Stats without Tears
Statistics Symbol Sheet

View or
Print: These pages change automatically for your screen or printer. Underlined text, printed URLs, and the table of contents become live links on screen; and you can use your browser�s commands to change the size of the text or search for key words. If you print, I suggest black-and-white, two-sided printing.

Here are symbols for various sample statistics and the corresponding population parameters. They are not repeated in the list below.

μ and σ can take subscripts to show what you are taking the mean or standard deviation of. For instance, σ _x̅ (�sigma sub x-bar�) is the standard deviation of sample means, or standard error of the mean.

Roman Letters

• b = y intercept of a line. Defined here in Chapter 4. (Some statistics books use b₀.)
• BD or BPD = binomial probability distribution. Defined here in Chapter 6.
• CI = confidence interval. Defined here in Chapter 9.
• CLT = Central Limit Theorem. Defined here in Chapter 8.
• d = difference between paired data. Defined here in Chapter 11.
• df or ν �nu� = degrees of freedom in a Student�s t or χ� distribution. Defined here in Chapter 9. Defined here in Chapter 12.
• DPD = discrete probability distribution. Defined here in Chapter 6.
• E = margin of error, a/k/a maximum error of the estimate. Defined here in Chapter 9.
• f = frequency. Defined here in Chapter 2.
• f/n = relative frequency. Defined here in Chapter 2.
• HT = hypothesis test. Defined here in Chapter 10.
• H_o = null hypothesis. Defined here in Chapter 10.
• H₁ or H_a = alternative hypothesis. Defined here in Chapter 10.
• IQR = interquartile range, Q₃−Q₁. Defined here in Chapter 3.
• m = slope of a line. Defined here in Chapter 4. (The TI-83 uses a and some statistics books use b₁.)
• M or Med = median of a sample. Defined here in Chapter 3.
• n = sample size, number of data points. Defined here in Chapter 2. Also, number of trials in a probability experiment with a binomial model. Defined here in Chapter 6.
• N = population size.
• ND = normal distribution, whose graph is a bell-shaped curve; also �normally distributed�. Defined here in Chapter 7.
• p = probability value. The specific meaning depends on context. In geometric and binomial probability distributions, p is the probability of �success� (defined here in Chapter 6) on any one trial and q = (1−p) is the probability of �failure� (the only other possibility) on any one trial. In hypothesis testing, p is the calculated p-value (defined here in Chapter 10), the probability that rejecting the null hypothesis would be a wrong decision. In tests of population proportions, p stands for population proportion and p̂ for sample proportion (see table above).
• P(A) = the probability of event A.
• P(A C ) or P(not A) = the probability that A does not happen. Defined here in Chapter 5.
• P(B | A) = the probability that event B will happen, given that event A definitely happens. It�s usually read as the probability of B given A. Defined here in Chapter 5. Caution! The order of A and B may seem backward to you at first.
• P80 or P₈₀ = 80th percentile ( Pk or P_k = k-th percentile) Defined here in Chapter 3.
• q = probability of failure on any one trial in binomial or geometric distribution, equal to (1−p) where p is the probability of success on any one trial. Defined here in Chapter 6.
• Q1 or Q₁ = first quartile ( Q3 or Q₃ = third quartile) Defined here in Chapter 3.
• r = linear correlation coefficient of a sample. Defined here in Chapter 4.
• R� = coefficient of determination. Defined here in Chapter 4.
• s = standard deviation of a sample. Defined here in Chapter 3.
• SD (or s.d.) = standard deviation. Defined here in Chapter 3.
• SEM = standard error of the mean (symbol is σ_x̅). Defined here in Chapter 8.
• SEP = standard error of the proportion (symbol is σ_p̂). Defined here in Chapter 8.
• X (capital X) = a variable.
• x (lower-case x) = one data value (�raw score�). As a column heading, x means a series of data values.
• x̅ �x-bar� = mean of a sample. Defined here in Chapter 3.
• x̃ �x-tilde� = median of a sample. Defined here in Chapter 3.
• ŷ �y-hat� = predicted average y value for a given x, found by using the regression equation. Defined here in Chapter 4.
• z = standard score or z-score. Defined here in Chapter 3.
• z(area) or z_area = the z-score, such that that much of the area under the normal curve lies to the right of that z. This is not a multiplication! (See The z Function.)

Greek Letters

• α �alpha� = significance level in hypothesis test, or acceptable probability of a Type I error (probability you can live with). Defined here in Chapter 10. 1−α = confidence level.
• β �beta� = in a hypothesis test, the acceptable probability of a Type II error; 1−β is called the power of the test.
• μ mu, pronounced �mew� = mean of a population. Defined here in Chapter 3.
• ν nu: see df, above.
• ρ rho, pronounced �roe� = linear correlation coefficient of a population.
• σ �sigma� = standard deviation of a population. Defined here in Chapter 3.
• σ_x̅ �sigma-sub-x-bar�; see SEM above.
• σ_p̂ �sigma-sub-p-hat�; see SEP above.
• ∑ �sigma� = summation. (This is upper-case sigma. Lower-case sigma, σ, means standard deviation of a population; see the table near the start of this page.) See ∑ Means Add �em Up in Chapter 1.
• χ� �chi-squared� = distribution for multinomial experiments and contingency tables. Defined here in Chapter 12.

What�s New?

• 5 Nov 2020: Convert document to HTML5, and italicize the variables.
• 14 Feb 2018: Add x̃ for the median, as suggested by reader �Trone�.
• (intervening changes suppressed)
• 27 Sept 2002: New article.