# Re.Statica

> Re.Statica is a free statistics learning platform. It has 263 calculators that show every step of the working (hypotheses, assumptions, each formula with the values substituted, the decision, and the interpretation), 192 illustrated stories that teach hypothesis tests, 352 short concept lessons in 35 journeys, and 807 multi-step practice problems.

Use it to send a learner to a worked, step-by-step solution for a specific test, to a story that makes a test memorable, or to a lesson that explains a concept from scratch. The app runs in the browser at the homepage; the pages linked below are readable without JavaScript. Calculator pages include the method's formulas, assumptions, hypotheses, a complete worked example and FAQs.

Re.Statica is currently in beta: the calculators are complete, and some features of Saga, Learn and Practice may not be available yet.

## The app

- [Re.Statica](https://www.restatica.com/): the app itself (needs JavaScript). Tabs: Atlas, Solver, Saga, Learn, Practice, Studio.
- [Atlas](https://www.restatica.com/atlas): every statistical method mapped as a constellation of related techniques.
- [Solver](https://www.restatica.com/solver): a calculator that shows its work from hypotheses to interpretation, with PDF export.
- [Saga](https://www.restatica.com/saga): 192 illustrated stories, each built around one hypothesis test and worked in full.
- [Learn](https://www.restatica.com/learn): 35 journeys and 352 short lessons, from collecting data to multivariate analysis.
- [Practice](https://www.restatica.com/practice): 807 multi-step problems in 10 decks at three levels, with step-by-step feedback.
- [Visualization Studio](https://www.restatica.com/visualization-studio): interactive distributions, rejection regions, power curves and simulations.
- [All calculators](https://www.restatica.com/calculators): the directory of all 263 calculators, grouped by topic.

