The following examples use StatKey to construct bootstrap distributions. When the bootstrap distribution is approximately normally distributed, we can use the standard error method to construct a confidence interval. Recall for a 95% confidence interval: \(statistic \pm 2 (standard\ error)\). The standard error method can only be used when the bootstrap distribution is approximately normal. If the distribution is not approximately normal, then the percentile method must be used. 

To construct a bootstrapped confidence interval using the standard error method follow these steps:

1. Determine what type of variable(s) you have and what parameters you want to estimate. StatKey will bootstrap a confidence interval for a mean, median, standard deviation, proportion, difference in two means, difference in two proportions, simple linear regression slope, and correlation (Pearson's r). 
2. Get your sample data into StatKey. There are some built-in datasets and you have the ability to enter in your own data. This procedure varies depending on the test you're conducting. For a proportion you need to enter the number of successes and number of trials. For anything involving quantitative data you will need to copy and paste your data into StatKey (this is the recommended method) or upload it as a txt, csv, or tsv file. 
3. Generate at least 5,000 bootstrap samples.
4. Confirm that your bootstrap distribution is approximately normal. If it's not approximately normal you should consider using the percentile method.
5. Use your original sample statistic and the standard error from your bootstrap distribution to construct a confidence interval.
   For a 95% confidence interval the formula is \(statistic \pm 2 (standard\ error)\)

It is possible to use the standard error method to construct confidence intervals at levels other than 95% if you have the appropriate multiplier.  Later in the course, in Lesson 7, we will learn more about how other multipliers can be found. 

Regardless of the shape of the bootstrap sampling distribution, we can use the percentile method to construct a confidence interval. Using this method, the 95% confidence interval is the range of points that cover the middle 95% of bootstrap sampling distribution. The following examples use StatKey.

To construct a 95% bootstrap confidence interval using the percentile method follow these steps:

1. Determine what type(s) of variable(s) you have and what parameters you want to estimate. StatKey will bootstrap a confidence interval for a mean, median, standard deviation, proportion, different in two means, difference in two proportions, regression slope, and correlation (Pearson's r). 
2. Get your sample data into StatKey.  There are some built-in datasets and you always have the ability to enter in your own data. This procedure varies depending on the test you're conducting.  For a proportion, you need to enter the number of successes and number of trials.  For anything involving quantitative data you will need to copy and paste your data into StatKey (this is the recommended method) or upload it as a txt, csv, or tsv file. 
3. Generate at least 5,000 bootstrap samples.
4. Check the "Two-Tail" box at the upper left corner of the bootstrap dotplot. By default, this will give you a 95% confidence interval.

The default in StatKey is to construct a 95% confidence interval. You can change the confidence level by clicking the "0.950" in the center and entering the confidence level you want. For example, for a 90% confidence interval you would enter "0.90." Below is a short video demonstrating this.