Generate Rmd file for analysis and correct choose results in 06_common.md

.gitignore

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 manuscript/images/Thumbs.db
 *.db
-*.db
-*.db
-*.db
-*.db
+.Rproj.user
+
+# History files
+.Rhistory
+.Rapp.history
+
+# Example code in package build process
+*-Ex.R
+
+# RStudio files
+.Rproj.user/
+
+# produced vignettes
+vignettes/*.html
+vignettes/*.pdf
+
+# OAuth2 token, see https://github.com/hadley/httr/releases/tag/v0.3
+.httr-oauth
+
+# more files
+manuscript/*.html
+*.Rproj
+*.bak
+

manuscript/01_introduction.Rmd

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+#Introduction
+
+## Before beginning
+This book is designed as a companion to the [Statistical Inference](https://www.coursera.org/course/statinference)
+Coursera class as part of the [Data Science Specialization](https://www.coursera.org/specialization/jhudatascience/1?utm_medium=courseDescripTop), a
+ten course program offered by three faculty, Jeff Leek, Roger Peng and Brian Caffo,
+at the Johns Hopkins University Department of Biostatistics.
+
+The videos associated with this book
+[can be watched in full here](https://www.youtube.com/watch?v=WkOinijQmPU&list=PLpl-gQkQivXiBmGyzLrUjzsblmQsLtkzJ),
+though the relevant links to specific videos are placed at the appropriate
+locations throughout.
+
+
+Before beginning, we assume that you have a working knowledge
+of the R programming language. If not, there is a wonderful Coursera class
+by Roger Peng, [that can be found here](https://www.coursera.org/course/rprog).
+
+The entirety of the book is on GitHub [here](https://github.com/bcaffo/LittleInferenceBook).
+Please submit pull requests if you find errata! In addition the course notes can be found
+also on GitHub [here](https://github.com/bcaffo/courses/tree/master/06_StatisticalInference).
+While most code is in the book, *all* of the code for every figure and analysis in the
+book is in the R markdown files files (.Rmd) for the respective lectures.
+
+Finally, we should mention `swirl` (statistics with interactive R programming).
+`swirl` is an intelligent tutoring system developed by Nick Carchedi, with contributions
+by Sean Kross and Bill and Gina Croft. It offers a way to learn R in R.
+Download `swirl` [here](http://swirlstats.com). There's a swirl
+[module for this course!](https://github.com/swirldev/swirl_courses#swirl-courses).
+Try it out, it's probably the most effective way to learn.
+
+## Statistical inference defined
+
+[Watch this video before beginning.](http://youtu.be/WkOinijQmPU?list=PLpl-gQkQivXiBmGyzLrUjzsblmQsLtkzJ)
+
+We'll define statistical inference as the process of generating conclusions about
+a population from a noisy sample. Without statistical inference we're simply
+living within our data. With statistical inference, we're trying to generate
+new knowledge.
+
+Knowledge and parsimony,
+(using simplest reasonable models to explain complex phenomena), go hand in hand.
+Probability models will serve as our parsimonious description of the world.
+The use of probability models as the connection between our data and a
+populations represents the most effective way to obtain inference.
+
+### Motivating example: who's going to win the election?
+
+In every major election, pollsters would like to know, ahead of the
+actual election, who's going to win. Here, the target of
+estimation (the estimand) is clear, the percentage of people in
+a particular group (city, state, county, country or other electoral
+grouping) who will vote for each candidate.
+
+We can not poll everyone. Even if we could, some polled
+may change their vote by the time the election occurs.
+How do we collect a reasonable subset of data and quantify the
+uncertainty in the process to produce a good guess at who will win?
+
+
+### Motivating example, predicting the weather
+
+When a weatherman tells you the probability that it will rain tomorrow is
+70%, they're trying to use historical data
+to predict tomorrow's weather - and to actually attach a probability to it.
+That probability refers to population.
+
+### Motivating example, brain activation
+
+An example that's very close to the research I do is trying to predict what
+areas of the brain activate when a person is put in the fMRI scanner. In
+that case, people are doing a task while in the scanner. For example, they
+might be tapping their finger. We'd like to compare when they are
+tapping their finger to when they are not tapping their finger and try to
+figure out what areas of the brain are associated with the finger tapping.
+
+
+## Summary notes
+
+These examples illustrate many of the difficulties of trying
+to use data to create general conclusions about a population.
+
+Paramount among our concerns are:
+
+* Is the sample representative of the population that we'd like to draw inferences about?
+* Are there known and observed, known and unobserved or unknown and unobserved variables that contaminate our conclusions?
