Statistical Symbols

Latin letters

We tend to use the letters at the end of the alphabet such as t, u, v, w, x, y, z to represent random variables. Subscripted versions of these letters (e.g. x₁ and x₂) are also used to represent random variables, although care must be taken since subscripted letters may be used to represent a sample: e.g. {x₁, x₂, …, x_n} can be used to represent a sample of values for the random variable x.

When x₁, x₂, …, x_k are used as random variables, however, we will tend to use double subscripts to represent a sample for these variables: e.g. {x_j1, x_j2, …, x_jn} could be used to represent a sample for the random variable x_j.

You will often see in other statistics texts capital letters such as X, Y, Z, etc. used as random variables. We generally reserve such letters for vectors or matrices, although certain capital letters are used as random variables in specific contexts where these letters are generally recognized (e.g. U for the Mann-Whitney statistics).

Letters at the beginning of the alphabet, such as a, b, c, d tend to be used as constants; letters such as i, j, k tend to be used as indices and letters such as k, m, n, p, r tend to be used as counts (such as the number of elements in a sample or the number of rows in a range).

Greek letters

We tend to use Greek letters (e.g. μ, σ, π, etc.) as population parameters and the corresponding Latin letters m, s, p, etc. as corresponding sample parameters (which are estimates of these parameters). You will see that in other statistics sources, it is common to put a hat on the population parameter when referring to its estimate (e.g. , , , etc.). We have usually not done this in order to keep the notation simple. Some symbols are so universal that we have retained them, most notably as the estimate of the population mean μ.

Critical values

We also commonly use notations such as t_n,α or t_df,α to refer to the critical value of a particular test (the t-test in this example). Again to keep our notation simple, we usually just use the notation t_crit where the values n and α are clear from the context.

Tilde

Throughout the website, we define various distributions, such as the normal distribution N(μ,σ), the binomial distribution B(n,π), etc. We use the notation x ∼ N(μ,σ), to mean that the random variable x has normal distribution N(μ,σ). We use the same notation when x is approximately distributed as N(μ,σ). Similarly, x ∼ B(n,π) means that the random variable x has binomial distribution B(n,π), etc. for other distributions. Also note that in other statistics texts the normal distribution is often represented as N(μ,σ²) instead of N(μ,σ).

Arrays and Ranges

We use R1, R2, etc. to represent Excel arrays or cell ranges.