A Brief Survey of Statistical Symbols, Study notes of Statistics

Download A Brief Survey of Statistical Symbols and more Study notes Statistics in PDF only on Docsity! A Brief Survey of Statistical Symbols Statistics uses many symbols and notation not used in algebra. This document discusses a small collection of the most common ones. We’ll begin with some broad categories, and finish with a list of common symbols, their meaning and alternate notations. Greek Letters Statistics uses many Greek letters to stand for important concepts or operations. In this section we’ll look at 8 of the ones used in a typical elementary statistics course. The third column of the table shows you how to draw the Greek letter. Start at the arrow and follow the direction of the arrow around the letter. Most Greek letters are drawn with a single stroke without overwriting what’s been drawn or picking up the pen. 𝛼 The Greek letter alpha is used to represent the significance level of a hypothesis test, and (1 − 𝛼) represents the confidence level of an estimate. The most common value assigned to 𝛼 is 0.05. 𝛽 The Greek letter beta is used in a couple of different places. It can be used to represent a change of a Type II hypothesis test error, with (1 − 𝛽) being the power of a test (similar to 𝛼). It is also used to represent the coefficients in a regressions equation. When it’s used in this second way, it usually has subscripts. 𝛿 The Greek letter delta is used to represent the true difference between two related values. Students typically encounter it in some two-sample hypothesis tests. 휀 The Greek letter epsilon (which can also appear as 𝜖) can be used in regression equations as the random error in a measurement. 𝜇 The Greek letter mu is one of the most commonly used symbols in elementary statistics. It represents the mean of the population. 𝜌 The Greek letter rho is used to represent the population correlation of linear regression data. 𝜎 The Greek letter sigma is one of the most commonly used symbols in statistics. It represents the standard deviation of a population. 𝜎2 is the variance of a population. Σ The Greek letter sigma (this is the capital form) is used to represent the operation addition on a set of numbers. In mathematics, this is sometimes described as a summation, or summation notation. Σ 𝜒 The Greek letter chi is used in some hypothesis tests. 𝜒2 is the name of the distribution used to test for independence and goodness-of-fit. If you go deeper into statistics, you’ll encounter more Greek letters, but this is a good start. There is one other that sometimes comes up that you’ve seen before: the Greek letter 𝜋. Subscripts Subscripts are a common notation used in statistics, typically to help reduce the number of symbols needed, or to indicate one element of a set, particularly an ordered set. 𝑥1 can represent the first element in a list, followed by 𝑥2, 𝑥3, … 𝑒𝑡𝑐. 𝑥𝑖 can represent any element in the list rather than a specific one. You may see this notation in formulas where you need to add up all the elements. 𝑏0, 𝛿0, 𝑒𝑡𝑐. The zero subscript typically refers to an initial or assumed value for a variable. 𝜎?̅? Sometimes subscripts will include other variables. In cases like this is a variable associated with the measurement of another variable. In this example, this is the standard deviation of measurements of the average/mean. Function Notation Function notation is a general algebraic rule you may have encountered in algebra. It’s used most commonly in probability notation. 𝑃(𝑥) is how we notate probabilities, and with the expression inside the parentheses we can say what it’s the probability of. Examples: 𝑃(𝑋 < 3), 𝑃(𝑔𝑟𝑒𝑒𝑛), etc. Bars and Hats A bar over a letter indicates the average or mean of the value. The most common place we see this in statistics is ?̅?, but this notation can be used outside of statistics to mean the same thing. For instance, 𝐶̅ could represent the average cost. A hat (or caret) over a letter (^) usually indicates an estimate to distinguish it from a population value. This is mostly commonly used in ?̂?, since 𝑝 is used for the population instead of 𝜋 (more on this later). But you can also see it in other situations including ?̂?, ?̂?, ?̂?0, etc.