Explore · Flashcard deck
Shared from Quizcard. Flip through the cards below, or copy the deck to edit and study it in your own account — free.
Space flips · arrows move · Esc exits
What does a 95% confidence interval mean?
Answer: If we repeated the sampling many times, about 95% of the intervals built this way would contain the true parameter.
It does not mean there is a 95% chance the parameter is in this particular interval.
What is a chi-square test of independence used for?
Answer: Testing whether two categorical variables are associated.
Compares observed counts with expected counts in a two-way table.
When do you use a t-test instead of a z-test for a mean?
Answer: When the population standard deviation is unknown and you estimate it from the sample.
The t distribution has heavier tails, especially for small samples.
What is statistical power?
Answer: The probability that a test correctly rejects a false null hypothesis.
Increases with sample size, effect size, and α.
Type I vs Type II error?
Answer: Type I: rejecting a true null (false positive, probability α). Type II: failing to reject a false null (false negative, probability β).
Power = 1 − β.
What is a p-value?
Answer: The probability of getting a result at least as extreme as the observed one if the null hypothesis were true.
Small p-values are evidence against H0.
What is the null hypothesis?
Answer: The statement of no effect or no difference that the test tries to find evidence against.
Written H0; the alternative is Ha.
General form of a confidence interval
Answer: estimate ± (critical value) × (standard error)
The margin of error is the second part.
What are the three principles of experimental design?
Answer: Control, randomization, and replication.
Blocking reduces variability from known nuisance variables.
Observational study vs experiment?
Answer: An observational study measures variables without intervening; an experiment assigns treatments.
Only well-designed experiments can establish causation.
What is a lurking (confounding) variable?
Answer: A variable not included in the analysis that affects both variables being studied.
Ice cream sales and drownings are both driven by hot weather.
What is a residual?
Answer: Observed y minus predicted y.
Patterns in a residual plot suggest a linear model is not appropriate.
What does r² (coefficient of determination) tell you?
Answer: The proportion of the variation in y explained by the linear relationship with x.
r² = 0.64 means 64% of the variation is explained.
Interpret the slope in a least-squares regression line.
Answer: The predicted change in y for a one-unit increase in x.
The intercept is the predicted y when x = 0, which may be meaningless.
What does the correlation coefficient r measure?
Answer: The strength and direction of a linear relationship between two quantitative variables, from −1 to 1.
r = 0 means no linear relationship, not necessarily no relationship.
Population vs sample?
Answer: A population is the entire group of interest; a sample is a subset used to learn about it.
Parameters describe populations; statistics describe samples.
What is a z-score?
Answer: The number of standard deviations a value is from the mean: z = (x − μ) / σ
Lets you compare values from different distributions.
How do you recognize right (positive) skew?
Answer: The tail stretches to the right and the mean is greater than the median.
Left skew is the mirror image.
What is the interquartile range (IQR)?
Answer: Q3 − Q1, the range of the middle 50% of the data.
Outliers are often flagged beyond 1.5 × IQR from the quartiles.
What does the standard deviation measure?
Answer: The typical distance of data values from the mean.
Variance is the standard deviation squared.
Mean, median, mode: which is resistant to outliers?
Answer: The median (and mode); the mean is pulled toward extreme values.
Use the median for skewed data such as incomes.
What is the standard error of the mean?
Answer: σ / √n, the standard deviation of the sampling distribution of the sample mean.
Larger samples give smaller standard errors.
What does the Central Limit Theorem say?
Answer: For large enough samples, the sampling distribution of the mean is approximately normal regardless of the population's shape.
Usually n ≥ 30 is considered large enough.
What is a simple random sample?
Answer: A sample in which every group of n individuals has an equal chance of being chosen.
Removes selection bias but not sampling variability.
What is sampling bias?
Answer: A systematic error that makes the sample unrepresentative of the population.
Voluntary response and convenience samples are common sources.
What are the conditions for a binomial setting?
Answer: Fixed number of trials, two outcomes, constant probability of success, independent trials.
Mean np, standard deviation √(np(1−p)).
State the addition rule for two events.
Answer: P(A or B) = P(A) + P(B) − P(A and B)
For mutually exclusive events the last term is zero.
What is conditional probability?
Answer: The probability of A given that B has occurred: P(A|B) = P(A and B) / P(B)
The basis of Bayes' theorem.
When are two events independent?
Answer: When the occurrence of one does not change the probability of the other: P(A and B) = P(A) · P(B).
Example: two separate coin flips.
What is the empirical (68-95-99.7) rule?
Answer: In a normal distribution, about 68% of values lie within 1 SD of the mean, 95% within 2, and 99.7% within 3.
Only applies to roughly bell-shaped data.
All Statistics decks → · Explore everything
Make your own deck like this
Upload a PDF, Word doc, or slides and Quizcard writes the cards for you, or build them by hand. Free to start, no credit card required.