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Symbols and their Meanings

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module defines symbols used throughout the Collaborative Statistics textbook.

Table 1: Symbols and their Meanings
Chapter (1st used) Symbol Spoken Meaning
       
Sampling and Data The square root of same
Sampling and Data ππ Pi 3.14159… (a specific number)
Descriptive Statistics Q1Q1 Quartile one the first quartile
Descriptive Statistics Q2Q2 Quartile two the second quartile
Descriptive Statistics Q3Q3 Quartile three the third quartile
Descriptive Statistics IQRIQR inter-quartile range Q3-Q1=IQR
Descriptive Statistics x ¯ x ¯ x-bar sample mean
Descriptive Statistics μμ mu population mean
Descriptive Statistics ss sxsx sxsx s sample standard deviation
Descriptive Statistics s2s2 sx2 sx2 s-squared sample variance
Descriptive Statistics σσ σxσx σxσx sigma population standard deviation
Descriptive Statistics σ2σ2 σx2 σx2 sigma-squared population variance
Descriptive Statistics ΣΣ capital sigma sum
Probability Topics { } {} brackets set notation
Probability Topics SS S sample space
Probability Topics AA Event A event A
Probability Topics P ( A ) P ( A ) probability of A probability of A occurring
Probability Topics P ( A B ) P ( A B ) probability of A given B prob. of A occurring given B has occurred
Probability Topics P ( A or B ) P ( A or B ) prob. of A or B prob. of A or B or both occurring
Probability Topics P ( A and B ) P ( A and B ) prob. of A and B prob. of both A and B occurring (same time)
Probability Topics A'A' A-prime, complement of A complement of A, not A
Probability Topics P ( A' ) P ( A' ) prob. of complement of A same
Probability Topics G 1 G 1 green on first pick same
Probability Topics P ( G 1 ) P ( G 1 ) prob. of green on first pick same
Discrete Random Variables PDFPDF prob. distribution function same
Discrete Random Variables XX X the random variable X
Discrete Random Variables X~X~ the distribution of X same
Discrete Random Variables BB binomial distribution same
Discrete Random Variables GG geometric distribution same
Discrete Random Variables HH hypergeometric dist. same
Discrete Random Variables PP Poisson dist. same
Discrete Random Variables λλ Lambda average of Poisson distribution
Discrete Random Variables greater than or equal to same
Discrete Random Variables less than or equal to same
Discrete Random Variables == equal to same
Discrete Random Variables not equal to same
Continuous Random Variables f ( x ) f ( x ) f of x function of x
Continuous Random Variables pdfpdf prob. density function same
Continuous Random Variables UU uniform distribution same
Continuous Random Variables ExpExp exponential distribution same
Continuous Random Variables kk k critical value
Continuous Random Variables f ( x ) = f ( x ) = f of x equals same
Continuous Random Variables mm m decay rate (for exp. dist.)
The Normal Distribution N N size 12{N} {} normal distribution same
The Normal Distribution z z size 12{z} {} z-score same
The Normal Distribution Z Z size 12{Z} {} standard normal dist. same
The Central Limit Theorem CLT CLT size 12{ ital "CLT"} {} Central Limit Theorem same
The Central Limit Theorem X¯ X X-bar the random variable X-bar
The Central Limit Theorem μ x μ x size 12{μ rSub { size 8{x} } } {} mean of X the average of X
The Central Limit Theorem μ x ¯ μ x ¯ size 12{μ rSub { size 8{ {overline {x}} } } } {} mean of X-bar the average of X-bar
The Central Limit Theorem σ x σ x size 12{σ rSub { size 8{x} } } {} standard deviation of X same
The Central Limit Theorem σ x ¯ σ x ¯ size 12{σ rSub { size 8{ {overline {x}} } } } {} standard deviation of X-bar same
The Central Limit Theorem ΣXΣX sum of X same
The Central Limit Theorem ΣxΣx sum of x same
Confidence Intervals CL CL size 12{ ital "CL"} {} confidence level same
Confidence Intervals CI CI size 12{ ital "CI"} {} confidence interval same
Confidence Intervals EBM EBM size 12{ ital "EBM"} {} error bound for a mean same
Confidence Intervals EBP EBP size 12{ ital "EBP"} {} error bound for a proportion same
Confidence Intervals t t size 12{t} {} student-t distribution same
Confidence Intervals df df size 12{ ital "df"} {} degrees of freedom same
Confidence Intervals t α 2 t α 2 student-t with a/2 area in right tail same
Confidence Intervals p'p' p ^ p ^ p-prime; p-hat sample proportion of success
Confidence Intervals q'q' q ^ q ^ q-prime; q-hat sample proportion of failure
Hypothesis Testing H 0 H 0 size 12{H rSub { size 8{0} } } {} H-naught, H-sub 0 null hypothesis
Hypothesis Testing H a H a size 12{H rSub { size 8{a} } } {} H-a, H-sub a alternate hypothesis
Hypothesis Testing H 1 H 1 size 12{H rSub { size 8{1} } } {} H-1, H-sub 1 alternate hypothesis
Hypothesis Testing α α size 12{α} {} alpha probability of Type I error
Hypothesis Testing β β size 12{β} {} beta probability of Type II error
Hypothesis Testing X1 ¯ X2 ¯ X1 ¯ X2 ¯ size 12{ {overline {X1}} - {overline {X2}} } {} X1-bar minus X2-bar difference in sample means
  μ 1 μ 2 μ 1 μ 2 size 12{μ rSub { size 8{1} } - μ rSub { size 8{2} } } {} mu-1 minus mu-2 difference in population means
  P ' 1 P ' 2 P ' 1 P ' 2 size 12{P' rSub { size 8{1} } - P' rSub { size 8{2} } } {} P1-prime minus P2-prime difference in sample proportions
  p 1 p 2 p 1 p 2 size 12{p rSub { size 8{1} } - p rSub { size 8{2} } } {} p1 minus p2 difference in population proportions
Chi-Square Distribution Χ 2 Χ 2 Ky-square Chi-square
  OO Observed Observed frequency
  EE Expected Expected frequency
Linear Regression and Correlation y = a + bx y=a+bx y equals a plus b-x equation of a line
  y^y^ y-hat estimated value of y
  rr correlation coefficient same
  εε error same
  SSESSE Sum of Squared Errors same
  1.9 s 1.9s 1.9 times s cut-off value for outliers
F-Distribution and ANOVA FF F-ratio F ratio

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