Power recap

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Power recap
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Power recap

• It is good to fake data
• BUT
• p-values of 1 fake data is crap!

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Power recap

• A 1000 simulation Power analyses is not crap!
• BUT
• Power depends on
• Sample size
• Effect size
• Variation

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Project considerations I

• Make graphs
• Check for outliers
• Check assumptions
• Decide if you want to transform y and or x
• Check VIF
• Are your assumtions still fkd up.
• ? Well, thats for today.

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Project considerations II

• Interpret interactions first!
• If they are significant? Are main effects
  still interpretable?
• Distinguish between y x1 and y x1
  given x2
• Simplify your models!

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2 ? 2 tables
Logistic regression
Categoric
Melica
1.0
0.8
0.6
Prob. of choosing Melica
0.4
0.2
0.0
Response variable
Luzula
4.5
5.5
6.5
7.5
Ant size
Regression
Anova
Continuous
-
-
Seed size
Continuous
Categoric
Explanatory variable
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Response variable
Regression
Anova
Continuous
-
-
Seed size
Continuous
Categoric
Explanatory variable
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Assumptions for parametric tests with continuous
response? i.e., also linear models!!

• About the same variation in all groups or along a
  continuous variable or along fitted values
• Pretty normal residuals ( noice)

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The residuals

• are the noice that is not explained by the
  explanatory variable(s)
• In a regression the residuals are the distance
  from the data points to the regression line
• In an Anova the residual are the distance to the
  group mean
• In a linear model the residuals are the distance
  from the data points to the fitted values.

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Residuals
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Residuals
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Assumption check
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Assumption check
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Assumption check
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Solutions

• Poisson for counts (generalized linear model)
• Non-parametric tests
• Resampling methods
• Permutation
• Bootstrap
• Binarize your response

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quasipoisson fit on Xanthoria
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Xanthoria reproduction again
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Poisson distribution

• Response Numbers (not true continuous)
• Examples
• Are there more maple seedlings close to a maple?
• Response number per square
• m1lt-glm(numberdistance,familyPoisson)

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Poisson distribution

• Usually log(y) also works fine.
• Poisson excells
• small means
• many zeroes
• Many zeroes ? Hurdle models

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break?
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Non-parametric tests

• Based on ranked values instead of actual data.

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Non-parametric tests

• Still often in use.
• Questionable with modern computers.
• ? In principle permutions of ranked values
• ? But worse than real permutations, because
  information about actual data values is
  discarded.

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Non-parametric tests

• Still often in use.
• Questionable with modern computers.
• ? In principle permutions of ranked values
• ? But worse (than real permutations) because
  information about actual data values is
  discarded.

BENEFIT Calm dow outliers!
?
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Response variable
Regression
Anova 2 groups also t-test
Continuous
-
-
Seed size
Continuous
Categoric
Explanatory variable
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Response variable
Kruskal-Wallis also Mann-Whitney U-test Paired
Sign test(binomial)
Kendall rank correlation also Spearman rank
Continuous
-
-
Seed size
Continuous
Categoric
Explanatory variable
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Permutations

• Does not require normal distribution
• BUT, does require distributions to be equal if
  your hypothesis is not true.
• ? Example
• If the lichens are equally large in the city as
  they are at campus, they must have the same
  variation and e.g., skewness.
• In principle a test of if the distributions
  differ.

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Ash seed dispersal
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Acer twigs plasticity
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Birch cost of reproduction
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bootstrap

• to pull oneself up by one's bootstraps
• to succeed only on one's own effort or
  abilities.

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shrimp-booting...
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Rumex crispus Rumex longifolius
300
250
250
200
200
150
150
100
100
50
50
0
0
1.0
1.1
1.2
1.3
1.4
1.5
1.25
1.30
1.35
1.40
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Confidence intervals

• shows how sure we are of a group mean.
• The confidence interval will contain the true
  mean in 95 of the time.
• The larger our sample size the more sure (
  confident!) we are of our sample mean ? the
  confidence interval decreases
• And (of course), the more variation within
  groups, the less sure we get ? confidence
  interval increases

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Bootstrap for tests
120
80
No. boot-samples
60
40
20
0
-5
0
5
10
15
20
25
boot.difference
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Bootstrap

• Does not require normal distribution of
  residuals.
• Does not require the same variation.
• Only requirement is that what you bootstrap
  (e.g., means) are the same if your hypothesis is
  not correct.
• And, in practice, a large, representative sample

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moss.shoot forest type
2000
1500
1000
500
0
0
5
10
15
Bootstrapped difference in moss shoot length
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Bootstrap

• We use the functionsample(row.names(d),replaceT
  )
• More advanced (and better)library(boot)?boot?
  boot.ci

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Binarize your response

• If all other efforts sucks
• Binarize your response
• Nothing vs Something
• Above the median vs Below the median
• bin.ylt-ifelse(y lt median(y),0,1)
• bin.ylt-factor(bin.y)
• ? Then do a logistic regression, 22, or a
  generalized linear model

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Wednesday seminar

• Read one powerpoint paper
• Read one book chapter on graphs
• Watch one youtube film
• Bring two graphs
• 3 groups
• Narin, Mandeep, Ruben, Mamun, Karolina
• Keshav, Hanna, Malin, Georg
• Lovisa, Dries, Andrea, Mehrnaz

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Friday Morning 09.00
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Friday afternoon 13.00
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Computer exercise

• Use yor own data.
• Or old data.
• Use either a continuous or categorical
  explanatory.
• Possible also for many explanatories?
• Non-parametric ? Well, usually not
• Permutation ? Yes, but hard
• Bootstrap ? Yes, easy
• Binarizing ? Yes, easy

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Mail me your data!

• excel file
• Help option booking list

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Exam

• Read Learning goals
• Read Crawley in relation to learning goals
• E.g., no GAM, Survival
• Check lecture powerpoints in relation to learning
  goals
• Practice on understanding the excercises (they
  ARE in the learning goals)

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Nice Books

• www.bokfynd.nu
• www.abebooks.com

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Lunch?

or
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Dedication!