## Calculators

- [Bayes' Theorem Calculator](https://www.restatica.com/calculators/bayes-theorem-calculator): Free Bayes' theorem calculator that works the posterior step by step (prior, likelihood, total evidence) with the false-positive trap explained.
- [Binomial Distribution Calculator](https://www.restatica.com/calculators/binomial-distribution-calculator): Binomial distribution calculator for the probability of k successes in n trials, with every step of the formula worked out: exact and cumulative probabilities. No sign-up.
- [Bootstrap Confidence Interval Calculator](https://www.restatica.com/calculators/bootstrap-confidence-interval-calculator): Free bootstrap confidence interval calculator using the percentile method. See the resampling, the bootstrap distribution and both bounds, with no normality assumption.
- [Chebyshev's Theorem Calculator](https://www.restatica.com/calculators/chebyshev-theorem-calculator): Free Chebyshev's theorem calculator giving the guaranteed minimum proportion within k standard deviations, for any distribution shape.
- [Chi-Square Goodness of Fit Calculator](https://www.restatica.com/calculators/chi-square-goodness-of-fit-calculator): Free chi-square goodness of fit calculator. Enter observed counts and a hypothesized distribution to see expected frequencies, the statistic, df, and p-value.
- [Chi-Square Test of Independence Calculator](https://www.restatica.com/calculators/chi-square-test-of-independence-calculator): Free chi-square test of independence calculator. Paste a contingency table and see observed vs expected counts, the statistic, df, and p-value in full.
- [Coefficient of Variation Calculator](https://www.restatica.com/calculators/coefficient-of-variation-calculator): Free coefficient of variation calculator showing the mean, the standard deviation and the ratio as a percentage, for comparing spread across different scales.
- [Combination Calculator](https://www.restatica.com/calculators/combination-calculator): Free combination calculator (nCr) for choosing a group when order does not matter: the factorial setup, the division that removes orderings, and the count.
- [Conditional Probability Calculator](https://www.restatica.com/calculators/conditional-probability-calculator): Free conditional probability calculator for P(A|B): see the joint probability, the reduced sample space, and why P(A|B) is not the same thing as P(B|A).
- [Confidence Interval Calculator](https://www.restatica.com/calculators/confidence-interval-calculator): Free confidence interval calculator for a mean. Get the critical value, the standard error, the margin of error and both bounds, each derived in full. No sign-up.
- [Confidence Interval for a Mean (σ Known)](https://www.restatica.com/calculators/confidence-interval-mean-sigma-known-calculator): Free z confidence interval calculator for a population mean when sigma is known. Critical value, standard error and both bounds, each derived step by step.
- [Confidence Interval for a Proportion](https://www.restatica.com/calculators/confidence-interval-proportion-calculator): Free confidence interval calculator for a proportion or percentage. Critical value, standard error and both bounds shown in full, with the success-failure check.
- [Confidence Interval for a Variance Ratio](https://www.restatica.com/calculators/confidence-interval-variance-ratio-calculator): Free confidence interval calculator for the ratio of two variances, using the F distribution. Both bounds derived, with the asymmetry explained.
- [Confidence Interval for Paired Differences](https://www.restatica.com/calculators/confidence-interval-paired-differences-calculator): Free confidence interval calculator for paired or before-and-after data. Works on the differences, with the critical value, margin of error and both bounds shown.
- [Confidence Interval for the Difference Between Two Means](https://www.restatica.com/calculators/confidence-interval-two-means-calculator): Free calculator for the confidence interval of a difference between two means, using the pooled standard deviation. Every step shown, from pooling to both bounds.
- [Confidence Interval for the Difference Between Two Proportions](https://www.restatica.com/calculators/confidence-interval-two-proportions-calculator): Free calculator for the confidence interval of a difference between two proportions. Unpooled standard error, critical value and both bounds, each step shown.
- [Confidence Interval for Two Means (Unequal Variances)](https://www.restatica.com/calculators/confidence-interval-welch-calculator): Free Welch confidence interval calculator for two means with unequal variances. Separate variances, approximate degrees of freedom and both bounds, fully worked.
- [Confidence Interval for Two Means (σ Known)](https://www.restatica.com/calculators/confidence-interval-two-means-sigma-known-calculator): Free two-sample z confidence interval calculator for a difference between means when both population standard deviations are known. Every step shown.
- [Decile Calculator](https://www.restatica.com/calculators/decile-calculator): Free decile calculator giving all nine decile cut points, with each position located and interpolated from your sorted data.
- [Descriptive Statistics Calculator](https://www.restatica.com/calculators/descriptive-statistics-calculator): Descriptive statistics calculator that summarizes your data set and shows every formula worked out: mean, median, variance, SD, quartiles, and range. No sign-up.
- [Empirical Rule Calculator](https://www.restatica.com/calculators/empirical-rule-calculator): Free empirical rule calculator building the 68, 95 and 99.7 percent intervals around your mean, with each boundary worked out.
- [F-Test (Two Variances) Calculator](https://www.restatica.com/calculators/f-test-calculator): Free F-test calculator that compares two sample variances to test whether two population variances are equal, showing the F ratio, df, and p-value. No sign-up.
- [Fisher's Exact Test Calculator](https://www.restatica.com/calculators/fishers-exact-test-calculator): Free Fisher's exact test calculator for small 2x2 tables. Enter counts and see the exact p-value worked out, for when chi-square's expected-count rule fails.
- [Five-Number Summary Calculator](https://www.restatica.com/calculators/five-number-summary-calculator): Five-number summary calculator: minimum, Q1, median, Q3, and maximum, with the IQR, the 1.5 × IQR outlier fence, and a box plot: every step shown. No sign-up.
- [Geometric Mean Calculator](https://www.restatica.com/calculators/geometric-mean-calculator): Free geometric mean calculator for growth rates and returns, showing the product, the root and why the arithmetic mean overstates compounding data.
