Terms

Covariance is a measure of the co-movement between two random variables. While variance measure how a random variable moves with itself, covariance measures how a random variable moves with another random variable.

cov_xy = {Σ[(X-E(X))(Y − E(Y))]} / (n − 1)

A negative covariance means that variables move in different directions. A positive covariance means they move in the same direction.

A histogram is a chart displaying how items in a data set fall over a range of values. The distribution is illustrated in a set of adjacent bars, which is the root of the histogram's name. It derives from the Greek histos--"anything set upright"--and gramma--"drawing."

Sample Histogram

A binomial random variable is a variable which only has two possible outcomes, like a coin flip. The outcomes of such a variable are often simplified to "success" and "failure."

Binomial Probability Function

When the probability of success, p, is constant and the trials are independent, the binomial probability function can be taken off the shelf to determine the probability of x successes in n trials.

p(x) = (number of ways to choose x from n)p^x(1-p)^n-x

A univariate distribution is the distribution of a single variable. A multivariate distribution specifies the probabilities associated with a group of random variables. It is only meaningful when each variable in the group is in some way depenedent upon the other variables in the group.

A discrete uniform distribution is characterized by an equal probability for each outcome. An example is the results of a single die roll.

A confidence interval is a range of values around an expected outcome within which the actual outcome is expected to fall a specified percentage of the time. In other words, it is a range for which one can assert with a given probability that it will contain a parameter it intends to estimate.

Construction of a Confidence Interval

where

Coefficient of variation is a common measure of relative dispersion. Relative dispersion is the amount of variability in a distribution relative to a reference point or benchmark.

Formula

A Type I Error is rejecting the null hypothesis--H₀--when it is actually true. The significance level is the probability of a Type I Error.

A Type II Error is failing to reject the H₀ when it is actually false. The power of test is 1 - Probabilty of a Type II Error.

There is a tradeoff for trying to minimize the chance of one of these errors. For a given sample size, decreasing the probability of a Type I Error increases the probability of Type II Error and vice versa.

A test statistic is a quantity calculated from a sample whose value is the basis for deciding whether or not to reject the null hypothesis.