# Statistics Notation

This web page describes how symbols are used on the Stat Trek web site to represent numbers, variables, parameters, statistics, etc.

## Capitalization

In general, capital letters refer to population attributes (i.e., parameters); and lower-case letters refer to sample attributes (i.e., statistics). For example,

• P refers to a population proportion; and p, to a sample proportion.
• X refers to a set of population elements; and x, to a set of sample elements.
• N refers to population size; and n, to sample size.

## Greek vs. Roman Letters

Like capital letters, Greek letters refer to population attributes. Their sample counterparts, however, are usually Roman letters. For example,

• μ refers to a population mean; and x, to a sample mean.
• σ refers to the standard deviation of a population; and s, to the standard deviation of a sample.

## Population Parameters

By convention, specific symbols represent certain population parameters. For example,

• μ refers to a population mean.
• σ refers to the standard deviation of a population.
• σ2 refers to the variance of a population.
• P refers to the proportion of population elements that have a particular attribute.
• Q refers to the proportion of population elements that do not have a particular attribute, so Q = 1 - P.
• ρ is the population correlation coefficient, based on all of the elements from a population.
• N is the number of elements in a population.

## Sample Statistics

By convention, specific symbols represent certain sample statistics. For example,

• x refers to a sample mean.
• s refers to the standard deviation of a sample.
• s2 refers to the variance of a sample.
• p refers to the proportion of sample elements that have a particular attribute.
• q refers to the proportion of sample elements that do not have a particular attribute, so q = 1 - p.
• r is the sample correlation coefficient, based on all of the elements from a sample.
• n is the number of elements in a sample.

## Simple Linear Regression

• Β0 is the intercept constant in a population regression line.
• Β1 is the regression coefficient (i.e., slope) in a population regression line.
• R2 refers to the coefficient of determination.
• b0 is the intercept constant in a sample regression line.
• b1 refers to the regression coefficient in a sample regression line (i.e., the slope).
• sb1 refers to the refers to the standard error of the slope of a regression line.

## Counting

• n! refers to the factorial value of n.
• nPr refers to the number of permutations of n things taken r at a time.
• nCr refers to the number of combinations of n things taken r at a time.

## Random Variables

• Z or z refers to a standardized score, also known as a z-score.
• zα refers to the standardized score that has a cumulative probability equal to 1 - α.
• tα refers to the t statistic that has a cumulative probability equal to 1 - α.
• fα refers to a f statistic that has a cumulative probability equal to 1 - α.
• fα(v1, v2) is a f statistic with a cumulative probability of 1 - α, and v1 and v2 degrees of freedom.
• Χ2 refers to a chi-square statistic.

## Special Symbols

Throughout the site, certain symbols have special meanings. For example,

• Σ is the summation symbol, used to compute sums over a range of values.
• Σx or Σxi refers to the sum of a set of n observations. Thus, Σxi = Σx = x1 + x2 + . . . + xn.
• sqrt refers to the square root function. Thus, sqrt(4) = 2 and sqrt(25) = 5.
• Var(X) refers to the variance of the random variable X.
• SD(X) refers to the standard deviation of the random variable X.
• SE refers to the standard error of a statistic.
• ME refers to the margin of error.
• DF refers to the degrees of freedom.