3.3/3.4 Bootstrap Confidence Intervals (Exam 2)

If 0 is not included in the interval..

-0 is not a possible number -therefore, there is a significant difference between the two proportions

Sampling with Replacement

-each case can be selected more than once

standard error from a bootstrap distribution

-estimated using the standard deviation of bootstrap distribution

How would you use the bootstrap sample to compute a bootstrap statistic?

-find the statistic in bootstrap sample 1 (phat*1) -find the statistic in bootstrap sample 2 (phat*2) -sample statistic (each dot in distribution)

bootstrap distribution

-many bootstrap samples must be drawn to create a distribution

Advantages of the percentile method

-more flexible -can compute 90,95,99% intervals *for skewed*

what does one dot refer to on the bootstrap distribution?

-one dot represents one bootstrap statistic based on one bootstrap sample

Disadvantages of SE

-only good for 95% confidence -may be less accurate than the percentile method

boostrap sample

-sample with replacement from original sample using the same sample size

How would you create a bootstrap statistic using cards?

-start with (sample #) of cards to represent one individual sample -write statistics of interest on the cards -randomly draw a card -record information -replace card -shuffle -randomly select card and repeat steps until you reach the same sample number -calculate population parameter and statistics

How do you create a bootstrap for difference in proportions?

-start with cards =n -split into two piles to represent the number of samples for each group size -for group 1, add specific info to each card for number in that sample -for group 2, add specific info to each card for number in that sample -For group 1, randomly choose 1 card, record results, replace, until you reach sample amount = bootstrap sample 1 -Repeat for group 2 = bootstrap sample 2

What is bootstrapping?

-take a random sample from the population -sample is a representative of your population -make many copies of sample -re-sample from same group

Grouping variable

-two groups (usually numbered 1 and 2) -order doesn't really matter as long as it's consistent -independent from each other

bootstrap statistic

-uses re-sampled cases in the bootstrap sample to compute the boostrap statistic of interest

Variable of interest: categorical

Inference for p1-p2

where should the bootstrap distribution be centered?

around the sample statistic

how do we get a more precise bootstrap?

use more samples

the standard error is from the ______________ distribution

bootstrap (simulation)

sample size

how many cases you have in one sample

number of bootstrap samples

how many times you run the bootstrap stimulation

quantitative variable: mew 1 (or 2)

mean of variable of interest in population 1 (or 2)

quantitative variable: xbar 1 (or 2)

mean of variable of interest in sample 1 (or 2)

_______________ will NOT affect the standard error

number of bootstrap samples

What test would be used for: one group + quantitative variable

population mean

the sampling bootstrap distribution is centered around the ___________________.

population parameter

What test would be used for: one group + categorical variable

population proportion

p1 (or 2)

proportion of category of interest in population 1 (or 2)

phat 1 (or 2)

proportion of category of interest in sample 1 (or 2)

each bootstrap sample should have the ___________sample size compared to the original/real sample?

same

___________________will affect the standard error

sample size

n1 (or 2)

sample size from sample 1 (or 2)

quantitative variable: n1 (or 2)

sample size from sample 1 (or 2)

the bootstrap distribution is centered around the ________________________.

sample statistic

where should a bootstrap statistic be centered?

sample statistic (we are taking multiple statistics from the same sample group with replacement)

bootstrap distributions can be used to estimate the _______________ distribution

sampling

Do the P% and SE methods give similar or different results?

similar

quantitative variable: s1 (or 2)

standard deviation of variable of interest in sample 1 (or 2)

the standard deviation of a bootstrap distribution is called ______________.

standard error

Phat 1- phat 2

statistic of interest

quantitative variable: xbar 1- xbar 2

statistic of interest

the process for creating bootstrap confidence intervals is _______________ for all parameters

the same

What test would be used for: two groups + quantitative variable

difference in population means

What test would be used for: two groups + categorical variable

difference in population proportions

As confidence increases, width of the interval __________________.

increases

Variable of interest: quantitative

inference for mew 1- mew 2

the statistic is from the real________________sample

original (not simulation)

quantitative variable: mew 1- mew2

parameter of interest

Advantages of standard error method

*for bell shaped* -relies on the fact that about 95% of statistics are within 2 standard error for bell shapes

Interpret a difference in population proportions confidence interval

*we are 95% confident* that the population proportion for (variable 1) is between (confidence interval) (higher/lower) than (variable 2)

2 methods for finding bootstrap intervals

1. estimate the standard error of the statistic by computing the standard deviation of the bootstrap distribution. Then generate a 95% confidence interval 2. Generate P% confidence interval as the range for the middle P% of bootstrap statistics

SE method is ONLY good for ______ confidence

95%

P1-P2

Parameter of interest

we don't care about the center, we care about ____________________

variability