+* Is there systematic bias created by missing data or the design or conduct of the study?
+* What randomness exists in the data and how do we use or adjust for it? Here randomness can either be explicit via randomization
+or random sampling, or implicit as the aggregation of many complex unknown processes.
+* Are we trying to estimate an underlying mechanistic model of phenomena under study?
+
+Statistical inference requires navigating the set of assumptions and
+tools and subsequently thinking about how to draw conclusions from data.
+
+## The goals of inference
+
+You should recognize the goals of inference. Here we list five
+examples of inferential goals.
+
+1. Estimate and quantify the uncertainty of an estimate of
+a population quantity (the proportion of people who will
+  vote for a candidate).
+2. Determine whether a population quantity
+  is a benchmark value ("is the treatment effective?").
+3. Infer a mechanistic relationship when quantities are measured with
+  noise ("What is the slope for Hooke's law?")
+4. Determine the impact of a policy? ("If we reduce pollution levels,
+  will asthma rates decline?")
+5. Talk about the probability that something occurs.
+
+
+## The tools of the trade
+
+Several tools are key to the use of statistical inference. We'll only
+be able to cover a few in this class, but you should recognize them anyway.
+
+1. *Randomization*: concerned with balancing unobserved variables that may confound inferences of interest.
+2. *Random sampling*: concerned with obtaining data that is representative
+of the population of interest.
+3. *Sampling models*: concerned with creating a model for the sampling
+process, the most common is so called "iid".
+4. *Hypothesis testing*: concerned with decision making in the presence of uncertainty.
+5. *Confidence intervals*: concerned with quantifying uncertainty in
+estimation.
+6. *Probability models*: a formal connection between the data and a population of interest. Often probability models are assumed or are
+approximated.
+7. *Study design*: the process of designing an experiment to minimize biases and variability.
+8. *Nonparametric* bootstrapping: the process of using the data to,
+  with minimal probability model assumptions, create inferences.
+9. *Permutation*, randomization and exchangeability testing: the process
+of using data permutations to perform inferences.
+
+## Different thinking about probability leads to different styles of inference
+
+We won't spend too much time talking about this, but there are several different
+styles of inference. Two broad categories that get discussed a lot are:
+
+1. *Frequency probability*: is the long run proportion of
+ times an event occurs in independent, identically distributed
+ repetitions.
+2. *Frequency style inference*: uses frequency interpretations of probabilities
+to control error rates. Answers questions like "What should I decide
+given my data controlling the long run proportion of mistakes I make at
+a tolerable level."
+3. *Bayesian probability*: is the probability calculus of beliefs, given that beliefs follow certain rules.
+4. *Bayesian style inference*: the use of Bayesian probability representation
+of beliefs to perform inference. Answers questions like "Given my subjective beliefs and the objective information from the data, what
+should I believe now?"
+
+Data scientists tend to fall within shades of gray of these and various other schools of inference.
+Furthermore, there are so many shades of gray between the styles of inferences
+that it is hard to pin down most modern statisticians as either Bayesian or
+frequentist. In this class, we will primarily focus on basic sampling models,
+basic probability models and frequency style analyses
+to create standard inferences. This is the most popular style of inference by far.
+
+Being data scientists,  we will also consider some inferential strategies that  
+rely heavily on the observed data, such as permutation testing
+and bootstrapping. As probability modeling will be our starting point, we first build
+up basic probability as our first task.
+
+## Exercises
+
+1. The goal of statistical inference is to?
+  - Infer facts about a population from a sample.
+  - Infer facts about the sample from a population.
+  - Calculate sample quantities to understand your data.
+  - To torture Data Science students.
+2. The goal of randomization of a treatment in a randomized trial is to?
+  - It doesn't really do anything.
+  - To obtain a representative sample of subjects from the population of interest.
+  - Balance unobserved covariates that may contaminate the comparison between the treated and control groups.
+  - To add variation to our conclusions.
+3. Probability is a?
+  - Population quantity that we can potentially estimate from data.
+  - A data quantity that does not require the idea of a population.
+