# Glossary of Symbols and Abbreviations

 y^x y to the power of x (also seen as y**x or yx) ^Key Ctrl + another Key / divided by (see calculator for operator precedence) * multiplied by (see calculator for operator precedence) abs(x), |x| absolute value of x without regard to sign alpha, α significance level of a hypothesis test (also type I error rate). 1-a is the level of the confidence interval ANOVA analysis of variance beta, β type II error rate (1-power) CI confidence interval, see confidence intervals df degrees of freedom e base of natural logarithms (2.718281...) k! factorial , in simplest terms factorial of k is the product of all integers from 1 to k, with 0! defined as 1, a fuller definition relates factorial to the gamma function as gamma (k+1) which enables the calculation of fractional factorials ln(x) natural (base e) logarithm of x, the natural logarithm of x is the value of y such that x is equal to the e constant raised to the power of y, remember that ln(1) = 0, ln(0) = minus infinity and ln(a/b)=ln(a)-ln(b), see also transformations MS mean square μ mean of a population - see also n sample size (population sized is usually referred to as N) P probability of the data (or more extreme data) arising by chance, see P values p proportion of a sample with a given characteristic q hat, the hat symbol above the q means "estimate of" r Pearson's product moment correlation coefficient SD standard deviation (of a sample, ) - a measure of variability around the mean - Greek lower case sigma (σ) is used for population standard deviation. SE standard error (of sample mean, ) - a measure of uncertainty of the estimate of a statistic (e.g. sample mean) and used to derive confidence intervals for the population value of the statistic sqr(x) square root of x, or  sum of all (1 to n) x values product of all (1 to n) x values (x1 * x2 * x3 etc.) VAR variance (of the mean, ), greek σ² for populations and s² for samples vs. versus x individual value from a population or sample x bar (bar symbol above the x denotes mean) is a sample mean (arithmetic mean, ), see also μ z, Φ standardized normal deviate (from standard normal distribution)