Name: bootstrapping in small sample statistics
Uploaded: 2025-01-09T15:14:08.000Z
Duration: 1 min 24 s
Channel: JoVE

Bootstrapping is a resampling method that uses samples randomly drawn from the already collected sample with replacement.
Imagine a paleontologist trying to determine the mean wing length of a prehistoric insect species with only five fossil specimens.
A higher sample size is desirable to make better inferences, but there is no way to obtain more fossils. In such cases, the bootstrap resampling method is beneficial.
These data from five specimens give a mean length of 10.7 cm.
To begin bootstrapping, randomly draw samples from the original sample set.
Notice that this sample has an identical sample size to the original one, but some values are repeated. This occurs because the bootstrap resampling is entirely random.
Several such bootstrap samples are drawn to estimate the mean wing length distribution. This way, confidence intervals can also be obtained to estimate the population mean more accurately.
Bootstrapping is easy and cost-effective, but it relies on a limited sample. If such a sample is biased or collected erroneously, the bootstrap resampling will remain as biased or erroneous as the original sample.

bootstrapping

Bootstrapping

The term &#34;bootstrap&#34; originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is small or the data is complex.
Bootstrapping, also known as bootstrap resampling, simulates the sampling process by drawing multiple random samples, with replacement, from an existing dataset. Here, the original sample acts as a stand-in &#34;population,&#34; and each resample is treated as an independent sample drawn from this &#34;population.&#34; The underlying assumption is that the original sample is a good representation of the broader population. This approach is especially valuable when sample sizes are limited, as in studies with rare fossils, ancient genomic samples, tissues from rare diseases, endangered species studies, and unique experiments that cannot easily be repeated.
The basic process of bootstrapping includes the following steps:
<ol>
	<li>Collect an initial sample of size n from the population to estimate a parameter of interest.</li>
	<li>Treat this sample as a &#34;population.&#34;</li>
	<li>Draw several new samples of size n, with replacement, from the original sample using random sampling.</li>
	<li>Use these &#34;bootstrap resamples&#34; for analysis to estimate the desired parameter.</li>
</ol>
Since resampling is with replacement, each new sample may include repeated values from the original data, reflecting the randomness in the resampling process. Bootstrapping typically requires a high number of resamples (often over 1,000) to achieve stable estimates, which can then be used to calculate statistics like the mean, variance, standard error, or confidence intervals for population parameters.
Bootstrapping is both cost-effective and accessible, offering a straightforward way to make inferences without needing additional data. However, it relies heavily on the original sample, meaning that any biases or errors in the original data will be present in the bootstrapped results as well.

Bootstrapping is a resampling method that uses samples randomly drawn from the already collected sample with replacement.
Imagine a paleontologist trying ...

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KEY TERMS AND CONCEPTS

bootstrapping in small sample statistics

Bootstrapping is a statistical resampling method used to estimate population parameters from an existing sample. It builds on the idea of the word bootstrap, which first appeared in the 19th century as a metaphor for doing something independently. In statistics, the method was developed by Dr. Bradley Efron in 1979.

Bootstrapping is also called bootstrap resampling. It works by drawing many random samples, with replacement, from the original dataset. Each bootstrap sample has the same size as the original sample. Because sampling is with replacement, some values can appear more than once in a resample.

In this method, the original sample acts like a stand-in population. Each new resample is treated as if it were another sample from that population. This only works if the first sample is a good match for the larger population. Bootstrapping is especially useful when the sample size is small or the data is complex.

This approach is helpful in studies with rare fossils, ancient genomic samples, tissues from rare diseases, endangered species, and experiments that cannot be repeated easily. The process starts with one sample of size n from the population. That sample is then resampled many times, often more than 1,000 times, to create stable results.

The bootstrap resamples can be used to estimate the mean, variance, standard error, or confidence intervals for population parameters. Bootstrapping is cost-effective and accessible because it does not require new data. However, it still depends on the original sample, so any bias or error in that sample will also appear in the bootstrap results.

Bootstrapping in Small Sample Statistics

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Bootstrapping is a statistical resampling method used to estimate population parameters from an existing sample. It builds on the idea of the word bootstrap, which first appeared in the 19th century as a metaphor for doing something independently. In statistics, the method was developed by Dr. Bradley Efron in 1979. Bootstrapping is also called bootstrap resampling. It works by drawing many random samples, with replacement, from the original dataset. Each bootstrap sample has the same size as...

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key terms and concepts

Learn how bootstrapping uses resampling with replacement to estimate mean, variance, standard error, and confidence intervals from small datasets.

Bootstrapping in Small Sample Statistics | JoVE K12

statistics

JoVE Core Statistics introduces the concepts and application of the collection, analysis, presentation, and interpretation of data to students. These animated lessons provide an understanding of statistics beneficial to students from a wide range of disciplines. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide

Bootstrapping in Small Sample Statistics

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