The need occasionally arises to produce a set of random observations on a pair of variables which have a precise degree of correlation between them. Most commonly the need for such data arises in the context of simulations to determine the effect on some outcome (e.g., value of a stock portfolio) of varying degrees of correlations among input or predictor variables. Other uses include creating graphic illustrations of specified degrees of bivariate correlation, examining the effect of predictor collinearity on regression weights and explained variance, and simulating the effects of correlated predictors on the outcomes of employment selection decisions.
Several efforts have been made to offer a quick and easy tool to produce the needed sets of observations, but the tools that been offered to date all contain a common serious flaw: They fail to account for the random level of correlation that inevitably occurs between the initial observations randomly generated for a pair of variables. Consequently, any procedures subsequently applied to impute the desired correlation will produce a correlation that deviates from the desired level by the amount of the originally occurring chance correlation. One fairly recent article even went so far as to assert that the application of the Box-Muller normality transformation to the variables eliminates any chance correlation between them, which is absurd.
The Correlated Random Variable Generator Excel macro offered on the "Stats Tools" tab of this website (see also the link below) is the only standalone tool currently available to produce normally distributed random bivariate data sets of any number of observations which have the precise (to 3 decimal places) degree of correlation between them that the user specifies. In addition, the user may specify the means and standard deviations of the two variables, and may limit the values of each variable to fall within specified upper and lower boundaries.
I should also mention that many researchers encounter the need for random data to be generated for 3 or more variables with a specified multivariate correlational structure, either with or without sampling error. I have developed a standalone compiled program for producing such data sets which is called, Monte Carlo/PC. This program sells for $150, and may be purchased from me. Please send requests for information about purchasing this program to inquiry@prostatservices.com or by calling Professional Statistical Services at the number in the contact tab of www.prostatservices.com.
The Correlated Random Variable Generator can be downloaded by clicking this link: Correlated Random Variable Generator (Excel macro)