Stats without Tears

Stats without Tears
Statistics Symbol Sheet

Updated 5 Nov 2020 (What’s New?)
Copyright © 2002–2020 by Stan BrownView or
Print:These pages change automatically for your screen or printer. If you print, I suggest black-and-white, two-sided printing.

Relational Symbols
  =  equals
is the same as
  ≠  is not equal to
is different from
  >  is greater than
is more than
exceeds
is above
  ≥
or >=  
is greater than or equal to
is at least
is not less than
  <  is less than
is fewer than
is below
  ≤
or <=  
is less than or equal to
is at most
does not exceed
is not greater than
is no more than
A < x < Bx is between A and B, exclusive
A ≤ x ≤ Bx is between A and B, inclusive
A ≈ BA is approximately equal to B

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

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sample
statistic
population
parameter
description
nNnumber of members of sample or population
 “x-bar”μ “mu”
or μx
mean
M or Med
or  “x-tilde”
(none)median
s
(TIs say Sx)
σ “sigma”
or σx
standard deviation
For variance, apply a squared symbol (s² or σ²).
rρ “rho”coefficient of linear correlation
 “p-hat”pproportion
z   t   χ²(n/a)calculated test statistic

μ and σ can take subscripts to show what you are taking the mean or standard deviation of. For instance, σ (“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 χ² 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.
  • Ho = null hypothesis. Defined here in Chapter 10.
  • H1 or Ha = alternative hypothesis. Defined here in Chapter 10.
  • IQR = interquartile range, Q3−Q1Defined 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  for sample proportion (see table above).
  • P(A) = the probability of event A.
  • P(AC) 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 ADefined 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 Pk = 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.
  • R² = 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). Defined here in Chapter 8.
  • SEP = standard error of the proportion (symbol is σ). 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.
  •  “x-bar” = mean of a sample. Defined here in Chapter 3.
  •  “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 zarea = 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 “sigma-sub-x-bar”; see SEM above.
  • σ “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.
  • χ² “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  for the median, as suggested by reader “Trone”.
  • (intervening changes suppressed)
  • 27 Sept 2002: New article.

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