https://teddyrookbook.com/math/probability-and-statistics/Recent content in Probability and Statistics on Teddy Rook Bookhttps://teddyrookbook.com/img/share.jpghttps://teddyrookbook.com/img/share.jpgHugoenhttps://teddyrookbook.com/math/probability-and-statistics/variable-types/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/variable-types/Tell whether data are labels or measured numbers. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/categorical-displays/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/categorical-displays/Read bar graphs, pie charts and relative frequencies. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/histograms-shape/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/histograms-shape/Describe shape as symmetric, skewed, unimodal or bimodal. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/center-resistance/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/center-resistance/The median resists outliers; the mean does not. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/standard-deviation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/standard-deviation/A typical distance from the mean. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/five-number-outliers/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/five-number-outliers/Use the 1.5 × IQR rule to flag outliers. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/compare-distributions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/compare-distributions/Compare shape, center and spread in context. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/z-scores/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/z-scores/z tells how many standard deviations a value is from the mean. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/transform-data/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/transform-data/Adding a constant moves the center; multiplying scales center and spread. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/normal-curve/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/normal-curve/About 68%, 95% and 99.7% of values lie within 1, 2 and 3 standard deviations. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/normal-probabilities/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/normal-probabilities/Find the proportion below, above or between values. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/inverse-normal/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/inverse-normal/Work backward from an area to a z-score to a value. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/scatterplots/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/scatterplots/Describe direction, form, strength and unusual points. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/correlation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/correlation/r measures the direction and strength of a linear pattern. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/least-squares-line/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/least-squares-line/The line that makes the sum of squared residuals smallest. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/interpret-regression/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/interpret-regression/Say what the slope and intercept mean in context, with units. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/residual-plots/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/residual-plots/A good linear fit leaves residuals with no pattern. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/r-squared/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/r-squared/r² is the fraction of the variation in y explained by the line. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/influential-points/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/influential-points/Some points pull the line toward themselves. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/nonlinear-models/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/nonlinear-models/Use logs to straighten curved data. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/correlation-causation-stat/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/correlation-causation-stat/Association alone does not show cause and effect. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/sampling-methods/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/sampling-methods/Simple random, stratified, cluster and systematic samples. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/sampling-bias/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/sampling-bias/Spot undercoverage, nonresponse and leading questions. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/observational-experimental/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/observational-experimental/Only a randomized experiment can show cause and effect. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/experimental-design/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/experimental-design/Use control, random assignment, replication and blocking. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/evaluate-reports/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/evaluate-reports/Judge claims in the news by how the data were produced. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/events-sample-spaces/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/events-sample-spaces/Describe events with "or," "and" and "not." Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/addition-rule/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/addition-rule/P(A or B) = P(A) + P(B) − P(A and B). Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/conditional-probability/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/conditional-probability/P(A ∣ B) is the probability of A among the outcomes where B happened. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/two-way-conditional/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/two-way-conditional/Divide by the row or column total that matches the condition. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/independence/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/independence/A and B are independent when P(A ∣ B) = P(A). Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/multiplication-rule/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/multiplication-rule/P(A and B) = P(A) · P(B ∣ A). Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/bayes-rule/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/bayes-rule/Reverse a conditional probability with a tree or a table. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/permutations/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/permutations/Count arrangements when order matters. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/combinations/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/combinations/Count selections when order does not matter. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/counting-probability/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/counting-probability/Use permutations and combinations to find probabilities. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/discrete-random-variables/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/discrete-random-variables/List values and their probabilities in a table. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/expected-value/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/expected-value/The long-run average outcome: Σ x · P(x). Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/random-variable-spread/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/random-variable-spread/Measure how much a random variable typically varies from its mean. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/combining-random-variables/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/combining-random-variables/Means add; for independent variables, variances add. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/binomial-distribution/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/binomial-distribution/Count successes in n independent trials with the same p. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/geometric-distribution/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/geometric-distribution/Count the trials until the first success. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/continuous-distributions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/continuous-distributions/Probability is area under a density curve. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/expected-value-decisions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/expected-value-decisions/Compare games, insurance and strategies by expected payoff. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/simulation-models/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/simulation-models/Use simulation to judge whether data fit a model. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/sampling-distribution-proportion/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/sampling-distribution-proportion/Sample proportions center on p with spread √(p(1 − p)/n). Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/sampling-distribution-mean/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/sampling-distribution-mean/Sample means are close to normal for large n, with spread σ/√n. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/confidence-interval-proportion/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/confidence-interval-proportion/Estimate ± margin of error. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/margin-of-error/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/margin-of-error/Quadrupling the sample size halves the margin of error. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/confidence-interval-mean/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/confidence-interval-mean/Use t when the population standard deviation is unknown. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/significance-tests/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/significance-tests/Ask how surprising the data would be if the null hypothesis were true. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/test-proportion/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/test-proportion/Carry out a one-proportion z test. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/test-mean/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/test-mean/Carry out a one-sample t test. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/errors-power/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/errors-power/Weigh the two kinds of mistakes a test can make. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/randomization-tests/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/randomization-tests/Reshuffle groups to see whether a difference could be chance. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/two-sample-inference/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/two-sample-inference/Compare two proportions or two means. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/chi-square-tests/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/chi-square-tests/Test goodness of fit and association in two-way tables. Probability and Statistics · Math Ladderhttps://teddyrookbook.com/math/probability-and-statistics/regression-inference/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/probability-and-statistics/regression-inference/Test and estimate the true slope from sample data. Probability and Statistics · Math Ladder