The<unk>  of a statistical<unk>  is the number of repeated measurements that constitute it.  It is typically denoted n, and is a non-negative integer (natural number).
Typically, different<unk> s lead to different accuracies of measurement. This can be seen in such statistical rules as the law of large numbers and the central limit theorem. All else being equal, a larger<unk>  n leads to increased precision in estimates of various properties of the population.
A typical example would be when a statistician wishes to estimate the arithmetic mean of a continuous random variable (for example, the height of a person). Assuming that they have a random<unk>  with independent observations, then if the variability of the population (as measured by the standard deviation σ) is known, then the standard error of the<unk>  mean is given by the formula:
It is easy to show that as n becomes large, this variability becomes very small. This yields to more sensitive hypothesis tests with greater Statistical power and smaller confidence intervals.
With more complicated<unk> ng techniques, such as Stratified<unk> ng, the<unk>  can often be split up into sub-samples. Typically, if there are k such sub-samples (from k different strata) then each of them will have a<unk>  ni, i = 1, 2, ..., k. These ni must conform to the rule that n1 + n2 + ... + nk = n (i.e. that the total<unk>  is given by the sum of the sub-sample<unk> s). Selecting these ni optimally can be done in various ways, using (for example) Neyman's optimal allocation.
Sample size
Attributable risk
Number needed to treat
Clinical trials terminology
Design of experiments
Cumulative incidence
Missing data
Statistical significance