Bootstrap is a derivation of Monte Carlo technique introduced by Efron in 1979. It uses the resampling with replacement method (unlike the resampling with no replacement method that we used in the Lotto Number Generator example). It is a convenient tool to extract estimates (such as standard deviation and confident interval) from a non-parametric data set (a data set with no underling distribution is assumed) or estimates that do not have a closed form (cannot be expressed in an equation). Another use of Bootstrap is to populate sample data when the original sample size is small (but notice that Bootstrap works the best with large sample size as all other statistical methods do).
In this example, we want to obtain the standard deviation of median from 15 GPA scores using Bootstrap. The bootstrap process is as followed:
- Obtain 20 GPA scores from the original 15 using resampling with placement
method.
- Compute the median from these 20 GPA scores and store the median value.
- Repeat process step one and two 500 times.
- Compute the mean and standard deviation from these 500 medians.
The bootstrap shows that the mean median is 3.0792 and the standard deviation is 0.0732. The chart in Figure 1 displays the distribution of the bootstrapped median.
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