Outline.Rmd

---
title: Outline
author: Emilio A. Laca
date: 9/24/2018
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

# Front Matter {-#chFront} 
# Contents {-#chContent} 
# Preface {-#chPreface} 

# Introduction to Applied Statistics {#chIntro} 
## Learning Objectives 
## Course Goals 
## Why Statistics? 
## Definition of Statistics 
## Learning Statistics {#LearnStats} 
## Going to the movies: PBS program on statistics 
## Methods and Concepts in this Book 
### Probability, estimation, inference {#estimationInference} 
## Statistics Defined 
## Book Organization and Overview 
## Use and Misuse of Statistics 
## Real-world problems 
### Detection of the Higgs boson 
## Exercises and Solutions 
### Exercise 1 
### Exercise 2 
### Exercise 3: three doors and two goats 
## Homework Problems 
## Laboratory Exercise 

# Statistics with R {#chStatsR} 
## Learning Objectives for Chapter 
## Background on R and RStudio 
## R Basics 
## Exploring RStudio 
### Terminal or Console Window 
### Markdown (Source) Window 
#### Saving Files 
### Files, Plots, Packages, Help Window 
#### Files 
#### Plots 
#### Packages 
#### Help 
### Environment and History Window 
#### Vectors and Data Frames 
#### Importing Data 
## Functions 
## Exercises 
## Laboratory Exercises 
### Plant Sciences 
#### Introduction to R and RStudio 
#### Create a dataframe and table 
#### Summary Statistics 
#### Frequency Table and Histogram 
#### Box-and-Whisker Plot and 5-Number Summary 
#### Analyses by Groups 
### Animal Sciences 
#### Introduction to R and RStudio 
#### Create a dataframe and table 
#### Summary Statistics 
#### Frequency Table and Histogram 
#### Box-and-Whisker Plot and 5-Number Summary 
#### Analyses by Groups 

# Required Math Skills and Symbols {#chMath} 
## Learning Objectives for Chapter {#mathObj} 
## Data Columns and Summation {#mathSum} 
## Two-dimensional Data Tables and Summation {#math2Dtbl} 
## Models {#mathModl} 
### The simplest model{#mathSmplMod} 
### A slightly more complex model {#mathBttrMod} 
### Grouping or Indicator Variables {#mathGroups} 
## Deviations, Errors and Residuals {#mathDevs} 
### Simulation: Population is Known {#mathSimu} 
## Optimization {#mathOptim} 
## Linear Models 
## Symbols and Terms{#mathSymbls} 
## Exercises and Solutions {#mathExe} 
### Exercise 1 
### Exercise 2 
### Exercise 3 
## Homework {#mathHwk} 
### Homework Exercise 
### Homework Exercise 
### Homework Exercise 
### Homework Exercise 

# Data Manipulation, Exploration and Summaries {#ch.data} 
## Learning Objectives for Chapter 
## Data curation 
## Data comes from samples 
## Measures of central tendency 
## Measures of dispersion 
## Frequency distributions and histograms 
## Five-number summary 
## Coefficient of variation 
## Exercises and Solutions 
## Homework 
## Laboratory Exercises 
### Plant Sciences Lab 
### Instructions 
### Example Question with Answer 
### Part 1. Data input [10 points] 
### Part 2. Coefficient of variation [15 points] 
### Part 3. Five number summary table of iris data [15 points] 
### Part 4. Frequency table and histogram [15 points] 
### Part 5. Box and whisker plot [15 points] 
### Part 6. fivenum() function [10 points] 
### Part 7. Making a vector [10 points] 
### Part 8. Knitting [10 points] 
### Animal Sciences Lab 
### Instructions 
### Example Question with Answer 
### Part 1. [10 points] 
### Part 2. [15 points] 
### Part 3. [15 points] 
### Part 4. [15 points] 
### Part 5. [15 points] 
### Part 6. [10 points] 
### Part 7. [10 points] 
### Part 8. [10 points] 

