Bootstrap Hypothesis Testing Continued
Day 13
Dr. Elijah Meyer
Duke University
STA 199 - Summer 2023
June 14th
Checklist
– Proposal feedback has been given. See issues.
– Exam 2 released at 5 (post in Slack if you have any questions)
— Start early. This is slightly longer than Exam 1
– Group Feedback Survey in Sakai Due by 5
– Lab Due by 5
– Keep up with Slack!
Warm Up - Notation Check
– \(\pi\)
– \(\bar{x}\)
– \(\mu\)
– \(\hat{p}\)
P-value of 0?
When would a p-value of 0 be reported? Let’s draw it.
In R, you will get this error…
Please be cautious in reporting a p-value of 0. This result is an approximation based on the number of reps chosen in the generate()
We have been very carful with our language
Here’s why
– \(\alpha\) > p-value (Reject Ho, Conclude Ha)
– \(\alpha\) < p-value (Fail to reject Ho, Weak evidence for Ha)
– Demo after airbnb example
The research process
– Set up your null and alternative
– Collect data
– Conduct a hypothesis test using simulation methods
– Talk about the results
When can we trust these results?
– When the sample we take is representative
We have a random sample
Sample size is not very small
CPR
Here we consider an experiment with patients who underwent CPR for a heart attack and were subsequently admitted to a hospital. Each patient was randomly assigned to either receive a blood thinner (treatment group) or not receive a blood thinner (control group). The outcome variable of interest was whether the patient survived for at least 24 hours. We are interested in if the proportion of patients who died were different between those who were given blood thinners or not. Note: We will considered “died” as a “success”
– Null
– Alternative
How do we simulate this distribution?
Let’s demonstrate!
Confidence Intervals
– Confidence Intervals are a statistical method uses to estimate population parameters
CI vs Hypo Testing
– Both are curious about population parameters
– Both use the idea of variability
CI vs Hypo Testing
– CIs do not assume a hypothesis
– The distribution used is not centered at the null value (more on this in a second)
Confidence vs Probability
– Before making confidence intervals, let’s define what it is and how it is different than probability.
- Takeaway: Being unknown is not the same as being random
Confidence
Confidence - the percentage of all possible confidence intervals, created under the same conditions, expected to include the true population parameter
– https://www.rossmanchance.com/applets/2021/confsim/ConfSim.html
– For your confidence interval, the parameter is not random
Confidence Interval
Now, let’s make one and talk through it!
