Collaborative Statistics: Symbols and their Meanings

Transcription

1 OpenStax-CNX module: m Collaborative Statistics: Symbols and their Meanings Susan Dean Barbara Illowsky, Ph.D. This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 2.0 Abstract This module denes symbols used throughout the Collaborative Statistics textbook. Symbols and their Meanings Chapter (1st used) Symbol Spoken Meaning Sampling and Data The square root of Sampling and Data π Pi (a specic number) Descriptive Statistics Q1 Quartile one the rst quartile Descriptive Statistics Q2 Quartile two the second quartile Descriptive Statistics Q3 Quartile three the third quartile Descriptive Statistics IQR inter-quartile range Q3-Q1=IQR Descriptive Statistics x x-bar sample mean Descriptive Statistics µ mu population mean Descriptive Statistics s s x sx s sample standard deviation Version 1.9: Mar 30, :24 pm

2 OpenStax-CNX module: m Descriptive Statistics s 2 s 2 x s-squared sample variance Descriptive Statistics σ σ x σx sigma population standard deviation Descriptive Statistics σ 2 σ 2 x sigma-squared population variance Descriptive Statistics Σ capital sigma sum Probability Topics {} brackets set notation Probability Topics S S sample space Probability Topics A Event A event A Probability Topics P (A) probability of A probability of A occurring Probability Topics P (A B) probability of A given B prob. of A occurring given B has occurred Probability Topics P (AorB) prob. of A or B prob. of A or B or both occurring Probability Topics P (AandB) prob. of A and B prob. of both A and B occurring ( time) Probability Topics A' A-prime, complement of A Probability Topics P (A') prob. of complement of A complement of A, not A Probability Topics G 1 green on rst pick Probability Topics P (G 1 ) prob. of green on rst pick PDF prob. distribution function X X the random variable X X the distribution of X B binomial distribution G geometric distribution

3 OpenStax-CNX module: m H hypergeometric dist. P Poisson dist. λ Lambda average of Poisson distribution greater than or equal to less than or equal to = equal to not equal to f (x) f of x function of x pdf prob. density function U uniform distribution Exp exponential distribution k k critical value f (x) = f of x equals m m decay rate (for exp. dist.) N normal distribution z z-score Z standard normal dist.

4 OpenStax-CNX module: m CLT Central Limit Theorem X X-bar the random variable X- bar µ x mean of X the average of X µ x mean of X-bar the average of X-bar σ x standard deviation of X σ x standard deviation of X- bar ΣX sum of X Σx sum of x Condence Intervals CL condence level Condence Intervals CI condence interval Condence Intervals EBM error bound for a mean Condence Intervals EBP error bound for a proportion Condence Intervals t student-t distribution Condence Intervals df degrees of freedom Condence Intervals t α 2 student-t with a/2 area in right tail Condence Intervals p' ^p p-prime; p-hat sample proportion of success Condence Intervals q' ^q q-prime; q-hat sample proportion of failure Hypothesis Testing H 0 H-naught, H-sub 0 null hypothesis Hypothesis Testing H a H-a, H-sub a alternate hypothesis Hypothesis Testing H 1 H-1, H-sub 1 alternate hypothesis

5 OpenStax-CNX module: m Hypothesis Testing α alpha probability of Type I error Hypothesis Testing β beta probability of Type II error Hypothesis Testing X1 X2 X1-bar minus X2-bar dierence in sample means µ 1 µ 2 mu-1 minus mu-2 dierence in population means P ' 1 P ' 2 P1-prime minus P2- prime dierence in sample proportions p 1 p 2 p1 minus p2 dierence in population proportions Chi-Square Distribution X 2 Ky-square Chi-square Linear Regression and Correlation O Observed Observed frequency E Expected Expected frequency y = a + bx y equals a plus b-x equation of a line ^y y-hat estimated value of y F-Distribution ANOVA and r correlation coecient ɛ error SSE Sum of Squared Errors 1.9s 1.9 times s cut-o value for outliers F F-ratio F ratio Table 1