# Random Sampling without Replacement

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A Random Sampling without Replacement is a random sampling (from a random experiment) where an Outcome (from a Sample Space) can only contribute once to the Trial.

## References

### 2008

- Chris Blais. (2008). “Random Without Replacement is not Random: Caveat emptor.” In: Behavior Research Methods, 40. doi:10.3758/BRM.40.4.961
- ABSTRACT: The vast majority of psychology labs rely on prepackaged software applications (e.g., E-Prime) for the programming of experiments. These programs are often used for stimulus selection, and many use a selection method referred to as random without replacement. We demonstrate how random without replacement deviates from random selection, and we detail selection biases that result. We also demonstrate, in a simple experiment, how these selection biases, if left unchecked, can influence behavior. Recommendations for reducing the impact of these biases on performance when random without replacement is used are discussed.

### 2001

- (Kochar & Korwar, 2001) ⇒ Subhash C. Kochar, and Ramesh Korwar. (2001). “On Random Sampling Without Replacement from a Finite Population.” In: Annals of the Institute of Statistical Mathematics, 53(3).
- ABSTRACT: We consider the three progressively more general sampling schemes without replacement from a finite population: simple random sampling without replacement, Midzuno sampling and successive sampling. We (i) obtain a lower bound on the expected sample coverage of a successive sample, (ii) show that the vector of first order inclusion probabilities divided by the sample size is majorized by the vector of selection probabilities of a successive sample, and (iii) partially order the vectors of first order inclusion probabilities for the three sampling schemes by majorization. We also show that the probability of an ordered successive sample enjoys the arrangement increasing property and for sample size two the expected sample coverage of a successive sample is Schur convex in its selection probabilities. We also study the spacings of a simple random sample from a linearly ordered finite population and characterize in several ways a simple random sample.