Following table shows the usage of various symbols used in Statistics
Capitalization
Generally lower case letters represent the sample attributes and capital case letters are used to represent population attributes.
· PP – population proportion.
· pp – sample proportion.
· XX – set of population elements.
· xx – set of sample elements.
· NN – set of population size.
· NN – set of sample size.
Greek Vs Roman letters
Roman letters represent the sample attributs and greek letters are used to represent Population attributes.
· μμ – population mean.
· x¯x¯ – sample mean.
· δδ – standard deviation of a population.
· ss – standard deviation of a sample.
Population specific Parameters
Following symbols represent population specific attributes.
· μμ – population mean.
· δδ – standard deviation of a population.
· μ2μ2 – variance of a population.
· PP – proportion of population elements having a particular attribute.
· QQ – proportion of population elements having no particular attribute.
· ρρ – population correlation coefficient based on all of the elements from a population.
· NN – number of elements in a population.
Sample specific Parameters
Following symbols represent population specific attributes.
· x¯x¯ – sample mean.
· ss – standard deviation of a sample.
· s2s2 – variance of a sample.
· pp – proportion of sample elements having a particular attribute.
· qq – proportion of sample elements having no particular attribute.
· rr – population correlation coefficient based on all of the elements from a sample.
· nn – number of elements in a sample.
Linear Regression
· B0B0 – intercept constant in a population regression line.
· B1B1 – regression coefficient in a population regression line.
· R2R2 – coefficient of determination.
· b0b0 – intercept constant in a sample regression line.
· b1b1 – regression coefficient in a sample regression line.
· sb1sb1 – standard error of the slope of a regression line.
Probability
· P(A)P(A) – probability that event A will occur.
· P(A|B)P(A|B) – conditional probability that event A occurs, given that event B has occurred.
· P(A′)P(A′) – probability of the complement of event A.
· P(A∩B)P(A∩B) – probability of the intersection of events A and B.
· P(A∪B)P(A∪B) – probability of the union of events A and B.
· E(X)E(X) – expected value of random variable X.
· b(x;n,P)b(x;n,P) – binomial probability.
· b∗(x;n,P)b∗(x;n,P) – negative binomial probability.
· g(x;P)g(x;P) – geometric probability.
· h(x;N,n,k)h(x;N,n,k) – hypergeometric probability.
Permutation/Combination
· n!n! – factorial value of n.
· nPrnPr – number of permutations of n things taken r at a time.
· nCrnCr – number of combinations of n things taken r at a time.
Set
· A⋒BA⋒B – intersection of set A and B.
· A⋓BA⋓B – union of set A and B.
· {A,B,C}{A,B,C} – set of elements consisting of A, B, and C.
· ∅∅ – null or empty set.
Hypothesis Testing
· H0H0 – null hypothesis.
· H1H1 – alternative hypothesis.
· αα – significance level.
· ββ – probability of committing a Type II error.
Random Variables
· ZZ or zz – standardized score, also known as a z score.
· zαzα – standardized score that has a cumulative probability equal to 1−α1−α.
· tαtα – t statistic that has a cumulative probability equal to 1−α1−α.
· fαfα – f statistic that has a cumulative probability equal to 1−α1−α.
· fα(v1,v2)fα(v1,v2) – f statistic that has a cumulative probability equal to 1−α1−α and v1v1 and v2v2 degrees of freedom.
· X2X2 – chi-square statistic.
Summation Symbols
· ∑∑ – summation symbol, used to compute sums over a range of values.
· ∑x∑x or ∑xi∑xi – sum of a set of n observations. Thus, ∑x=x1+x2+…+xn∑x=x1+x2+…+xn.