Statistics Notations Flashcards

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?

Proportion of population elements with a specific attribute Signup and view all the answers

What does Q represent?

Proportion of population elements without a specific attribute Signup and view all the answers

What does ρ signify?

Population correlation coefficient Signup and view all the answers

What does N refer to?

Number of elements in a population Signup and view all the answers

What does x̄ represent?

Sample mean Signup and view all the answers

What does s signify?

Standard deviation of a sample Signup and view all the answers

What does s² represent?

Variance of a sample Signup and view all the answers

What does p refer to?

Proportion of sample elements with a specific attribute Signup and view all the answers

What does q represent?

Proportion of sample elements without a specific attribute Signup and view all the answers

What does r signify?

Sample correlation coefficient Signup and view all the answers

What does n represent?

Number of elements in a sample Signup and view all the answers

What does Β₀ signify?

Intercept constant in a population regression line Signup and view all the answers

What does Β₁ indicate?

Regression coefficient in a population regression line Signup and view all the answers

What does R² refer to?

Coefficient of determination Signup and view all the answers

What does b₀ signify?

Intercept constant in a sample regression line Signup and view all the answers

What does b₁ represent?

Slope of a sample regression line Signup and view all the answers

What does sb₁ refer to?

Standard error of the slope of a regression line Signup and view all the answers

What does P(A) represent?

Probability of event A occurring Signup and view all the answers

What does P(A/B) signify?

Probability of event A occurring given event B has occurred Signup and view all the answers

What does P(A') represent?

Probability of the complement of event A Signup and view all the answers

What does P(A ∩ B) signify?

Probability of the intersection of events A and B Signup and view all the answers

What does P(A ∪ B) refer to?

Probability of the union of events A and B Signup and view all the answers

What does E(X) indicate?

Expected value of random variable X Signup and view all the answers

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

Binomial probability Signup and view all the answers

What does n! refer to?

Factorial value of n Signup and view all the answers

What does nPr signify?

Number of permutations of n things taken r at a time Signup and view all the answers

What does nCr denote?

Number of combinations of n things taken r at a time Signup and view all the answers

What does A ∩ B refer to?

Intersection of events A and B Signup and view all the answers

What does A ∪ B represent?

Union of events A and B Signup and view all the answers

What does {A, B, C} signify?

The set of elements consisting of A, B, and C Signup and view all the answers

What does {∅} represent?

Null set Signup and view all the answers

What does H₀ denote?

Null hypothesis Signup and view all the answers

What does H₁ or Ha refer to?

Alternative hypothesis Signup and view all the answers

What does α represent?

Probability of Type I error Signup and view all the answers

What does Β signify?

Probability of committing a Type II error Signup and view all the answers

What does Z or z signify?

Z score Signup and view all the answers

What does Zα represent?

Z score with cumulative probability equal to 1 - α Signup and view all the answers

What does Tα denote?

t score with cumulative probability equal to 1 - α Signup and view all the answers

What does fα refer to?

f statistic that has a cumulative probability equal to 1 - α Signup and view all the answers

What does fα(v₁, v₂) signify?

f statistic with v₁ and v₂ degrees of freedom Signup and view all the answers

What does Χ² represent?

Chi-square statistic Signup and view all the answers

What does Σ signify?

Summation symbol for computing sums Signup and view all the answers

What does Σx or Σxi signify?

Sum of a set of n observations Signup and view all the answers

What does sqrt refer to?

Square root function Signup and view all the answers

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.
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.

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This quiz focuses on essential statistics notations and their meanings. Each card presents a notation commonly used in statistics along with its definition, helping you understand and memorize important terms. Perfect for students or anyone looking to brush up on statistical vocabulary.