Sampling variability and bootstrapping
What this lesson covers
- Sample statistics vary from sample to sample.
- A bootstrap resample is the same size, drawn with replacement.
- Thousands of resamples show the spread of an estimate.
The bootstrap
- Take your one random sample.
- Draw a new sample of the same size with replacement.
- Calculate the statistic and repeat 1000 or more times.
- The spread of those results shows the uncertainty.
Reading a bootstrap
- 1000 resampled means, sorted from lowest.
- 2.5th percentile = 47.2
- 97.5th percentile = 53.8
- 95% interval: 47.2 to 53.8
Common mistakes
- Sampling without replacement.That only rebuilds the same sample.
- Thinking bootstrapping adds new data.It only measures uncertainty from what you have.
Your turn
- 1. Why draw with replacement?
- 2. What size is each resample?
Show answer
1. So each resample differs from the original 2. The same as the original sample
What to take away
- One sample can show its own uncertainty.
- It still has to be a random sample.
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