The bootstrap principle for proportions

With this app you can examine the bootstrap method for estimation the average or standard deviation of a population. And also for the difference of the averages at two populations. This app is designed for continuous distributions. For yes-no distributions a separate app is available.

An easy job is to verify that the bootstrap does not always work well in extreme situations. For example, with a small sample.
The upper screen shows the distribution. This can be changed with the mouse. For example, to a two peak distribution.

Each time a sample is drawn from the population and the bootstrap method is executed on the sample .
With slow speed each experiment will take two steps. First, a sample is drawn. The mean and the standard deviation of the sample are shown on the left.
The bootstrap method is carried out at the second step. So a lot of drawns from the sample. How many times an element has been selected in the final bootstrap you can see the thickness of the border of the sample circle. With each new bootstrap again a drawing with replacement. is done from the sample This leads to the bootstrap distribution. The bootstrap method is the confidence interval is the center piece. What proportion of the edges is taken into account depends on the confidence level. (Percentage).
This interval is drawn in the third screen.
As more and more bootstraps are taken from the sample this results finally in a new confidence interval.
The program then checks whether the population parameter really is in the calculated interval. Bottom right is the percentage of times that this method was performed and was successful.

Also for the bootstrap distribution is that the root-n-law is applicable.
confidence level
The confidence level can change during simulation.
In theory you can choose any percentage for the confidence level, but because of the possibility of change is chosen for a limited number.

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