Statistics for Human Genetics
1
Preface
1.1
Acknowledgements
1.2
About the author
2
New Intro
I Statistics and Programming
3
Why we use statistics
4
An introduction to R
4.1
Installing R and Rstudio
4.2
Using R as a calculator
4.3
Using variables
4.4
Bring some external data into R
4.5
Analyze the data
4.6
Making a plot
4.7
Saving the plot and saving everything
4.8
Keeping a record of everything using R markdown.
5
Summary statistics
5.1
Central tendency
5.1.1
Mean
5.1.2
Median
5.2
Variability
5.2.1
Variance
5.2.2
Standard deviation
5.3
Degrees of freedom
6
Sampling from populations
6.1
Sampling from populations
6.2
Simulating a population of student heights
6.2.1
Generate a histogram that summarizes the distribution of heights in the entire population.
6.2.2
Simulating the process of sampling from a large population.
6.3
Repeating the process of sampling over and over
6.4
Exercises
7
Statistical testing
II Part II: Mendelian Genetics
8
The distribution of human phenotypes
8.1
Human Phenotypes
8.1.1
Binary traits
8.1.2
Continuous traits
8.2
The genetics of human phenotypes
9
Mendel’s Experiments
9.1
Mendel’s monohybrid crosses
9.2
Some key terminology
10
Mendel’s Model
10.1
Mendel’s first law
10.2
Mendel’s second law
10.3
Probability
10.3.1
Additive Law of Probability
10.3.2
Multiplicative Law of Probability
11
Chi squared test
11.1
Chi-squared probability densities
11.2
Chi-square cumulative probability distributions
11.3
Assess results of mendel’s dihybrid cross using chi-square test statistic
11.4
Assessing the results from the Bateson and Punnetts’s dihybrid cross using chi-square test statistic
11.4.1
Log transformation
11.5
Analysis of Bateson and Punnett’s data using internal R functions
12
Mendelian inheritance in humans
12.1
Five Basic Mendelian Patterns in Humans
12.1.1
Autosomal
12.1.2
Sex linked
12.1.3
Special cases
12.2
Variations on Mendelian Inheritance in Humans
12.2.1
Incomplete Dominance
12.2.2
Co-dominance
12.2.3
Expressivity
12.2.4
Penetrance
12.3
Drawing pedigrees in R
13
Pedigree analysis
13.1
Human Pedigrees
13.2
Drawing pedigrees in R
14
The binomial distribution
14.1
Combinations
14.2
The binomial distribution
14.3
Binomial probabilities and sample size
15
The poisson distribution
16
Likelihood
17
LOD scores
17.1
Phase known
17.2
Phase unknown
18
Conditional Probability
19
Bayes Theorem
20
Hardy Weinberg Equilibrium
21
Inbreeding
22
Genetic Drift
23
Selection
24
Genetic Diversity
III Part IV: Quantitative Genetics
25
The normal distribution
25.1
Many Human Phenotypes are normally distributed
26
The normal distribution
27
The t test
27.1
One sample t test
27.2
Exploring T-tests
27.3
Produce the null distribution of the t statistic by simulation
28
ANOVA: analysis of variance
28.1
Performing ANOVA in R
28.2
The F distribution
29
Covariance and correlation
29.1
Covariance
29.2
Correlation
29.3
Generaing simulated datasets
30
Linear Regression
30.1
Linear Regression in R
30.2
Diagnostics
31
Nonparametric methods
31.1
The sign test.
31.2
Performing sign tests in R
31.3
A more interesting example.
31.4
The Mann-Whitney test.
31.5
Spearman (rank) correlation
31.5.1
Comparing spearman and pearson correlation
IV Part V: Genomics
32
Looking at all the genes
32.1
How do we analyze thousands of genes
33
Simulation
34
Randomization
35
Bootstrapping
36
Statistical Power
36.1
What is statistical power?
36.2
Performing Power Analysis
37
The Winner’s Curse
37.1
Simulating the winners curse when using a t-test
References
Made using bookdown
Statistics for Human Genetics
Chapter 19
Bayes Theorem