Study Guide for Quiz 1(Jul 21st)

Primary resources (desceding order by importance)

• Lecture notes with emphasis on
  • How do we define each concept?
  • Practice questions – reasoning for every options(why correct? why wrong?)
• R Session code with emphasis on
  • Why are we running this code? What do we want to check by running the code?
  • What does specific code mean? Which element is needed for running a sepcific function?
• Recommended exercises in OS
  • Emphasis on how the related concepts can be used in real-life example
• Sample quiz
  • Thoroughly review lecture notes, R code and practice questions from the textbook prior to working on the sample quiz

Chapter 1. Introduction to data

Learning Objective

• Variable Types: Numerical vs. Categorical/ Response vs. Explanatory/ Obervational vs. Experimental
• Sampling method: Simple random sampling, Cluster sampling, Stratified sampling
• Causation vs. Correlation/Association

Resource

Lecture note

Exercises

• (p.11) Exercise 1.2: Sinusitis and antibiotics
• (p.19) Exercise 1.5: Cheaters, study components
• (p.20) Exercise 1.8: Sinusitis and antibiotics Part II
• (p.31) Exercise 1.27: Sampling strategies
• (p.35) Exercise 1.30: Vitamin Supplements
• (p.36) Exercise 1.37: Chia seeds and weight loss
• (p.37) Exercise 1.39: Flawed reasoning
• (p.37) Exercise 1.41: Eat better, feel better

R Session

• How do we use the following packages: tidyverse, ggplot2?
• [arbuthnot]Interpret the trend on the number of new born boys/girls.

Chapter 2. Summarizing the data

Learning Objective

• Numerical Data
  • Graphical Summary: Histogram, Boxplot, Scatterplot
  • Numerical Summary: Mean and Variance
• Categorical Data: Frequnecy table, Contingency table, Barplot, Mosaic plot
• Overview for Hypothesis Testing(Malaria vaccine)

Resource

Lecture note

• Special emphasis on the simulation for malaria vaccine
• Sec 2.3. Case study: malaria vaccine

Exercises

• (p.56) Exercise 2.2: Associations
• (p.56) Exercise 2.5: Parameters and statistics
• (p.57) Exercise 2.10: Mix-and-match
• (p.58) Exercise 2.12: Median vs. Mean
• (p.70) Exercise 2.24: Raise taxes
• (p.76) Exercise 2.26: Heart transplants
• (p.77) Exercise 2.31: Oscar winners
• (p.78) Exercise 2.34: Marathon winners

R Session

• The important part is
  • why this particular graph is useful in summarizing the data
  • how to interpret the graph

Chapter 3. Proabibility

Learning Objective

• Definition of Probability: Frequentist vs. Bayesian
• Law of Large Numbers
• Independent vs. Disjoint vs. Complementary
• Product rule for independent Events: $P(A \cap B) = P(A) \times P(B)$
• General addition rule: $P(A \cap B) = P(A) + P(B) - P(A \cap B)$
• Sampling with, without replacement

Resource

Lecture note

Exercises

• (p.92) Exercise 3.1: Ture or false
• (p.92) Exercise 3.5: Coin flips
• (p.93) Exercise 3.9: Disjoint vs. independent
• (p.109) Exercise 3.13 (a), (b)-i, (b)-ii, (c)
• (p.114) Exercise 3.23: Marbles in an urn
• (p.114) Exercise 3.27: Student outfits
• (p.124) Exercise 3.29: College smokers
• (p.124) Exercise 3.31: Heart win
• (p.129) Exercise 3.40: Health coverage, frequencies
• (p.130) Exercise 3.44: Scooping Ice cream

R Session

• Special emphasis on Law of Large Numbers simulation

Chapter 4. Distributions of Random Variables

Learning Objective

• Normal Distribution
  • Parameters: \mu(mean), \sigma(standard deviation)
  • Calculate the probability using pnorm
  • Calculate the percentile using qnorm
  • Z-score and standard normal distribution
• Bernoulli Distribution: Milgram experiment
• Binomial Distribution
  • Parameters: n(the number of trials), p(probability of success)
  • Normal approximation to binomial distribution
• Poisson Distribution

Resource

Lecture note

• Sec 4.5. Poisson distribution – to see the examples potentially following poisson distribution

Exercises

• (p.142) Exercise 4.3: GRE scores, Part I – use pnorm to calculate the probability
• (p.142) Exercise 4.5: GRE scores, Part II – use qnorm to calculate the percentile
• (p.148) Exercise 4.11: Is it Bernoulli?
• (p.148) Exercise 4.12: With and without replacement
• (p.157) Exercise 4.22: Arachnophobia
• (p.166) Exercise 4.27: University admissions
• (p.166) Exercise 4.39: Auto insurance premiums

R Session

• Emphasis on the usage of pnorm