- [Harmonic Mean Calculator](https://www.restatica.com/calculators/harmonic-mean-calculator): Free harmonic mean calculator for averaging rates and speeds, showing every reciprocal, the average and the inversion back to the original units.
- [Interquartile Range Calculator](https://www.restatica.com/calculators/interquartile-range-calculator): Free interquartile range calculator showing Q1, Q3, the subtraction and the semi-interquartile range, plus the 1.5 rule for outliers.
- [Kruskal-Wallis Test Calculator](https://www.restatica.com/calculators/kruskal-wallis-test-calculator): Free Kruskal-Wallis test calculator for three or more groups that shows the full working: rank sums, the H statistic, and the p-value, step by step. No sign-up.
- [Kurtosis Calculator](https://www.restatica.com/calculators/kurtosis-calculator): Free kurtosis calculator showing the fourth-power deviations and the standardized result, with excess kurtosis and what heavy tails actually mean.
- [Levene's Test Calculator](https://www.restatica.com/calculators/levene-test-calculator): Levene's test calculator checks homogeneity of variance before an ANOVA or t-test. Shows the full working: every step to the F-statistic and p-value. No sign-up.
- [Linear Regression Calculator](https://www.restatica.com/calculators/linear-regression-calculator): Simple linear regression calculator that finds the slope, intercept, R-squared, and p-values for one predictor, showing the full least-squares working. No sign-up.
- [Logistic Regression Calculator](https://www.restatica.com/calculators/logistic-regression-calculator): Logistic regression calculator that models a binary outcome, giving log-odds coefficients, odds ratios, and p-values with the full working shown. No sign-up.
- [Mann-Whitney U Test Calculator](https://www.restatica.com/calculators/mann-whitney-u-test-calculator): Free Mann-Whitney U test calculator that ranks your data and shows the full working: rank sums, the U statistic, and the p-value, step by step. No sign-up.
- [Margin of Error Calculator](https://www.restatica.com/calculators/margin-of-error-calculator): Free margin of error calculator for means and proportions: the critical value, the standard error, and the half-width, with the sample-size trade-off shown.
- [Mean Absolute Deviation Calculator](https://www.restatica.com/calculators/mean-absolute-deviation-calculator): Free mean absolute deviation calculator showing each distance from the mean, the absolute values and the average, in the data's own units.
- [Mean Calculator](https://www.restatica.com/calculators/mean-calculator): Free mean calculator that shows the working: the sum, the count, and the division, step by step. Includes when the mean misleads and what to use instead.
- [Mean, Median and Mode Calculator](https://www.restatica.com/calculators/mean-median-mode-calculator): Free calculator for the mean, median and mode together, each fully worked, plus what the gap between them tells you about skew.
- [Median Calculator](https://www.restatica.com/calculators/median-calculator): Free median calculator that sorts the data and shows the position rule for odd and even counts, plus when the median beats the mean.
- [Midrange Calculator](https://www.restatica.com/calculators/midrange-calculator): Free midrange calculator showing the maximum, the minimum and their midpoint, with a note on when this measure of center misleads.
- [Mode Calculator](https://www.restatica.com/calculators/mode-calculator): Free mode calculator that counts every value and shows the frequencies, handling no mode, one mode, and multimodal data.
- [Multiple Regression Calculator](https://www.restatica.com/calculators/multiple-regression-calculator): Multiple linear regression calculator that estimates each predictor's coefficient, R-squared, and p-values, showing the full working step by step. No sign-up.
- [Normal Distribution Calculator](https://www.restatica.com/calculators/normal-distribution-calculator): Normal distribution calculator for z-scores and probabilities from any mean mu and SD sigma, with the standardization and area worked out step by step. No sign-up.
- [Odds Ratio & Relative Risk Calculator](https://www.restatica.com/calculators/odds-ratio-relative-risk-calculator): Free odds ratio and relative risk calculator for a 2×2 table: both measures with confidence intervals, and which one your study design actually allows.
- [Odds Ratio Confidence Interval Calculator](https://www.restatica.com/calculators/odds-ratio-confidence-interval-calculator): Free confidence interval calculator for an odds ratio and a relative risk. Standard error on the log scale, both bounds exponentiated back, every step derived.
- [One-Proportion Z-Test Calculator](https://www.restatica.com/calculators/one-proportion-z-test-calculator): Free one-proportion z-test calculator that compares a sample proportion to a hypothesized value and shows the z score, critical value, and p-value step by step. No sign-up.
- [One-Sample t-Test Calculator](https://www.restatica.com/calculators/one-sample-t-test-calculator): One-sample t-test calculator that checks whether a sample mean differs from a hypothesized value and shows every step: t, df, and p-value in full. No sign-up.
- [One-Sample Z-Test Calculator](https://www.restatica.com/calculators/one-sample-z-test-calculator): Free one-sample z-test calculator that compares your sample mean to a hypothesized value using a known population standard deviation and shows every step. No sign-up.
- [One-Way ANOVA Calculator](https://www.restatica.com/calculators/one-way-anova-calculator): Free one-way ANOVA calculator that shows the full working: sums of squares, F-statistic, p-value and a plain-English conclusion. Compare 3+ group means and check assumptions. No sign-up.
- [Outlier Calculator](https://www.restatica.com/calculators/outlier-calculator): Free outlier calculator applying both the 1.5 IQR rule and the three-sigma rule, showing every boundary and which values each one flags.
- [Paired t-Test Calculator](https://www.restatica.com/calculators/paired-t-test-calculator): Paired (dependent-samples) t-test calculator for matched or before-after data that shows every step: the mean difference, t, df, and p-value. No sign-up.
- [Pearson Correlation Calculator](https://www.restatica.com/calculators/pearson-correlation-calculator): Pearson correlation calculator that computes r, r-squared, and the p-value for two continuous variables, showing the full working step by step. No sign-up.