# Probability in Applied Statistics {#chProb} 
## Learning Objectives for Chapter 
## Variables and parameters 
### What does \random\ mean? 
### \Just due to Chance\ 
## Probability 
### Frequentist and Bayesian probability 
### Outcomes, sample space and events 
### Combinatorics 
### Probability of two events {#Pof2Events} 
### Conditional probability and independence 
## Bayes Rule 
### Bayesian data analysis 
### Frequentist data analysis 
## de Méré's dice problem 
## Next steps 
## Exercises and Solutions 
### Exercise 
### Exercise 
## Homework 
### Outcomes and events 
## Laboratory Exercises 
### Plant Sciences 
### Animal Sciences 

# Random Variables, Sampling and Distributions {#chSampling} 
## Learning Objectives for Chapter 
## Random variables 
### Types of Variables and Notation 
### Using random variables 
## Probability Distributions 
## Parameters and Moments 
### Expectation, Mean or First Moment 
### Variance or Second Moment 
### Covariance and Correlation between two RV's 
### Parameters are not necessarily the moments 
### Properties of Mean and Variance 
### Standardized variables 
## Common distributions 
### Discrete Uniform Distribution {#DUnifDist} 
### Continuous Uniform Distribution {#CUnifDist} 
### Binomial Distribution {#BinDist} 
### Poisson Distribution {#PoisDist} 
### Normal Distribution {#NormDist} 
### $\\chi^2$ Distribution {#chisqDist} 
### Student's t Distribution {#tDist} 
### F Distribution {#FDist} 
## Sampling and samples 
### Universe, population and sample 
### No Representative samples allowed 
### No Biased samples allowed 
### Sampling methods 
### Estimators 
### Variance of the sample average 
## Central Limit Theorem 
## Sampling distributions 
## Estimation vs. inference and prediction 
## Exercises and Solutions 
### Exercise 
### Exercise 
### Exercise 
## Homework 
## Laboratory Exercises 
### Plant Sciences 
### Animal Sciences 

# Confidence intervals and Hypothesis testing {#chHotest} 
## Learning Objectives for Chapter 
## Testing a hypothesis 
## Logic of Null Hypothesis test with ANOVA 
## Theme: compare A and B 
## Confidence intervals 
## Confidence interval and test of one mean 
## What is the meaning of the p-value? 
## Types of Errors in Hypothesis testing 
## Exercises and Solutions 
## Pitfalls to avoid 
## Facts to remember 
## Homework 
## Laboratory Exercises 
### Plant Sciences Lab 
### Instructions 
### Part 1. Normal Distribution R functions [10 points]
### Part 2. Normal PDF [10 points]
### Part 3. Students's t Distribution [20 points]
### Part 4. Effect of sample size on CI width [20 points]
### Part 5. Interpretation of the CI [10 points]
### Part 6. Test of null hypothesis [20 points]	
### Part 7. Knit report [10 points]
### Animal Sciences Lab 
### Instructions 
### Normal Distribution Part 1. [10 points] 
#### Normal Distribution Part 2 [10 points] 
### Student's t distribution Part 1 [20 points] 
### Student's t distribution Part 2. [20 points] 
### Student's t distribution Part 3 [10 points] 
### Student's t distribution Part 4 [20 points]\t 
### Student's t distribution Part 5. [10 points] 

