Statistics Notations Flashcards

Statistical Notations and Their Meanings

• μ: Represents the population mean, the average value of a dataset.
• σ: Signifies the standard deviation of a population, indicating data dispersion.
• σ²: Denotes the variance of a population, measuring data variance.
• P: Indicates the proportion of a population with a specific attribute.
• Q: Represents the proportion without a specified attribute, calculated as Q = 1 - P.
• ρ: Refers to the population correlation coefficient, quantifying the correlation between two variables within the population.
• N: Specifies the total number of elements in a population.
• x̄: Indicates the sample mean, the average of a sampled dataset.
• s: Denotes the standard deviation of a sample, reflecting variability in the sampled data.
• s²: Represents the variance of a sample, measuring dispersion within a sample.
• p: Signifies the proportion of sample elements possessing a specific attribute.
• q: Indicates the sample proportion lacking a specific attribute, calculated as q = 1 - p.
• r: Refers to the sample correlation coefficient, quantifying the relationship between two variables in a sample.
• n: Indicates the number of elements within a sample.

Regression Notations

• Β₀: Represents the intercept constant in a population regression line.
• Β₁: Denotes the regression coefficient (slope) in a population regression line.
• R²: Represents the coefficient of determination, measuring the proportion of variation explained by a model.
• b₀: Indicates the intercept constant in a sample regression line.
• b₁: Represents the regression coefficient (slope) in a sample regression line.
• sb₁: Represents the standard error of the slope of a regression line.

Probability Notations

• P(A): Indicates the probability that event A will occur.
• P(A/B): Represents the conditional probability that event A occurs given event B has occurred.
• P(A'): Refers to the probability of the complement of event A.
• P(A ∩ B): Represents the probability of both events A and B occurring.
• P(A ∪ B): Indicates the probability that at least one of events A or B occurs.

Expectation and Binomial Probability

• E(X): Represents the expected value of a random variable X.
• b(x; n, P): Represents binomial probability for x successes in n trials with probability P.

Factorial and Permutation/Combination Notation

• n!: Represents the factorial value of n, the product of all positive integers up to n.
• nPr: Indicates the number of permutations of n elements taken r at a time.
• nCr: Denotes the number of combinations of n elements taken r at a time.

Set and Hypothesis Notation

• A ∩ B: Represents the intersection of events A and B, those outcomes common to both.
• A ∪ B: Indicates the union of events A and B, outcomes that are in either event.
• {A, B, C}: Represents a set containing elements A, B, and C.
• {∅}: Indicates the null set, a set with no elements.
• H₀: Represents the null hypothesis, a statement of no effect or no difference.
• H₁ or Ha: Denotes an alternative hypothesis, suggesting some effect or difference.

Error and Score Notations

• α: Represents the significance level, the threshold for rejecting the null hypothesis.
• Β: Represents the probability of committing a Type II error, failing to reject a false null hypothesis.
• Z or z: Indicates a standardized score (z-score) that represents how many standard deviations a data point is from the mean.

Additional Statistical Notations

• Zα: Represents the standardized score with cumulative probability equal to 1 - α.
• Tα: Denotes the t-score with cumulative probability equal to 1 - α.
• fα: Represents the F statistic with cumulative probability equal to 1 - α.
• fα(v₁, v₂): Indicates the F statistic with v₁ and v₂ degrees of freedom and a cumulative probability of 1 - α.
• Χ²: Denotes the chi-square statistic, a measure used in hypothesis testing.
• Σ: Represents the summation symbol, utilized to compute the sum of a series of values.
• Σx or Σxi: Refers to the sum of a set of observations, calculated as Σxi = x1 + x2 + ... + xn.
• sqrt: Indicates the square root function, such as sqrt(4) = 2.