Resampling

The process of sampling from the observations in a sample, in order to obtain estimates and confidence intervals for population parameters without making assumptions about the form of the population distribution. Suppose that we have taken a random sample of n observations, and assume, for simplicity, that all the sample values x₁, x₂,..., x_n are different. If we have no other information about the population then the obvious estimate of the population mean, μ, is the sample mean x̄. This is not contentious. However, it is equally true that an unbiased estimate of the probability of the value x_j is 1/n. In a sense the sample is a surrogate for the population — if we want to know what other samples from the population might have looked like, we can find out by sampling from the sample. This is the process called resampling.

As an example, suppose that we wish to estimate the median of a distribution. We take ten observations and obtain the values

A simple estimate of the median of the distribution is the median that we have observed, namely 4.75. Resampling enables us to derive an empirical confidence interval for this estimate. Using the pseudo-random numbers in the first row of Appendix XIV, which begins 07552 37078, we generate a new sample
which has median 5.2. Further resampling produces successive sets of ten 'observations' with medians 5.6, 4.4, 5.35, 4.4, 3.8, 4.25, 3.95, 4.75, 4.4, 4.75, 4.1. The fifteen resampled medians have mean 4.61 and standard deviation 0.548 so that an approximate 95% confidence interval for the median is (3.5, 5.7). See also bootstrap; jackknife.

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Resizing an image by reducing or increasing its number of pixels. An image can also be resized for printing without resampling and altering its physical structure. If resampling is turned off in the resizing dialog in Photoshop or other image editor, changing the print size changes only the resolution that will be used to convert the image to paper. If the print size is decreased by 50%, the resolution will be increased by 50% and vice versa.

Resizing the Original

Resampling changes the original image. In this Photoshop dialog, selecting Resample Image (bottom left) and changing Height in Pixel Dimensions (in this case, from 660 to 330) means that the original image will be permanently altered.

Resizing for Printing

When resampling is not done, the print resolution can be changed without affecting the original image. In this Photoshop dialog, unchecking Resample Image causes the Pixel Dimensions at the top of the dialog to be grayed, which means the size of the image cannot be modified. Changing Width in Print Size from 7.347 to 5 inches changed the resolution (dots per inch) for the printer only.

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