Simple random sample

In statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way. In SRS, each subset of k individuals has the same probability of being chosen for the sample as any other subset of k individuals. Simple random sampling is a basic type of sampling and can be a component of other more complex sampling methods.

In statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way. In SRS, each subset of k individuals has the same probability of being chosen for the sample as any other subset of k individuals. Simple random sampling is a basic type of sampling and can be a component of other more complex sampling methods. &= 1 - \frac{N-1}{N} \cdot \frac{N-2}{N - 1} \cdot \cdots \cdot \frac{N-n}{N - (n - 1)} \\[8pt] &\stackrel{\text{Canceling:}}{=} 1 - \frac{N - n}N \\[8pt] &= \frac nN \\[8pt] &= \frac{100}{1000} \\[8pt] &= 10\% \end{align} 2. In the case that any selected person is returned to the selection pool (i.e., can be picked more than once): P = 1-\left(1-\frac{1}{N}\right)^n = 1 - \left(\frac{999}{1000}\right)^{100} = 0.0952\dots \approx 9.5\% This means that every student in the school has in any case approximately a 1 in 10 chance of being selected using this method. Further, any combination of 100 students¹ has the same probability of selection. If a systematic pattern is introduced into random sampling, it is referred to as "systematic (random) sampling". An example would be if the students in the school had numbers attached to their names ranging from 0001 to 1000, and we chose a random starting point, e.g. 0533, and then picked every 10th name thereafter to give us our sample of 100 (starting over with 0003 after reaching 0993). In this sense, this technique is similar to cluster sampling, since the choice of the first unit will determine the remainder. This is no longer simple random sampling, because some combinations of 100 students have a larger selection probability than others – for instance, {3, 13, 23, ..., 993} has a 1/10 chance of selection, while {1, 2, 3, ..., 100} cannot be selected under this method. ==See also== Multistage sampling Nonprobability sampling Opinion poll Quantitative marketing research Sampling design Bernoulli sampling Poisson sampling ==References== ==External links==

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