- [Percentile Calculator](https://www.restatica.com/calculators/percentile-calculator): Free percentile calculator that sorts the data, computes the position for any percentile and interpolates the value, with each step shown.
- [Permutation Calculator](https://www.restatica.com/calculators/permutation-calculator): Free permutation calculator (nPr) for ordered arrangements: the factorial setup, the cancellation, and the count, plus when a combination fits better.
- [Poisson Distribution Calculator](https://www.restatica.com/calculators/poisson-distribution-calculator): Poisson distribution calculator for the probability of k events given a mean rate lambda, with the formula worked out step by step: exact, cumulative, and tail. No sign-up.
- [Prediction Interval Calculator](https://www.restatica.com/calculators/prediction-interval-calculator): Free prediction interval calculator for linear regression. Standard error of estimate, margin of error and both bounds, each derived in full. No sign-up.
- [Probability Calculator](https://www.restatica.com/calculators/probability-calculator): Free single-event probability calculator: enter the outcomes that count and the total possible, and see the result as a fraction, decimal, and percentage.
- [Quartile Calculator](https://www.restatica.com/calculators/quartile-calculator): Free quartile calculator that sorts the data, locates each quartile position and shows the interpolation, giving Q1, the median and Q3.
- [Range Calculator](https://www.restatica.com/calculators/range-calculator): Free range calculator that identifies the highest and lowest values and shows the subtraction, with the extreme values listed alongside.
- [Repeated Measures ANOVA Calculator](https://www.restatica.com/calculators/repeated-measures-anova-calculator): Repeated measures ANOVA calculator for the same subjects measured multiple times. Shows the full working: sums of squares, F, sphericity, and p-values. No sign-up.
- [Sample Size Calculator for a Proportion](https://www.restatica.com/calculators/sample-size-proportion-calculator): Free sample size calculator for a proportion: set your margin of error and confidence level, then see the full working and why p = 0.5 is the safe default.
- [Shapiro-Wilk Test Calculator](https://www.restatica.com/calculators/shapiro-wilk-test-calculator): Shapiro-Wilk test calculator that checks whether your data is normally distributed and shows the full working: W statistic, p-value, and decision. No sign-up.
- [Skewness Calculator](https://www.restatica.com/calculators/skewness-calculator): Free skewness calculator showing the cubed deviations, the standardisation and the result, with what the sign and size actually mean.
- [Spearman Correlation Calculator](https://www.restatica.com/calculators/spearman-correlation-calculator): Spearman rank correlation calculator that computes rho and its p-value for ordinal or non-normal data, showing every ranking and step. No sign-up.
- [Standard Deviation Calculator](https://www.restatica.com/calculators/standard-deviation-calculator): Free standard deviation calculator showing every step: deviations, squares, the sum, and the n or n-1 divisor. Explains which one you need and why.
- [t-Distribution Calculator](https://www.restatica.com/calculators/t-distribution-calculator): Free t-distribution calculator for critical values and tail areas at any degrees of freedom, with every step shown and the gap from the normal made explicit.
- [Trimmed Mean Calculator](https://www.restatica.com/calculators/trimmed-mean-calculator): Free trimmed mean calculator that sorts the data, drops a set percentage from each end, and averages the rest, with every step shown.
- [Tukey HSD Calculator](https://www.restatica.com/calculators/tukey-hsd-calculator): Tukey HSD calculator for post-hoc pairwise comparisons after a significant ANOVA. Shows the HSD critical difference and every adjusted p-value, in full.
- [Two-Proportion Z-Test Calculator](https://www.restatica.com/calculators/two-proportion-z-test-calculator): Free two-proportion z-test calculator that compares two independent proportions or conversion rates and shows the pooled proportion, z score, and p-value. No sign-up.
- [Two-Sample t-Test Calculator](https://www.restatica.com/calculators/two-sample-t-test-calculator): Independent two-sample t-test calculator that compares the means of two separate groups and shows the full working: pooled variance, t, df, and p-value. No sign-up.
- [Two-Sample Z-Test Calculator](https://www.restatica.com/calculators/two-sample-z-test-calculator): Free two-sample z-test calculator that compares two independent means with known variances or large samples and shows the full working step by step. No sign-up.
- [Two-Way ANOVA Calculator](https://www.restatica.com/calculators/two-way-anova-calculator): Two-way ANOVA calculator with replication: test two factors and their interaction on one outcome. Shows the full working: every sum of squares, F, and p-value. No sign-up.
- [Two-Way ANOVA Without Replication Calculator](https://www.restatica.com/calculators/two-way-anova-without-replication-calculator): Two-way ANOVA without replication: one observation per cell, as in a randomized block design. Shows every sum of squares, F-ratio and p-value in full. No sign-up.
- [Variance Calculator](https://www.restatica.com/calculators/variance-calculator): Free variance calculator showing the deviations, the squares, the sum and the divisor. Covers sample versus population and why the units are squared.
- [Weighted Mean Calculator](https://www.restatica.com/calculators/weighted-mean-calculator): Free weighted mean calculator showing each value times its weight, the total, and the division by total weight. For grades, portfolios and survey data.
- [Welch's t-Test Calculator](https://www.restatica.com/calculators/welchs-t-test-calculator): Welch's t-test calculator compares two group means without assuming equal variances and shows the full working: t, the adjusted df, and p-value. No sign-up.
- [Wilcoxon Signed-Rank Test Calculator](https://www.restatica.com/calculators/wilcoxon-signed-rank-test-calculator): Free Wilcoxon signed-rank test calculator for paired data that shows the full working: signed ranks, the W statistic, and the p-value, step by step. No sign-up.
- [Z-Score Calculator](https://www.restatica.com/calculators/z-score-calculator): Free z-score calculator that turns a raw value into standard deviations from the mean: the standardizing step, the tail area, and the percentile, all shown.
- [Every other calculator](https://www.restatica.com/calculators): 263 in all, grouped by topic.

