Bootstrapping

BOOTSTRAPPING!
Bootstrapping is cool and common.
•You will hear about it in:
–Univariate Statistics
–Multivariate Statistics
–Factor Analysis
–Structural Equation Modeling
–Item Response Theory
–… and more I haven’t been exposed to.
What is bootstrapping?•Randomly sampling, with replacement, from an original dataset for use in obtaining statistical estimates.
–Start with a set of values.
–Randomly draw a value from the “population”.
•The value stays in the available population of values.
–Randomly draw another value from the population.
–Do this N number of times to fill your dataset.
–Perform an analysis on your dataset(s)
–Do this 10,000 times
–Utilize the results of your 10,000 analyses to draw
conclusions.
Why bootstrap?•Good question.
•Small sample size.
•Little to no parametric modeling.•Non‐normal distribution of the sample.•A test of means for two samples.
–Not as sensitive to N.
What bootstrapping looks like: /~mbrannic/files/softwar e/boots_ind_t.sas
•All done in SAS IML.
Bootstrap T‐Test Explained
•2 Samples
•Create 10,000 dataset samples (2 for each cycle) from the original 2 samples.
•For each sample pair, run the t‐test.
–Save the t value in a matrix
•Sort that matrix of 10,000 t‐test values from high to low.
•Select 95% of the values from middle of the distribution.
–Removes the extremes.
•This results in a “Bootstrap Confidence Interval”
–Want this to not contain zero.。