Glossary of Statistical Terms

A

Alternative Hypothesis

Any negation of the null hypotheses. For example, if the null hypothesis is "mean 1 is equal to mean 2". The alternative hypothesis are "mean 1 is not equal to mean 2" and mean 1 is greater than/less than mean 2."

Analysis of Variance

A method for determining the proportion of the variation in a sample that is explained by one or more classification factors.

B

Bar Graph

A graph representing values as bars, where the length of the bars reflect the values.

Box Plot

A graphical representation that depicts the distribution of a response for different levels of a categorical predictor.

C

Central Probability

The probability that a value of a random variable with a distribution symmetric about zero (like the normal distribution) would be closer to zero that a given value (x).

Classical Analysis

A method that assumes knowledge of the distribution underlying the sample.  Classical analysis
uses statistical tests based on estimates of the parameters of the underlying population,   such as the mean and the variance. Such tests are called parametric tests.

Confidence Interval

A range of values that have at least the specified probability of containing the parameter value
being estimated.

Correlation

A measure of the extent to which two variables tend to be associated, vary, or occur together. Correlation can be positive or negative and is scaled to lie between -1 and +1. If two variables are positively correlated, their values tend to increase and/or decrease together. If two samples are negatively correlated, the values of one increase while the values of the other decrease. In addition, correlation can be linear or non-linear. If two samples are linearly correlated, there values tend to fall along a straight line when plotted against one another. If two samples are nonlinearly correlated, their values tend to follow a nonlinear pattern.

Covariance

A measure of the extent to which two variables tend to vary together linearly. The covariance between two variables is their linear correlation times the product of each of their standard deviations.

D

Degrees of Freedom

1) A parameter of certain families of probability distributions (e.g., the chi squared distribution); 2) a measure of the number of dimensions in statistical data or model structure. The degrees of freedom of the structure are the number of quantities that can vary independently in that structure.

Descriptive Statistics

Statistical measures of data that reflect properties of the data and provide a means of assessing the general nature of the underlying distribution. Examples include mean, standard deviation, range.

Dispersion

The extent to which data are spread out rather than clustered close to their mean or median.

Distribution

The relative frequency in which values of a variable in a data sample or in a population are distributed across the range of possible values.

H

Histogram

Represents the frequency distribution of values of a variable by rectangular bars. The width of the
bars represent classifications or ranges of values of the variable. The heights of the bars represent the frequencies of values falling into the corresponding classification or range.

Hypothesis

An assertion or conjecture about the distributions of one or more variables.

K

Kurtosis

A measure of the degree of peakedness and outlier-proneness of a distribution. Kurtosis can be positive or negative. The standard normal distribution has a kurtosis of zero and is the standard against which the kurtosis values for other distributions are measured. The larger the kurtosis, the more peaked the distribution and the more frequent the outliers. The smaller the kurtosis the flatter the distribution.

M

Mean

The sum of values in a sample, divided by the count (total number of values). The mean us similar to the median in that it estimates the "center" of the distribution of data.

Median

An estimate of the center of the distribution of the data. It is the value above and below which lie an equal number of data values when the data are arranged in increasing or decreasing order. If the count of the sample is odd, the median is the middle value. If the count is even, the median is the average of the two middle values.

Model

An equation relating responses and predictors. A statistical model contains two parts: a model for the signal and a model for the noise, or error, associated with the signal. The model for the signal is an equation describing how the mean of the responses depends on certain predictor variables. The model for the noise, or error, describes the distribution of the deviations of responses from the signal.

N

Null Hypothesis

A hypothesis that asserts either the equivalence of two unknown quantities or the positive statement of a condition (for example, "mean 1 is equal to mean 2" or "the population is normal"). It is used in hypothesis testing as the default hypothesis in contrast to the alternative hypothesis.

O

Outlier

An extreme value in a data sample that is far from the central cluster of values in the sample. An outlier is extraordinary either because it is "far away" from the other values or because it fails to conform to the patter of the other values.

P

Parameters

Quantities that characterize or are functions of the distribution of a population, such as mean and variance.

Parametric Tests

Statistical tests based on knowledge of the parameter form of the distribution of the underlying population.  Parameter tests are used in classical analysis.

Population Mean

The unknown mean of the underlying population from which data values are drawn.

Predicted Values

Values predicted by a fitted model.

Probability Distribution

A representation of the probabilities associated with values of a random variable.

R

Random Variable

A variable whose value is determined by the outcome of an event or experiment.

Range

The difference between the maximum and the minimum values in a group of data.

Regression Analysis

Analysis that is used to depict the relation between dependent and independent variables derived from a study. The goal of regression is to find a mathematical model that best explains how changes in the independent predictor variables affect the dependent response variables. A fitted regression model estimates the relation between predictors and responses and may be used to forecast or predict values of the responses.

S

Skewed Distribution

A distribution that is not symmetrical about its mean, but instead has values concentrated on one side or the other of the mean. If the distribution is concentrated to the left of the mean and is more spread out to the right of the mean (when graphed), the distribution is positively skewed. If the reverse is true, the distribution is negatively skewed

Skewness

A measure of the degree of asymmetry of the data around the sample mean. If the data is distributed symmetrically around the mean, the skewness is 0.0. From a graphical point of view, negative skewness indicates that the data are more spread out to the left of the mean than to the right of it. The reverse is true for positive skewness.

Standard Deviation

A measure of the average deviation of data values from the sample mean. The standard deviation is equal to the square root of the variance.

U

Unimodal

A distribution whose histogram has just one "hump", as in a bell-shaped curve. (Bimodal distribution would have two "humps" )

V

Variable

A measurement or attribute of each member of a sample or population, for example, weight, height, age.

Variance

The average of the squared differences between the values of a variable and the mean. The variance estimates the spread of a distribution.

W

Weighted

In order to adjust for the fact that some data are less valuable or less reliable than other data, a statistical analysis may down weight the less reliable points for certain computations.

X

X-Y Graph

A visual representation that depicts the relationship between a continuous predictor and a continuous response; can be a scatter plot or a line plot.