# Chapter 29 Review + Fun data sets if you need them

## 29.1 Review

You should be pretty comfortable with the ideas of

• Parameters vs Estimates
• Sampling and what can go wrong
• Null hypothesis significance testing
• Common test statistics
• F
• t
• Calculating Sums of Squares
• Interpreting stats output like that below
ToothGrowth <- mutate(ToothGrowth, dose = factor(dose))
tooth_lm <- lm(len ~ supp * dose, data = ToothGrowth)

summary(tooth_lm)   
##
## Call:
## lm(formula = len ~ supp * dose, data = ToothGrowth)
##
## Residuals:
##    Min     1Q Median     3Q    Max
##  -8.20  -2.72  -0.27   2.65   8.27
##
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)    13.230      1.148  11.521 3.60e-16 ***
## suppVC         -5.250      1.624  -3.233  0.00209 **
## dose1           9.470      1.624   5.831 3.18e-07 ***
## dose2          12.830      1.624   7.900 1.43e-10 ***
## suppVC:dose1   -0.680      2.297  -0.296  0.76831
## suppVC:dose2    5.330      2.297   2.321  0.02411 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.631 on 54 degrees of freedom
## Multiple R-squared:  0.7937, Adjusted R-squared:  0.7746
## F-statistic: 41.56 on 5 and 54 DF,  p-value: < 2.2e-16
anova(tooth_lm)
## Analysis of Variance Table
##
## Response: len
##           Df  Sum Sq Mean Sq F value    Pr(>F)
## supp       1  205.35  205.35  15.572 0.0002312 ***
## dose       2 2426.43 1213.22  92.000 < 2.2e-16 ***
## supp:dose  2  108.32   54.16   4.107 0.0218603 *
## Residuals 54  712.11   13.19
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova(tooth_lm, type = "II")   
## Anova Table (Type II tests)
##
## Response: len
##            Sum Sq Df F value    Pr(>F)
## supp       205.35  1  15.572 0.0002312 ***
## dose      2426.43  2  92.000 < 2.2e-16 ***
## supp:dose  108.32  2   4.107 0.0218603 *
## Residuals  712.11 54
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 29.2 Quiz

Reflection questions on [canvas] ## Potential data sets

Spend the weekend pushing forward on your linear model project.

Recall that a major assumption of linear models is that errors are normally distributed.

Although linear models are robust to minor violations of these assumptions, they are not a good choice for a categorical response variable – so if your early analyses had categorical response variables you probably need a new data set. Here are some currated options.

### Consequences of extinction

Functional extinction of a desert rodent: implications for seed fate and vegetation dynamics. Gordon and Letnic (2016) . data for project (.xlsx format), paper, full data on dryad.

Image from paper [dont try to recreate this]

### Moving and other stresses might shorten telomeres

Migration and stress during reproduction govern telomere dynamics in a seabird. Schultner et al. (2014). data for project (.xlsx format), paper.

### Associations between neurons and IQ

Large and fast human pyramidal neurons associate with intelligence. Goriounova et al. (2018). data for project (.xlsx format), paper, dryad.

### Inbreeding and fitness

A high-quality pedigree and genetic markers both reveal inbreeding depression for quality but not survival in a cooperative mammal. Wells et al. (2018). data for project annual reproduction (.csv format), yearling weight (.csv format). paper, dryad.

### References

Gordon, Christopher E, and Mike Letnic. 2016. “Functional Extinction of a Desert Rodent: Implications for Seed Fate and Vegetation Dynamics.” Ecography 39 (9): 815–24.
Goriounova, Natalia A, Djai B Heyer, René Wilbers, Matthijs B Verhoog, Michele Giugliano, Christophe Verbist, Joshua Obermayer, et al. 2018. “Large and Fast Human Pyramidal Neurons Associate with Intelligence.” Edited by David Badre, Timothy E Behrens, and Christof Koch. eLife 7 (December): e41714. https://doi.org/10.7554/eLife.41714.
Schultner, Jannik, Børge Moe, Olivier Chastel, Claus Bech, and Alexander S Kitaysky. 2014. “Migration and Stress During Reproduction Govern Telomere Dynamics in a Seabird.” Biology Letters 10 (1): 20130889–89. https://doi.org/10.1098/rsbl.2013.0889.
Wells, David A., Michael A. Cant, Hazel J. Nichols, and Joseph I. Hoffman. 2018. “A High-Quality Pedigree and Genetic Markers Both Reveal Inbreeding Depression for Quality but Not Survival in a Cooperative Mammal.” Molecular Ecology 27 (9): 2271–88. https://doi.org/https://doi.org/10.1111/mec.14570.