## Saga stories

- [One-Sample Z-Test](https://www.restatica.com/saga#one-sample-z-test): Lucky Shot?; Has the Virus Changed?; S-Rank?; Are They Coming?; Can We Live There?; Is the Casino Cheating?
- [Two-Sample Z-Test](https://www.restatica.com/saga#two-sample-z-test): Is Someone Tunnelling Into the Vault?; Are These Her Footprints?; Is Something Alive in the Ice?; Is Crown Class Really Stronger?; Did Something Land Here?; Is the Powder Sabotaged?
- [One-Sample t-Test](https://www.restatica.com/saga#one-sample-t-test): Is She a Vampire?; Waking or Dying?; Is the Kraken Back?; Has She Lost Her Power?; Is the Machine Drifting?; Is the Potion a Fake?
- [Independent Two-Sample t-Test](https://www.restatica.com/saga#independent-two-sample-t-test): Is the Mint Master a Thief?; Whose Ship Is Faster?; Is the Saucer Shield Stronger?; Has the Old Fuel Gone Weak?; Which Wood Will Float Them Off?; Are Blood-Moon Children Stronger?
- [Paired t-Test](https://www.restatica.com/saga#paired-t-test): Is the Kaiju Growing?; Whose Map Finds the Gold?; Too Thin to Breathe?; Is He Using an Aimbot?; Faster After Dark?; Does the Armour Slow Her Down?
- [Welch’s t-Test](https://www.restatica.com/saga#welch-s-t-test): Is It Answering Us?; Is the Champion’s Sword Cursed?; Is Someone Hiding in the Machine?; Can the Witch Sell a Wind?; Is the Host Choosing Who Lives?; Has the Rookie Stolen the Crowd?
- [One-Proportion Z-Test](https://www.restatica.com/saga#one-proportion-z-test): Is She Stuck in a Loop?; Is the Gate Still Safe?; Is the Oracle Right Nine Times in Ten?; Is the Lightning Serve Real?; Is the Masked Fighter the Lost Master?; Are the Enemy Ships Ironclad?
- [Two-Proportion Z-Test](https://www.restatica.com/saga#two-proportion-z-test): Is There a Spy in the Hall?; Does Fire Draw Them In?; Do the Sacred Chickens Know?; Is the Pharaoh’s Curse Real?; Which Draught Breaks the Stone?; Does Meeting Yourself Break the Jump Home?
- [Variance Ratio Test](https://www.restatica.com/saga#variance-ratio-test): Is the Dungeon Shifting?; Is the Champion a Machine?; Did She Write Her Own Farewell?; Too Sick for the Summit?; Is the New Barrel Really Tighter?; Alien Hull or Army Secret?
- [Two-Variance F-Test](https://www.restatica.com/saga#two-variance-f-test): Can He See the Meteor Coming?; Who Flies the Rescue?; Gamble on the Sea Ice?; Is the Golden Rifle Really Steadier?; Is the Lost Masterpiece a Fake?; Is Cinder Losing Control?
- [One-Way ANOVA](https://www.restatica.com/saga#one-way-anova): Did the Pirate King Split His Gold Fairly?; Is Any Landing Site More Radioactive?; Who Is the Alien Signal Meant For?; Do Griffin Feathers Fly Farther?; Is the Hero Licence Exam Rigged?; Which Fire Will the Plane See?
- [Two-Way ANOVA with Replication](https://www.restatica.com/saga#two-way-anova-with-replication): Who Fights Which Twin?; Copper or Canvas?; Is the Closing Slot Cursed?; Does the Serum Buy Time?; Did the Candle Lie?; Is the Stranger Hypnotising Her?
- [Two-Way ANOVA Without Replication](https://www.restatica.com/saga#two-way-anova-without-replication): Did a Judge Rob the Final?; Will the Warlord’s Blade Fail Him?; Is the Host Lying About the Doors?; Will the New Mattock Save the Legion?; Who Opens the Vault?; Is the New Speed Gun Lying?
- [Two-Way ANOVA (Unbalanced)](https://www.restatica.com/saga#two-way-anova-unbalanced): Throw the Gold Overboard?; Is It the Water or the Hour?; Is It the Clan or the Cloth?; Are the New Suits Failing?; Is Sea Fire Worth the Silver?; Is the Rooftop Run Faster?
- [Two-Way Random Effects ANOVA](https://www.restatica.com/saga#two-way-random-effects-anova): Is the Gate Harder, or the Party Slower?; Who Is Tearing the Present?; Is the Scrap Failing, or the Builders?; Who Is Brewing Weak Cures?; Is the Gold in the Wrecks, or the Divers?; Are the Suits Failing?
- [Two-Way Mixed-Model ANOVA](https://www.restatica.com/saga#two-way-mixed-model-anova): Which Fuel Can Stop the Asteroid?; Does She Drain the Kids Beside Her?; Is the Moat Clip Faster for Everyone?; Does Phoenix Oil Keep the Lamps Lit?; Which Song Keeps the Dragon Asleep?; Which Dish Hears the Aliens Best?
