Notation Guide
Introduction
Throughout the semester, you will see a wide variety of symbols used repeatedly from week to week. These symbols are usually defined when the text introduces them, but it is sometimes hard to remember exactly what symbols/operators mean what. Here are two handy reference tables to keep them straight. This list is not exhaustive, rather it is designed to include symbols that are used often, not just as a "one-off." Also note that in some occasions, the text will sometimes use certain symbols/variables for purposes other than the ones listed here. For example, π usually refers to the population proportion and r usually refers to the coefficient of correlation. However, on occasions the textbook will use π to refer to the numerical constant 3.1415926... and in chapter 11, r is used as the number of factors in a 2 way ANOVA. You should ensure that the usage in the text matches the description given here.

The first table contains symbols, the second operators. In this first table, the first column contains the symbol itself and the second column a brief definition of what that symbol refers to. In cases where there is a particular equation defined by the symbol, a page reference can be found in the third column. Some of the symbols rely upon having a browser that will render HTML 4.0 and a unicode font installed on your computer, so if you have trouble seeing any of the symbols you may need to switch browsers or update your browser. Symbol | Meaning/Definition | Page Ref. | N | Population Size | | n | Sample Size | | μ | Population Mean. In equations where population means of multiple variables are needed, the variable name will be subscripted, e.g. μx or μincome. | 118 | x̄ | Sample Mean. Putting a bar above a variable is standard shorthand for the sample mean of that variable, which is something you might see in equations where sample means of multiple variables are needed. Another convention in this case would be to subscript the variable name after the xbar | 97 | π | Population Proportion (usually; in some cases it stands for the mathematical constant pi=3.1415926..., such as in the standardized normal probability density function) | | p | Sample Proportion | | σ | Population Standard Deviation. In equations where standard deviations of multiple variables are needed, the variable name will be subscripted, e.g. σx or σincome. | 120, 182 | σ2 | Population Variance. In equations where variances of multiple variables are needed, the variable name will be subscripted, e.g. σ2x or σ2income. | 119, 182 | S | Sample Standard Deviation. In equations where standard deviations of multiple variables are needed, the variable name will be subscripted, e.g. Sx or Sincome. | 107 | S2 | Sample Variance. In equations where variances of multiple variables are needed, the variable name will be subscripted, e.g. S2x or S2income. | 107 | Cov | Covariance. Typical context is Cov(X,Y) which is the covariance of variables X and Y. Sometimes written as σXY. | 127, 185 | r | Coefficient of Correlation. Related to r2 in regression analysis (see below). | 128 | e | Mathematical constant e=2.71828..., seen in many of the distribution functions. | | σx̄ | Standard Error of the Mean | 264 | σp | Standard Error of the Proportion | 273 | Z | Z=(X-μ)/σ, can refer to a Z statistic for a specific data point or a Z critical value | 111, 221 | tx | Generally refers to a critical value taken from the t-distribution. The subscripted number or equation (usually something like n-1 or n-2) indicates the degrees of freedom in the t distribution. For example, tn-1 where n=54 means you want a critical value from the t distribution with 53 degrees of freedom | 290, 292 | H0, H1 | In hypothesis testing, H0 refers to the null hypothesis and H1 refers to the alternative hypothesis | 328 | α | The typical context of alpha is the level of significance of a statistical test. More intuitively, it is the probability that your statistical results are not correct. 1-α is your confidence level and is the probability of a Type I error. | | β | In hypothesis testing, refers to the probability of a type II error. Has a different interpretation in regression analysis (see below). | | FU | Refers to the upper tail of the F-Distribution. FU is defined by two sets of degrees of freedom, one for the denominator and one for the numerator. | | QU | Refers to the upper tail of the Studentized range distribution (the Q distribution). QU is defined by two sets of degrees of freedom, one for the denominator and one for the numerator. Of all the distributions discussed in the text, this is the only one that Excel does not have the ability to compute. | | d.f. | Abbreviation, short for degrees of freedom. | | β | In regression analysis, coefficients for the population of either the Y intercept or the slopes of the independent variables. Usage typically includes subscripts, where β0 is the Y intercept, β1 is the coefficient for the slope of variable X1, β2 is the coefficient for the slope of variable X2, and so forth. | | ε | In regression analysis, epsilon is the error term. | | Ŷ | Read as "Y-Hat," putting a hat on a variable name refers to the predicted value of that variable. For example, in regression analysis, Ŷi refers to the predicted value of Y given the estimated coefficients. | | b | In regression analysis, b (though it is often still referred to as a beta) is the estimated Y intercept or slope value of the independent variables. Usage typically includes subscripts, where b0 is the Y intercept, b1 is the coefficient for the slope of variable X1, b2 is the coefficient for the slope of variable X2, and so forth. | | r2 | Coefficient of determination. Related to the correlation coefficient mentioned above. R-square must be between 0 and 1, and is used as a measure of goodness of fit for a regression model. Higher values of r2 indicate better fit. | 526 |
Next, here is a list of operators/operations that you will see throughout this semester Operator | Meaning/Definition | ∑ | Sigma indicates a summation. The summation notation typically has notation both above and below it. In most cases, the notation below is "i=1" and the notation above is "n". The number on the bottom tells you where to start your summation, the number on the top tells you where to stop. | √ | The radical, or square root sign, tells you to find the square root of the number under the radical. For example, √4=2 | P | The context here is P(X), where P means probability. You would read the expression P(X) as "The probability of event X." | E | The context here is E(X), where E means expected value. You would read the expression E(X) as "The expected value of X," where X is a discrete random variable. Concept is similar to that of μ, the population mean. | nCX | Combinatorial Function. Calculates the number of combinations of selecting X objects out of n objects. Equation is nCX=n!/(X!(n-X)!). Alternate notation for the Combinatorial function can be found on page 202. | ! | Factorial. X! is the product of X and every whole number less than it. For example, 5! is 5x4x3x2x1=120. By definition, 0!=1 | ± | Plus or Minus sign. Seen in confidence interval equations, is a shorthand method of combining two similar equations into one. For example, 2±7 implies two equations; 2+7 AND 2-7. |