Statistics Notations Flashcards

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Questions and Answers

What does μ refer to?

  • Variance of a population
  • Standard deviation of a sample
  • Population mean (correct)
  • Sample mean

What does σ represent?

  • Standard deviation of a population (correct)
  • Proportion of sample elements
  • Regression coefficient
  • Population size

What does σ² represent?

  • Expected value of random variable
  • Proportion of population elements
  • Variance of a population (correct)
  • Population mean

What does P refer to?

<p>Proportion of population elements with a specific attribute (D)</p> Signup and view all the answers

What does Q represent?

<p>Proportion of population elements without a specific attribute (B)</p> Signup and view all the answers

What does ρ signify?

<p>Population correlation coefficient (C)</p> Signup and view all the answers

What does N refer to?

<p>Number of elements in a population (B)</p> Signup and view all the answers

What does x̄ represent?

<p>Sample mean (B)</p> Signup and view all the answers

What does s signify?

<p>Standard deviation of a sample (C)</p> Signup and view all the answers

What does s² represent?

<p>Variance of a sample (D)</p> Signup and view all the answers

What does p refer to?

<p>Proportion of sample elements with a specific attribute (A)</p> Signup and view all the answers

What does q represent?

<p>Proportion of sample elements without a specific attribute (A)</p> Signup and view all the answers

What does r signify?

<p>Sample correlation coefficient (D)</p> Signup and view all the answers

What does n represent?

<p>Number of elements in a sample (C)</p> Signup and view all the answers

What does Β₀ signify?

<p>Intercept constant in a population regression line (B)</p> Signup and view all the answers

What does Β₁ indicate?

<p>Regression coefficient in a population regression line (C)</p> Signup and view all the answers

What does R² refer to?

<p>Coefficient of determination (A)</p> Signup and view all the answers

What does b₀ signify?

<p>Intercept constant in a sample regression line (D)</p> Signup and view all the answers

What does b₁ represent?

<p>Slope of a sample regression line (D)</p> Signup and view all the answers

What does sb₁ refer to?

<p>Standard error of the slope of a regression line (D)</p> Signup and view all the answers

What does P(A) represent?

<p>Probability of event A occurring (C)</p> Signup and view all the answers

What does P(A/B) signify?

<p>Probability of event A occurring given event B has occurred (D)</p> Signup and view all the answers

What does P(A') represent?

<p>Probability of the complement of event A (C)</p> Signup and view all the answers

What does P(A ∩ B) signify?

<p>Probability of the intersection of events A and B (B)</p> Signup and view all the answers

What does P(A ∪ B) refer to?

<p>Probability of the union of events A and B (C)</p> Signup and view all the answers

What does E(X) indicate?

<p>Expected value of random variable X (B)</p> Signup and view all the answers

What does b(x; n, P) represent?

<p>Binomial probability (C)</p> Signup and view all the answers

What does n! refer to?

<p>Factorial value of n (B)</p> Signup and view all the answers

What does nPr signify?

<p>Number of permutations of n things taken r at a time (D)</p> Signup and view all the answers

What does nCr denote?

<p>Number of combinations of n things taken r at a time (A)</p> Signup and view all the answers

What does A ∩ B refer to?

<p>Intersection of events A and B (A)</p> Signup and view all the answers

What does A ∪ B represent?

<p>Union of events A and B (B)</p> Signup and view all the answers

What does {A, B, C} signify?

<p>The set of elements consisting of A, B, and C (C)</p> Signup and view all the answers

What does {∅} represent?

<p>Null set (D)</p> Signup and view all the answers

What does H₀ denote?

<p>Null hypothesis (D)</p> Signup and view all the answers

What does H₁ or Ha refer to?

<p>Alternative hypothesis (D)</p> Signup and view all the answers

What does α represent?

<p>Probability of Type I error (B)</p> Signup and view all the answers

What does Β signify?

<p>Probability of committing a Type II error (B)</p> Signup and view all the answers

What does Z or z signify?

<p>Z score (B)</p> Signup and view all the answers

What does Zα represent?

<p>Z score with cumulative probability equal to 1 - α (A)</p> Signup and view all the answers

What does Tα denote?

<p>t score with cumulative probability equal to 1 - α (A)</p> Signup and view all the answers

What does fα refer to?

<p>f statistic that has a cumulative probability equal to 1 - α (D)</p> Signup and view all the answers

What does fα(v₁, v₂) signify?

<p>f statistic with v₁ and v₂ degrees of freedom (C)</p> Signup and view all the answers

What does Χ² represent?

<p>Chi-square statistic (C)</p> Signup and view all the answers

What does Σ signify?

<p>Summation symbol for computing sums (D)</p> Signup and view all the answers

What does Σx or Σxi signify?

<p>Sum of a set of n observations (C)</p> Signup and view all the answers

What does sqrt refer to?

<p>Square root function (D)</p> Signup and view all the answers

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Study Notes

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.
  • : Indicates the sample mean, the average of a sampled dataset.
  • s: Denotes the standard deviation of a sample, reflecting variability in the sampled data.
  • : 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.
  • : 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

  • : Represents the standardized score with cumulative probability equal to 1 - α.
  • : Denotes the t-score with cumulative probability equal to 1 - α.
  • : 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.

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