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 $.



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