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1. Bootstrapping – estimations beyond mean
a. When to use bootstrapping
i. If using median
b. Bootstrapping assumption: for each observation in the sample, there may be many others like it in a
population
c. Bootstrapping scheme:
i. Take bootstrap sample – random sample taken with replacement from the original sample of
the same size as the original sample
ii. Calculate bootstrapping statistic – a statistic (mean, median, proportion) computed on
bootstrap samples
iii. Repeat many times with replacement
d. :Bootstrapping Limitations
i. Extremely skewed/ sparse distribution gives an unreliable bootstrap interval
ii. Biased / non-representative sample gives a biased / non-generalizable estimate
e. Bootstrapping v. Sampling: both distributions of a sample
i. Bootstrapping replaces from sample
ii. Sampling replaces from population
f. How to Confidence interval using Bootstrapping Percentile Method
i. Identify the parameters of interest: median of population =
ii. Identify the point estimate: median of sample =
iii. Calculate number of points on distribution you are looking for
1. P p-value * n dots = x dots that qualify
2. n dots – x dots = dots of interest / 2 = dots for each side
iv. Find values at lower and upper bound
v. Interpret results
1. We are p% confident that the difference between the averages of A and B is between
X and Y.
2. We are x% confidence that A is X to Y higher than B.
g. How to Confidence interval using Bootstrapping Standard Error Method
i. Identify the parameters of interest: median of population =
ii. Identify the point estimate: median of sample =
iii. Identify variables of interest
1. SEboot (usually given)
iv. Calculate confidence interval
v. xxboot +/- z* SEboot
vi. Find values at lower and upper bound
vii. Interpret results
1. We are p% confident that the difference between the averages of A and B is between
X and Y.
2. We are x% confidence that A is X to Y higher than B.
viii. Interpret results
1. We are p% confident that the difference between the averages of A and B is between
X and Y.
2. We are x% confidence that A is X to Y higher than B.
2. t-distribution
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