Foundations for Statistical Inference

Study Design, Inference using randomization and the Normal Model

Learning Path

Where we’ve been

  • Learning how to explore and visualize our data.
  • Visually consider patterns, identify potential relationships

Where we’re at

  • Think about how data come to be. That is, if the data are to be used to make broad and complete conclusions, then it is important to understand who or what the data represent.
    • Knowing how the observational units were selected will allow for generalizations back to the population from which the data were selected.
    • By understanding the structure of the study, causal relationships can be separated from those relationships which are only associated.
  • Revisiting null value hypothesis testing (NVHT) from a randomization perspective
  • Revisiting the Normal distribution model, and getting a feel for how probability (and thus p-values) are calculated.

Objectives

Items
Identify and distinguish between a parameter and a statistic
Describe multiple sampling methods
Identify if a causal statement can be made given a data collection method
Explain how to test a hypothsis using randomization
Assess a research question using a hypothesis test
Use the Normal distribution to calculate a probability
Describe the concept of sampling variability
Calculate the mean and sd of the sampling distribution based on population parameters
Explain the Central Limit Theorem
Construct and Interpret a confidence interval in context of the problem
Use a confidence interval to make an inferential hypothesis statement

Learning Materials

Slides (Will open in full screen. Right click to open in a new tab)

Items
lec06a
lec06b

📚 Reading

Items
Topic Overview
IMS Chapter 11-11.1
IMS - Chapter 13.1-13.3
IMS - Chapter 2

📝 Active Learning

We will be using the Jigsaw technique, which is a method of learning by teaching. You have been assigned to read and summarize one section in the textbook.

Items
Study Design
Bias in hiring
CLT Explorer
HW06

Assessment

Items
Quiz 05
Quiz 06