TEME flashcards
TEME · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Expected value
- The long-run average of a random variable, computed as the sum of each possible value multiplied by its probability. For a discrete variable X, E[X] = Σ x·P(X=x).
- Variance
- A measure of spread equal to the expected squared deviation from the mean. It can be computed as E[X²] − (E[X])², and its square root is the standard deviation.
- Binomial distribution
- The distribution of the number of successes in n independent trials, each with the same success probability p. Its mean is np and its variance is np(1−p).
- Bayes' theorem
- A rule for updating probabilities: P(A|B) = P(B|A)·P(A)/P(B). It expresses a posterior probability in terms of the prior and the likelihood.
- Independence of events
- Two events A and B are independent when P(A∩B) = P(A)·P(B). Knowing one occurred does not change the probability of the other.
- Mutually exclusive events
- Events that cannot occur together, so P(A∩B) = 0. If both have positive probability they are dependent, not independent.
- Central limit theorem
- For sufficiently large samples, the sampling distribution of the sample mean is approximately normal with mean μ and standard error σ/√n, regardless of the population shape.
- Type I error
- Rejecting a null hypothesis that is actually true. Its probability is the significance level α, chosen before the test is conducted.
- Type II error
- Failing to reject a null hypothesis that is actually false. Its probability is β, and statistical power equals 1 − β.
- Statistical power
- The probability of correctly rejecting a false null hypothesis, equal to 1 − β. Power increases with larger sample size, larger effect size, and higher α.
- Null hypothesis
- A statement of no effect or no difference that a hypothesis test attempts to reject. It is assumed true when computing the p-value.
- Alternative hypothesis
- The claim that contradicts the null hypothesis, such as a nonzero difference or association. It may be one-sided or two-sided.
- Probability mass function
- A function giving the probability that a discrete random variable equals each possible value. Its values are nonnegative and sum to one.
- Conditional probability
- The probability of event A given that B has occurred, written P(A|B) and defined as P(A∩B)/P(B) when P(B) > 0.
- Standard normal distribution
- A normal distribution with mean 0 and standard deviation 1. Any normal variable can be standardized using z = (x − μ)/σ.
- Sampling distribution
- The probability distribution of a statistic, such as the sample mean, over repeated samples of the same size from a population.
- Confidence interval
- A range of plausible values for a population parameter, constructed so that a stated proportion of such intervals capture the parameter in repeated sampling.
- p-value
- The probability, assuming the null hypothesis is true, of obtaining a test statistic at least as extreme as the observed one. Smaller values indicate stronger evidence against the null.
- Significance level
- The threshold α chosen before testing, typically 0.05. The null hypothesis is rejected when the p-value is less than or equal to α.
- Correlation coefficient
- A measure of the strength and direction of a linear relationship, ranging from −1 to 1. Its square gives the proportion of variance explained in a simple linear model.
- Linear regression slope
- In simple linear regression, the estimated slope equals r·(s_y/s_x), where r is the correlation and s_y and s_x are the sample standard deviations.
- Coefficient of determination
- Denoted r², it is the proportion of variability in the response variable explained by the explanatory variable in a linear regression model.
- Sensitivity
- The probability that a test correctly identifies a positive case, computed as true positives divided by all actual positives: TP/(TP+FN).
- Specificity
- The probability that a test correctly identifies a negative case, computed as true negatives divided by all actual negatives: TN/(TN+FP).
- Positive predictive value
- The probability that a person with a positive test result truly has the condition, computed as TP/(TP+FP). It depends strongly on disease prevalence.
- Negative predictive value
- The probability that a person with a negative test result truly does not have the condition, computed as TN/(TN+FN). It rises as prevalence falls.
- Multiplication rule
- For any two events, P(A∩B) = P(A)·P(B|A). When A and B are independent, this simplifies to P(A)·P(B).
- Addition rule
- For any two events, P(A∪B) = P(A) + P(B) − P(A∩B). For mutually exclusive events the intersection term is zero.
- Margin of error
- The half-width of a confidence interval, equal to the critical value multiplied by the standard error. It shrinks as sample size increases.
- Standard error of the mean
- The standard deviation of the sample mean, equal to σ/√n when the population standard deviation σ is known. It decreases with larger samples.
- z-score
- The number of standard deviations a value lies from the mean, computed as z = (x − μ)/σ. It permits comparison across different normal distributions.
- Two-sided hypothesis test
- A test in which the alternative hypothesis allows a difference in either direction. The p-value counts extreme results in both tails of the distribution.