Statistics - Notations

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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 $.