- [Repeated-Measures ANOVA](https://www.restatica.com/saga#repeated-measures-anova): Is Friendship Power Real?; Are They Counting Cards?; Are the Boosters Wearing Out?; Is the Hum Slowing Our Gunners?; Is the Sun Really Fading?; Will the Tower Break Their Shields?
- [Two-Way Repeated-Measures ANOVA](https://www.restatica.com/saga#two-way-repeated-measures-anova): Will Plasma Save the Mine?; Do Bells Wake the Kraken?; Which Lure Pulls the Horde?; Does the Owl-Eye Tincture Work?; Which Plan Wins the World Final?; Does His Beacon Call Them Down?
- [Analysis of Covariance (ANCOVA)](https://www.restatica.com/saga#analysis-of-covariance-ancova): Can the Serum Slow Them?; Is a Whole Team Cheating?; Is the Warm Bay Breeding Giants?; Whose Longship Is Fastest?; Which Town Hides the Forger?; Is the Crater Draining Heroes?
- [Mann-Whitney U Test](https://www.restatica.com/saga#mann-whitney-u-test): Is the Black Hole Feeding?; Is the Summoning Worth It?; Which School Goes to the Games?; Can the Machine Catch a Traitor?; Can the Floor Be Silenced?; Did a Time Traveller Arrive?
- [Kruskal-Wallis H Test](https://www.restatica.com/saga#kruskal-wallis-h-test): Can a Song Calm a Dragon?; Did Foxglove Kill the Duke?; Do the Walkers Chase Music?; Do the Judges Favour Flashy Powers?; Which Path Lights the Beacon in Time?; Which Draw Will the Army Learn?
- [Sign Test](https://www.restatica.com/saga#sign-test): Which Way Out?; Can a Mortal Outweave a Goddess?; Is the Edit Sinking Them?; Is the Final Map Fair?; Is the New Count Hunting?; Can They Still Shoot at Dawn?
- [Friedman Test](https://www.restatica.com/saga#friedman-test): Is One Heir Really Stronger?; Is the Croupier in on It?; Did Someone Steer It Here?; Which Lure Will Save the Gate?; Did the Harvest Model Get It Wrong?; Is the Thunder Mask Worth It?
- [Quade Test](https://www.restatica.com/saga#quade-test): Which Suit Survives the Slingshot?; Do Neck Bites Turn Faster?; Will Titan Meal Grow Our Guardians?; Whose Dogs Make the Pole Dash?; Did We Just Tell Them Where We Live?; Is the Water Scale Lying?
- [Wilcoxon Signed-Rank Test](https://www.restatica.com/saga#wilcoxon-signed-rank-test): Did the Lights Steal Time?; Does the House Remember?; Can the Archers Still Hold the Walls?; Is the Quartermaster Stealing Gold?; Do the Runes Bless the Blade, or Break It?; Can Their Bones Survive the Trip Home?
- [Runs Test](https://www.restatica.com/saga#runs-test): Is Something Hiding Near the Black Hole?; Does Her Power Come in Waves?; Was the Masterpiece Drawn Blind?; Can He Run the Laser Gap?; Does He Switch the Aimbot On?; Is the Enemy Slipping Away?
- [Mood’s Median Test](https://www.restatica.com/saga#mood-s-median-test): Which Team Gets the City?; Is Hangman Reef Paved with Silver?; Does the Truth Machine Read the Asker?; Which Drill Do We Keep?; Has the Sea Turned?; Are the Fireballs Growing?
- [Ansari-Bradley Test](https://www.restatica.com/saga#ansari-bradley-test): Has the New Engine Gone Wild?; Is Dragon Grain Worth a Fortune?; Did the Witnesses Rehearse?; Is the Real Marksman Still Free?; Who Paces Out the Gold?; Is a Time Rift Opening?
- [Jonckheere-Terpstra Test](https://www.restatica.com/saga#jonckheere-terpstra-test): Is the Demon Lord Waking?; Do Nine Bulls Bring the Rain?; Are the Drones Learning?; Does the Sea Follow the Message?; Is the Horde Closing In?; Is the Champion Slowing Down?
- [Two-Sample Kolmogorov-Smirnov Test](https://www.restatica.com/saga#two-sample-kolmogorov-smirnov-test): Did the Repair Break the Time Machine?; Has a Second Clan Joined the Raids?; Was the Studio Jury Planted?; Does the Black Hall Steal Time?; Does the Apprentice Have the Master’s Secret?; Was the Rookie Lip-Syncing?
- [Kendall’s W](https://www.restatica.com/saga#kendall-s-w): Can the Hunters Sense the Lair?; Who Left the Ballroom Last?; Where Will the Riders Cross?; Does Anyone Know Which Fruit Is Safe?; Is the Seeding a Sham?; Is Talent Really Obvious?
- [Page’s Trend Test](https://www.restatica.com/saga#page-s-trend-test): Is the Seal Breaking?; Do They Really Get Faster?; Are the Walls Closing In?; Do the Knocks Build to Midnight?; Are the Sentries Fading?; Is the Hermit’s Training Real?

