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