# Statistics – Notations

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.

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