# Two Populations Means {#ch2pops} 
## Learning Objectives for Chapter {#LearnObj8} 
## Two Populations 
## Hypothesis Testing 
## Sampling Methods 
### Independent Samples 
### Paired Samples 
## Calculating Sample Averages and the Average of the Difference 
## Calculating the Sample Variances 
## Calculating the F-statistic 
### F-test Decision 
## Calculating the Pooled Sample Variance, the Standard Error of the Difference, and the t-statistic 
### Case 1: Independent samples with equal population variances (#Case1) 
### Case 2: Independent samples with unequal population variances (#Case2) 
### Case 3: Paired samples (#Case3) 
## Confidence Intervals 
## Decision to Reject or Fail to Reject the Null Hypothesis 
## Bean Drought Example 
### Stating the Hypotheses 
### Sampling Method 
### Calculating Sample Averages and the Mean Difference 
### Calculating Sample Variances 
#### Calculate the Individual Sample Variances 
#### Using an F-test to determine if Population Variances are Equal 
#### Pooling Sample Variances 
### Calculating the Standard Error of the Difference 
### Calculating the t-statistic 
## Bean Drought Example - Paired 
### Stating the Hypotheses 
### Sampling Method 
### Calculating Sample Averages and the Average of the Difference 
### Calculating the Variance of the Difference 
### Calculating the Standard Error of the Difference 
### Calculating the t-statistic 
## Exercises 
## Homework : Two Population Means 
### Walking Spiders 
### Rat Life 
## Laboratory Exercises 
### Plant Sciences 
#### Part 1. Equality of variances [25 points]
#### Part 2. Difference between means with independent samples [30 points]
#### Part 3. Difference between means with paired samples [30 points]
#### Part 4: Paired or independent? [15 points] 
##### A. Aphids on soybeans 
##### B. Compost for broccoli 
##### C. Habanero chili 
##### D. Fish oil and triglycerides 
##### E. Botanical composition after restoration 
### Animal Sciences 
#### Part 1 [25 points] 
#### Part 2 [30 points] 
#### Part 3 [30 points] 
#### Part 4: Paired or independent? [15 points] 
##### A. High protein diet 
##### B. Organic dairy feed 
##### C. Cowabunga 
##### D. Fish oil and blood triglycerides 
##### E. Rumen flora 

# Analysis of Variance {#chAnova} 
## Learning Objectives for Chapter 
## Introduction to ANOVA 
## Model and Partitioning of Variance 
## Degrees of freedom (The bulk of this section should be moved to the first time df are mentioned) 
## ANOVA Table 
## Assumptions of ANOVA 
## ANOVA example 
###Formulas and calculations in R 
### Detailed calculations 
## Exercises and Solutions 
## Homework 
### Introduction to ANOVA 
### Need for ANOVA 
### Comparison of Diets 
### Use of ANOVA 
### Test of Equality of Variances 
### Estimation of the Variance Between and Within Samples 
## Laboratory Exercises 
### Plant Sciences {#LabCh09PLS} 
#### Instructions 
#### Part 1. Inspection and summary of data [25 points] 
#### Part 2. Partition of Sum of Squares and Degrees of Freedom [30 points] 
#### Part 3. ANOVA using R functions.[20 points] 
#### Part 4. Confidence intervals for treatment means [25 points] 
### Animal Sciences {#LabCh09ANS} 
#### Instructions 
#### Part 1. Inspection and summary of data [25 points] 
#### Part 2. Partition of Sum of Squares and Degrees of Freedom [30 points] 
#### Part 3. ANOVA using R functions.[20 points] 
#### Part 4. Confidence intervals for treatment means [25 points] 

# Experimental Design {#chEdesign} 
## Learning Objectives for Chapter 
## Experimental Design and Treatment Structure 
## Elements of Experimental Design 
## Exercises and Solutions 
## Homework 
## Laboratory Exercises 
### Plant Sciences 
### Animal Sciences 

# ANOVA with Blocks {#chRcbd} 
## Learning Objectives for Chapter 
## Exercises and Solutions 
## Homework 
## Laboratory Exercises 
### Plant Sciences {#LabRCBD} 
#### Instructions 
#### Part 1. Read in, inspect and summarize data [15 points] 
#### Part 2. Analyze data ignoring the blocking design [25 points] 
#### Part 3. RCBD Sum of Squares and Degrees of Freedom [35 points] 
#### Part 4. ANOVA for RCBD using R functions.[25 points] 
### Animal Science {#LabCh11ANS} 
#### Instructions 
#### Part 1. Read in, inspect and summarize data [15 points] 
#### Part 2. Analyze data ignoring the blocking design [25 points] 
#### Part 3. RCBD Sum of Squares and Degrees of Freedom [35 points] 
#### Part 4. ANOVA for RCBD using R functions.[25 points] 

