# Statistics

By Levi Clancy for Student Reader on
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###### In statistics, we try to draw inferences about a population based on a sample, a technique called statistical inference.

The inference is valid if the sample is random, and the bigger the sample the more reliable the inference. Any measure computes on a population is called a population parameter or simply a parameter, such as population size. Any descriptive measure based on a sample is called a sample statistic or simply a statistic. Subjects are the entities whose characteristics are being studied in a particular experiment.

###### Collection of data elements equals data set. May be of population or sample.

Whether it is one or the other must be conveyed by the data analyst as otherwise it cannot be determined. Variability is the characteristic of dispersion. There are several measures of variability -- population range, either like two to eighteen or sixteen'' population variance, the sigma squared, population variance is based on deviations from the mean. Data elements aka data points are representations of a particular characteristic or variable such as age in Yeats or weight in kilograms. Data elements are measured as numbers of subjects or units of measurement.

TermOverview

Population Size
N

The number of subjects in a population.

Sample Size
n

The number of subjects in a sample.

Summation
Σ

The capital sigma Σ denotes summation.

X

Placeholder for the measurement under consideration. X1 where x is the variable name and the subscript refers to a particular data element.

Dispersion

Dispersion can be measured with the mean absolute deviations (from the mean), but this is less popular than the sample standard deviation. Another method for measuring dispersion in a data set is the range.

Variable

Variables can be defined as continuous or discrete, and a discrete variable is either ordinal or nominal (categorical).

VariableOverview

Continuous

Any value between the minimum and maximum on a particular measurement scale. Variables like age height weight. The standard data summary consists of the sample size (n), the sample mean (x), and sample standard deviation (s); and commonly also the median and quartiles.

Discrete

Limited number of values or categories.

Ordinal

Limited number of values or categories, but they are ordered... such as symptoms of pain being good fair or bad, of performance, etc.

Categorical

Limited number of values or categories and not ordered, such as gender or voting preference.

## Biostatistics

n biostatistics, statisticians apply their techniques to health-related fields. As in other fields, statistics helps health professional formulate research strategies, organize research data, understand the data, draw conclusions and ascertain how confident they may be in these conclusions. This makes biostatistics an integral part of health care from research and development, to making decisions about implementation based on risk knowledge that has been drawn from inferences.