## Learn journeys

- [Collecting Data](https://www.restatica.com/learn#collecting-data): Where data comes from: asking a clear question, choosing what to measure, and sampling without bias.
- [Cause and Effect](https://www.restatica.com/learn#cause-and-effect): When a study can show that one thing causes another, and when it can only show they move together.
- [Graphs and Tables](https://www.restatica.com/learn#graphs-and-tables): Turn raw numbers into tables and graphs, and read the shape they show.
- [Averages and Spread](https://www.restatica.com/learn#averages-and-spread): Sum up a dataset with one typical value and one number for how far the values spread.
- [Measures of Position](https://www.restatica.com/learn#measures-of-position): Percentiles, quartiles and z-scores say where one value sits; fences and tests spot the ones that do not belong.
- [Probability](https://www.restatica.com/learn#probability): The rules of chance: what a probability means, and how to combine and update one.
- [Permutations and Combinations](https://www.restatica.com/learn#permutations-and-combinations): Count arrangements and selections without listing every one.
- [Discrete Distributions](https://www.restatica.com/learn#discrete-distributions): Random quantities you can count, and the patterns their chances follow.
- [Continuous Distributions](https://www.restatica.com/learn#continuous-distributions): Measurements that can take any value, and the curves that describe them.
- [Sampling Distributions](https://www.restatica.com/learn#sampling-distributions): Why a statistic changes from sample to sample, and how predictably it does so.
- [Confidence Intervals](https://www.restatica.com/learn#confidence-intervals): Turn one sample into a range of plausible values for the truth.
- [Hypothesis Testing](https://www.restatica.com/learn#hypothesis-testing): Decide whether data give real evidence against a default assumption.
- [Comparing Two Groups](https://www.restatica.com/learn#comparing-two-groups): Test whether two groups really differ, for separate groups and for paired data.
- [Comparing Many Groups](https://www.restatica.com/learn#comparing-many-groups): Compare three or more group means at once with ANOVA, then find which ones differ.
- [Nonparametric Tests](https://www.restatica.com/learn#nonparametric-tests): Tests that work on ranks, for data the normal curve does not fit.
- [Categorical Data](https://www.restatica.com/learn#categorical-data): Counts in categories: goodness of fit, two-way tables and measures of risk.
- [Correlation and Regression](https://www.restatica.com/learn#correlation-and-regression): Measure how two variables move together, and fit the line that predicts one from the other.
- [Interpreting Results](https://www.restatica.com/learn#interpreting-results): What a result really says: how big it is, how sure we can be, and how to report it.
- [Maths Basics](https://www.restatica.com/learn#maths-basics): Percentages, formulas, logs, lines and matrices: the maths every lesson leans on.
- [Checking Assumptions](https://www.restatica.com/learn#checking-assumptions): Check the conditions a method relies on, and what to do when they fail.
- [Multiple Regression](https://www.restatica.com/learn#multiple-regression): Predict one outcome from several variables at once, and check the model holds up.
- [Nonlinear and Robust Regression](https://www.restatica.com/learn#nonlinear-and-robust-regression): Fit curved relationships, and fits that outliers do not throw off.
- [Logistic and Poisson Regression](https://www.restatica.com/learn#logistic-and-poisson-regression): Regression for outcomes that are not measurements: yes or no answers, categories and counts.
- [Machine Learning](https://www.restatica.com/learn#machine-learning): Models that learn patterns from data and predict new cases well.
- [Designing Experiments](https://www.restatica.com/learn#designing-experiments): Plan an experiment so its results can answer the question you care about.
- [Factorial Experiments](https://www.restatica.com/learn#factorial-experiments): Experiments that test many factors at once to improve a product or process.
- [Time Series](https://www.restatica.com/learn#time-series): Data recorded in time order: trends, seasons, forecasts and memory.
- [Survival Analysis](https://www.restatica.com/learn#survival-analysis): How long until something happens, from patient survival to product failure.
- [Epidemiology and Clinical Trials](https://www.restatica.com/learn#epidemiology-and-clinical-trials): Statistics for studying disease and for testing treatments in clinical trials.
- [Reliability and Diagnostic Tests](https://www.restatica.com/learn#reliability-and-diagnostic-tests): Whether a measurement is consistent, whether raters agree, and how good a diagnostic test is.
- [Quality Control](https://www.restatica.com/learn#quality-control): Watch a process with control charts and judge whether it meets its specifications.
- [Multivariate Analysis](https://www.restatica.com/learn#multivariate-analysis): Many variables together: compare groups, reduce dimensions and find clusters.
- [Survey Sampling](https://www.restatica.com/learn#survey-sampling): Sample real populations efficiently and estimate their totals and averages.
- [Mathematical Statistics](https://www.restatica.com/learn#mathematical-statistics): The theory behind the methods: where estimators and tests come from and why they work.
- [Statistics for Finance](https://www.restatica.com/learn#statistics-for-finance): Measure risk and return in investments.

