Learn two ways to build confidence intervals from bootstrap samples. The percentile method uses the 2.5th and 97.5th percentiles of your bootstrap distribution. The standard-error method takes your sample statistic plus or minus a t value times the bootstrap standard deviation.
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In the previous courses in the series, you have already discussed percentile and standard error methods for constructing bootstrap confidence intervals. In this video, we'll review these methods. Here's our bootstrap distribution comprised of 15,000 bootstrap medians. Each observation in this plot is a median from a bootstrap sample. And remember that each bootstrap sample is a sample taken with replacement from the original sample and of the same size as the original sample. It's really important to understand what with replacement means in this context as well as the purpose it serves. Say I had a bag in my hand with 20 cards in it, each card showing the rent for one of the apartments in my original sample. Taking a bootstrap sample from this bag would mean picking a card, noting the rent on that card, and then putting the card back into the bag before selecting the next card. So the first card becomes a candidate for the second draw as well. Suppose that the first apartment we select from the sample has a rent of $2,000. The idea behind sampling with replacement is that there may be many other such apartments in the population. So if we had the luxury to go back and sample from the population, we could conceivably get more such apartments in our sample. Using this bootstrapping distribution, we can calculate a confidence interval in one of two ways. The first is the percentile method, where we estimate, say, a 95% confidence interval simply as the middle 95% of the bootstrap distribution. So the bounds of a 95% confidence interval are the 2.5 and the 97.5 percentiles of the bootstrap distribution. A second and a more accurate method is the standard error method. In this method, we calculate the interval as the sample statistic plus or minus t times the bootstrap standard error. The degrees of freedom for the critical T score is N1, where N is the original sample size. The bootstrap standard error is just the standard deviation of the bootstrap distribution Time. To put this into parameter.