# Treatment Structures and Comparisons {#chTrtstr} 
## Learning Objectives for Chapter {#LearnObj12} 
## Pairwise Comparisons {#PairComp} 
### Least Significant Difference 
### Experiment-wise and Family-wise Error Rates 
## Factorials {#Factorials} 
### Interactions 
### Interactions and Main Effects 
### Model and Calculations in Factorials 
#### R Code for Factorial in RCBD 
#### Detailed Calculations for Factorial in RCBD 
### Advantages of factorials 
#### Effects of Irrigation alone 
#### Effects of Nitrogen alone 
#### Combined Effects of Irrigation and Nitrogen 
## Contrasts {#Contrasts} 
## Linear Combinations {#LinCombo} 
## Exercises and Solutions {#ExSol12} 
## Homework {#Hwk12} 
## Laboratory Exercises 
### Plant Sciences {#Lab12PLS} 
#### Instructions 
#### Part 1. Factorial ANOVA using R functions [ points] 
##### 1a. Random assignment of treatments to plots 
##### 1.b Add columns with factor levels to the data 
##### 1.c Perform a test of the Ho that all treatment means are equal. 
#### Part 2. Factorial ANOVA detailed calculations [ points] 
#### Part 3. Multiple comparison of means using Fisher's PLSD [ points] 
### Animal Sciences {#Lab12ANS} 

# Linear Regression {#chLinReg} 
## Learning Objectives for Chapter 
##Introduction to Simple Linear Regression 
##Simple Linear Regression Visualized 
##Fitting the least squares line 
##Analysis of variance of regression 
##Confidence Interval for $\\hat{\\beta_1}$ 
##Confidence Interval for $\\hat{\\beta}_0$ 
##Confidence Intervals for $\\hat{Y}_i$ 
##Coefficient of Determination, $R^2$ 
##Correlation Coefficient, r 
##Fitness of the regression model 
## Exercises and Solutions 
## Homework 
## Laboratory Exercises {#LabCh13PLS} 
### Plant Sciences 
#### Part 1. Plot of data and estimation of parameters. [25 points] 
#### Part 2. Test of null hypothesis and R-square. [30 points] 
#### Part 3. Make a 95% confidence interval for the RGR or slope. [25 points] 
#### Part 4. Make a 95% confidence interval for mean plant size at a given age. [20 points] 
### Animal Sciences 
#### Part 1. Plot of data and estimation of parameters. [25 points] 
#### Part 2. Test of null hypothesis and R-square. [30 points] 
#### Part 3. Make a 95% confidence interval for the estimation of the slope. [25 points] 
#### Part 4. Make a 95% confidence interval for mean heart weight at a given body weight. [20 points]

# Chi-square: Goodness of Fit and Test of Independence {#chChisq} 
## Learning Objectives for Chapter 
## The $\\chi^2$ distribution 
## Goodness of Fit: Discrete distributions 
## Goodness of Fit: Continuous distributions 
## The $\\chi^2$ Test of Independence: Contingency Tables 
## Exercises and Solutions 
## Homework Problems 
## Laboratory Exercises {#LabCh14PLS} 
### Plant Sciences 
#### Part 1. Create contingency table 
#### Part 2. Expected Frequencies 
#### Part 3. Calculate $\\chi^{2}$ 
#### Part 4. Results 
### Animal Sciences 
#### Part 1. Create contingency table 
#### Part 2. Expected Frequencies 
#### Part 3. Calculate $\\chi^{2}$ 
#### Part 4. Results