These are Glossary entries S-Z. For Additional Notes, click on the bar within or at the end of the entry.
S T U V W X Y Z
s [regular old letter s] is the sample standard deviation; to be distinguished from the population or regular standard deviation, which is indicated by Greek s (sigma, or s]. For the formulas, see below under Standard Deviation.
Sample. A set of test values drawn from a larger group called the population. The measures for a sample are conventionally distinguished from those of the population from which it is drawn. Here is a chart of the respective terms:
For the formulas, see the Standard Deviation and Variance entries.
Sample Mean (m). The mean or average of the sample values. It is conventionally represented by x-bar, but in these pages by m.
Sample Space. A list or diagram of all the possible outcomes of an experiment or series of observations, including their probabilities. This is a confusing term, and we use instead the term Frequency Profile.
Sample Standard Deviation (s). The standard deviation of the sample, rather than that of the population. Its formula is importantly different from that of the population standard deviation; see below under Standard Deviation.
Sample Variance (sv). See below under Variance.
s: [Greek lower-case letter sigma] is the usual symbol for [population] standard deviation. This is the measure of dispersion for a normally distributed population (not for a sample drawn from that population). The standard deviation is the square root of the sum of the squares of the differences between each data value and the mean of those values, divided by the number (n) of values. In equation form:
s = r[S([x-m]*2)/(n)]
It is easier to compute s in steps than to work directly from that formula, which however is a handy mnemonic for the steps in question. See further below under Standard Deviation.
S [Greek upper-case sigma] is the usual symbol for the sum of certain specified numbers.
S(n) = sum of all the values of n, or all values within prescribed limits. The limits may be specified when necessary in postposed brackets, thus
S(x²) [1 ~ 10) = sum of x² from x = 1 to x = 10 inclusive
Standard Deviation (s). A measure of the "spread" of the normal distribution curve for a given data set. It is one of two parameters for the normal curve; the other is the mean. It is always symbolized by a lower-case Greek sigma (s). The standard deviation of the population itself is the square root of the sum of the squares of the differences between each data value and the mean (m) of all the data values, divided by their number (n). As a formula,
s = r[S([x-m]*2)/(n)]
The Sample Standard Deviation (s rather than s) requires use of the sample mean (m rather than m) and a correction from (n) to (n - 1), thus
s = r[S([x-m]*2)/(n - 1)]
Sum. For the sum of a series of values, see Sigma.
sv = Sample Variance. See below under Variance.
T Distribution. The name given by Gosset (under his pseudonym "Student") to a distribution that arises in the study of small samples, and in various other ways as well. It is one of the thoroughly useful perceptions of modern statistics.
U. The name for Mann-Whitney test, which is the nonparametric counterpart of Gosset's T test.
Urn. A container holding balls of varied colors from which someone draws one ball without being able to see what kind it is.
v = [Population] Variance. Distinguish Sample Variance (sv), and see the Additional Note under the Variance entry, below. The population variance is conventionally given as s² (since the population standard deviation s is the square root of it), but we think it well to give Variance its own abbreviation.
Variance (v). A measure of the amount of variability in a population. The variability of a data set which is drawn from that population is the Sample Variance (sv).
x-bar. An x with a bar or macron over it, the standard symbol for "mean of all values x." The x values are usually understood as the sample values, and for their mean we will use the symbol "m." Compare the population mean, m (mu).
z. The number of standard deviations (s) which a given divergence from the mean (m) represents. The z-score for a given value x is thus
z = x/s
The z-score is a measure of the statistical significance of the departure of that data point from the norm: the likelihood that it is not a random result.
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