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These n h must conform to the rule that n 1 + n 2 + ... + n H = n (i.e., that the total sample size is given by the sum of the sub-sample sizes). Selecting these n h optimally can be done in various ways, using (for example) Neyman's optimal allocation.
Proportionate allocation uses a sampling fraction in each of the strata that are proportional to that of the total population. For instance, if the population consists of n total individuals, m of which are male and f female (and where m + f = n), then the relative size of the two samples (x 1 = m/n males, x 2 = f/n females) should reflect this proportion.
A riffle box is a box containing a number (between 3 and 12) of "chutes" - slotted paths through which particles of the sample may slide. The sample is dropped into the top, and the box produces two equally divided subsamples. Riffle boxes are commonly used in mining to reduce the size of crushed rock samples prior to assaying.
Suppose that we take a sample of size n from each of k populations with the same normal distribution N(μ, σ 2) and suppose that ¯ is the smallest of these sample means and ¯ is the largest of these sample means, and suppose S 2 is the pooled sample variance from these samples. Then the following random variable has a Studentized range ...
As an example, consider a dataset of birds for classification. The feature space for the minority class for which we want to oversample could be beak length, wingspan, and weight (all continuous). To then oversample, take a sample from the dataset, and consider its k nearest neighbors (in feature space).
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