FHS course
Analysis of Variance in Minitab
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An introduction to the FHS course
Analysis of Variance in Minitab
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An introduction to the FHS course
Analysis of Variance in Minitab
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An introduction to the FHS course
Analysis of Variance in Minitab
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An introduction to the FHS course
Geometry and Analysis of Variance
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An introduction to the FHS course
Geometry and Analysis of Variance
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An introduction to the FHS course
Geometry and Analysis of Variance
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An introduction to the FHS course
Geometry and Analysis of Variance
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An introduction to the FHS course
Geometry and Analysis of Variance
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An introduction to the FHS course
Geometry and Analysis of Variance
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An introduction to the FHS course
Geometry and Analysis of Variance
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An introduction to the FHS course
Geometry and Analysis of Variance
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An introduction to the FHS course
Geometry and Analysis of Variance
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An introduction to the FHS course
Geometry and Analysis of Variance
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An introduction to the FHS course
Geometry and Analysis of Variance
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An introduction to the FHS course
3 partitions: MY = MF + FY (vector or data addition)Sums of squares add (Pythagoras)Degrees of Freedom add (dimensions)
(1) (3)
(30)
deviations of group means from grand mean
deviations of plot values from group means
deviations of plot values from grand mean
MF
FYMY
[2]
[27][29]
M F
Y
Geometry and Analysis of Variance
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An introduction to the FHS course
Geometry and Analysis of Variance
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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