Finish CI and Hypo Testing
Day 15
Dr. Elijah Meyer
Duke University
STA 199 - Summer 2023
June 22nd
Checklist
– Clone ae-15
– Homework 4 is Live (Due 6-26)
– Project Report Draft Due Tonight
– Lab Today is a Project Work Day
– Group Feedback Survey-2 in Sakai Coming Today
– Instructor Evaluations
Evaluations (5-10 minutes)
– Please go to: eval-duke.evaluationkit.com.
– I take these seriously
– Duke takes these seriously
By the way…
You have been my favorite summer session to teach…
Project Talk: Rough Draft
The draft and peer review will focus primarily on the exploratory data analysis and initial interpretations.
– Write the draft in the report.qmd
– Make sure you are Building your entire website (demo)
– Change author information
Project Talk: Rough Draft
– Introduction and data (incorporate feedback / add missing details)
– Methodology
+ include visualizations and summary statistics relevant to your research question
+ justify the choice of statistical method(s) used to answer your research question– Results
+ Provide the main results from your analysisTypical Feedback / Questions
– Do your methods actually answer your research question?
– Do you have the data to answer your research question?
– Did you consider including any other variables in your model? (modeling question)
Presentation
– The presentation should be between 5-15 minutes
– Short QA after
– Record presentation part if you can not make it due to an extreme circumstance + follow up with an email I send of questions
– Use whatever platform you are most comfortable with. Google slides is recommended for collaboration
Presentation Tips
– More plots; Less words
– Make sure the audience understands..
+ Why
+ What your research question is – Your plots are distracting if your labels are hard to read. Make them bigger than you think you need on your slides!
– Don’t read from slides. You are welcome to note cards (but don’t just read from those either)
– Everyone needs to contribute something meaningful
– Practice
Questions?
Warm Up
– Why do we make confidence intervals? What is the purpose of confidence intervals?
– Where are bootstrap distributions centered? Why does this make sense?
A Review from Last Time
– We can use the CLT to create confidence intervals (last-ae) and conduct hypothesis tests (this-ae)
– The CLT states for a sufficiently large sample from the population, the distribution of the sample statistic will be approximately normally distributed
– Which we need for our statistical inference methods
Assumptions
– Independence
– Large sample size
Large sample size
Quantitative Response
– n > 30 (in each group if multiple)
– At least 10 successes and 10 failures (in each group if multiple)
Last Time:
Pokemon Heights
estimate \(\pm\) Margin of Error
Margin of error = \(t_{df}^* * \frac{s}{\sqrt(n)}\)
Today: Difference in Means
ae-15
Hypothesis Testing using CLT
– First, we need to standardize our estimate
Standardized test statistic: (statistic - null value)/(standard error of the statistic).
Standardized test statistics are a way for you to compare your results to a “normal” distribution of statistics
Hypothesis Testing using CLT
Then use pt to calculate the p-value!
The Categorical Cases
The Categorical Cases (Confidence Intervals)
– Very similar to what we have done
– Notice the \(z^*\) instead of the \(t*\)
The Categorical Cases (Hypothesis Testing)
– Very similar to what we have done