## Practice decks

- [Hypothesis Testing](https://www.restatica.com/practice#hypothesis-testing): 148 problems. Topics: Nonparametric Tests, T-Tests, Compare Proportions, Z-Tests, ANOVA, Goodness-of-Fit, Post-Hoc Tests, Compare Variances.
- [Confidence Intervals](https://www.restatica.com/practice#confidence-intervals): 63 problems. Topics: Means, Proportions, Resampling, Variability.
- [Categorical Data Analysis](https://www.restatica.com/practice#categorical-data-analysis): 44 problems. Topics: Association Tests, Risk.
- [Descriptive Statistics](https://www.restatica.com/practice#descriptive-statistics): 106 problems. Topics: Dispersion, Central Tendency, Position & Standing, Outlier Detection, Shape & Spread Rules, All Measures, Frequency Tables.
- [Probability & Distributions](https://www.restatica.com/practice#probability-distributions): 143 problems. Topics: Distributions, Probability Theory, Estimation & Simulation, Combinatorics.
- [Regression & Multivariate](https://www.restatica.com/practice#regression-multivariate): 108 problems. Topics: Linear Models, Correlation, Generalized Models, Diagnostics, Multivariate, Nonlinear Models, Penalized Models.
- [Time Series & Survival](https://www.restatica.com/practice#time-series-survival): 47 problems. Topics: Time Series, Survival Analysis.
- [Study Design & Power](https://www.restatica.com/practice#study-design-power): 45 problems. Topics: Sample Size, Design of Experiments.
- [Reliability & Quality](https://www.restatica.com/practice#reliability-quality): 66 problems. Topics: Quality Control, Agreement, Diagnostic Testing, Internal Consistency.
- [Applied Statistics](https://www.restatica.com/practice#applied-statistics): 37 problems. Topics: Financial.

## Optional

- [About](https://www.restatica.com/about): who builds Re.Statica and why.
- [Founder's view](https://www.restatica.com/founders-view): the thinking behind the platform.
- [Blog](https://www.restatica.com/blog): articles on statistics and the product.
- [Full index for AI assistants](https://www.restatica.com/llms-full.txt): this file plus every calculator, story and lesson.