Estimating the sampling distribution using Bootstrap-04-oct-2023
Today I have gained knowledge on Bootstrap. Bootstrapping is a statistical method for estimating the sampling distribution of a statistic without assuming a known underlying distribution. It works by repeatedly resampling the data with replacement and calculating the statistic of interest on each resampled dataset. It can be used to estimate the sampling distribution of any statistic, including the sample median, sample variance, and sample correlation coefficient. It is a powerful tool for statistical inference, and it can be used in a variety of settings.
Here is an example of how bootstrapping can be used:
Suppose we want to test the hypothesis that the average height of men is different from the average height of women. We could collect a sample of heights from men and a sample of heights from women, and then use bootstrapping to estimate the sampling distribution of the difference in sample means.
To do this, we would draw bootstrap samples from the men’s and women’s samples with replacement, and then calculate the difference in sample means on each bootstrap sample. The distribution of the difference in sample means from the bootstrap samples would be an estimate of the sampling distribution of the difference in sample means.
We could then use this distribution to calculate a p-value for the hypothesis test. The p-value would be the proportion of bootstrap samples that had a difference in sample means that was as large or larger than the difference in sample means from the original sample. If the p-value is less than a significance level of 0.05, then we would reject the null hypothesis and conclude that there is a statistically significant difference in the average heights of men and women.
Bootstrapping is a versatile and powerful statistical tool that can be used for a variety of purposes. It is a good choice for researchers who want to make inferences about their data without assuming a known underlying distribution.