# 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.

• $P$ - population proportion.

• $p$ - sample proportion.

• $X$ - set of population elements.

• $x$ - set of sample elements.

• $N$ - set of population size.

• $N$ - set of sample size.

## Greek Vs Roman letters

Roman letters represent the sample attributs and greek letters are used to represent Population attributes.

• $\mu$ - population mean.

• $\bar x$ - sample mean.

• $\delta$ - standard deviation of a population.

• $s$ - standard deviation of a sample.

## Population specific Parameters

Following symbols represent population specific attributes.

• $\mu$ - population mean.

• $\delta$ - standard deviation of a population.

• ${\mu}^2$ - variance of a population.

• $P$ - proportion of population elements having a particular attribute.

• $Q$ - proportion of population elements having no particular attribute.

• $\rho$ - population correlation coefficient based on all of the elements from a population.

• $N$ - number of elements in a population.

## Sample specific Parameters

Following symbols represent population specific attributes.

• $\bar x$ - sample mean.

• $s$ - standard deviation of a sample.

• ${s}^2$ - variance of a sample.

• $p$ - proportion of sample elements having a particular attribute.

• $q$ - proportion of sample elements having no particular attribute.

• $r$ - population correlation coefficient based on all of the elements from a sample.

• $n$ - number of elements in a sample.

## Linear Regression

• $B_0$ - intercept constant in a population regression line.

• $B_1$ - regression coefficient in a population regression line.

• ${R}^2$ - coefficient of determination.

• $b_0$ - intercept constant in a sample regression line.

• $b_1$ - regression coefficient in a sample regression line.

• $^{s}b_1$ - standard error of the slope of a regression line.

## Probability

• $P(A)$ - probability that event A will occur.

• $P(A|B)$ - conditional probability that event A occurs, given that event B has occurred.

• $P(A')$ - probability of the complement of event A.

• $P(A \cap B)$ - probability of the intersection of events A and B.

• $P(A \cup B)$ - probability of the union of events A and B.

• $E(X)$ - expected value of random variable X.

• $b(x; n, P)$ - binomial probability.

• $b*(x; n, P)$ - negative binomial probability.

• $g(x; P)$ - geometric probability.

• $h(x; N, n, k)$ - hypergeometric probability.

## Permutation/Combination

• $n!$ - factorial value of n.

• $^{n}P_r$ - number of permutations of n things taken r at a time.

• $^{n}C_r$ - number of combinations of n things taken r at a time.

## Set

• $A \Cap B$ - intersection of set A and B.

• $A \Cup B$ - union of set A and B.

• $\{ A, B, C \}$ - set of elements consisting of A, B, and C.

• $\emptyset$ - null or empty set.

## Hypothesis Testing

• $H_0$ - null hypothesis.

• $H_1$ - alternative hypothesis.

• $\alpha$ - significance level.

• $\beta$ - probability of committing a Type II error.

## Random Variables

• $Z$ or $z$ - standardized score, also known as a z score.

• $z_{\alpha}$ - standardized score that has a cumulative probability equal to $1 - \alpha$.

• $t_{\alpha}$ - t statistic that has a cumulative probability equal to $1 - \alpha$.

• $f_{\alpha}$ - f statistic that has a cumulative probability equal to $1 - \alpha$.

• $f_{\alpha}(v_1, v_2)$ - f statistic that has a cumulative probability equal to $1 - \alpha$ and $v_1$ and $v_2$ degrees of freedom.

• $X^2$ - chi-square statistic.

## Summation Symbols

• $\sum$ - summation symbol, used to compute sums over a range of values.

• $\sum x$ or $\sum x_i$ - sum of a set of n observations. Thus, $\sum x = x_1 + x_2 + ... + x_n$.