Symbol Sheet
for MATH200 (Statistics)

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

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

Other symbols — Roman letters

• b = y intercept of a line (Some statistics books use b₀.)
• CLT = Central Limit Theorem
• d = difference between paired data
• df or ν “nu” = degrees of freedom in a Student’s t or χ² distribution
• E = maximum error of the estimate
• f = frequency
• f/n = relative frequency
• H_o = null hypothesis
• H_a or H₁ = alternative hypothesis
• IQR = interquartile range, Q₃−Q₁
• m = slope of a line (The TI-83 uses a and some statistics books use b₁.)
• n = sample size, number of data points, or number of trials in a probability experiment
• or _nC_x = number of combinations of n things taken x at a time = number of different ways you could pick x things when you have a set of n things to choose from and order doesn’t matter. (You are not responsible for computing combinations as such.)
• _nP_x = number of permutations of n things taken x at a time = number of different ways you could choose and arrange x things when you have a set of n things to choose from. See examples in Probability of Shared Birthdays. (You are not responsible for computing permutations as such.)
• p = probability value. In binomial probability distributions p is the probability of “success” (however defined) 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, the probability that rejecting the null hypothesis would be a wrong decision. In tests of population proportions, p stands for population proportion and p′ or p̂ for sample proportion (see table above). You have to rely on context to know what “p” means.

• P(A) = the probability of event A. (Sometimes P′(A) is used to distinguish the experimental probability of event A from the theoretical probability.)
• = probability of not-A, the probability that A does not happen
• P(B | A) = the probability that event B will happen, given that event A definitely happens. (Caution! The order of A and B seems backward to many people. See examples in False Positives and False Negatives.)
• P80 or P₈₀ = 80th percentile (Pk or P_k = k-th percentile)
• q = probability of failure in binomial distribution, equal to 1 − p
• Q1 or Q₁ = first quartile (Q3 or Q₃ = first quartile)
• R² = coefficient of determination
• SEM = standard error of the mean (symbol is σ_x̄)
• SEP = standard error of the proportion (symbol is σ_p̂)
• SS( ) = sum of squares of deviations. SS(x) = sum of squares of deviations in x, computed as either ∑(x−x̄)² or ∑x² − (∑x)²/n.
  SS(y) has a similar meaning. SS(xy) is ∑xy − (∑x)(∑y)/n.
• x = a variable or a data value (raw score). As a column heading, x means a series of data values.
• ŷ “y-hat” = y value predicted for a given x by using the regression equation
• z = standard score or z-score. Using the individual score x, the mean μ, and the standard deviation σ, the formula is
  Using a sample mean x̄ and comparing it to the distribution of sample means, the formula is
• 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!

Greek letters (see also the table above):

• α “alpha” = significance level in hypothesis test, or acceptable probability of a Type I error (probability you can live with); 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
• σ_x̄ “sigma-sub-x-bar” = standard error of the mean (abbreviated SEM)
• σ_p̂ “sigma-sub-p-prime” = standard error of the proportion (abbreviated SEP)
• ∑ “sigma” = summation. (This is upper-case sigma. Lower-case sigma means standard deviation of a population; see the table above.) Be careful with the order of operations, such as ∑x² versus (∑x)².
• χ² “chi-squared” = distribution for multinomial experiments and contingency tables