Stats Without Walls User Guide

Stats Without Walls is a free statistical tool for all levels. It runs entirely in your browser: nothing you load is uploaded anywhere, there is no account, and it never costs anything. This guide explains every menu, what each option does, and how to read what comes back.

1. Start here

Three ways to run it

1. Web. Open learnwithoutwalls.com/stats in any modern browser (Chrome, Edge, Safari, Firefox). This version always has the newest features.
2. Install from the browser. In Chrome or Edge, click the install icon in the address bar (or Chrome menu, then "Install Stats Without Walls"). It opens in its own window and works offline after the first visit.
3. Desktop app. For now the browser version is the better choice: the app is updated almost daily and the desktop app cannot update itself yet (a self-updating version is coming). If you need it, download the Mac or Windows installer from the download page. Mac: pick Apple Silicon (M1 to M4) or Intel. The first time you open it on a Mac, right-click the app and choose Open, because it is not signed with an Apple developer certificate. If your Mac says the app is damaged and offers no Open Anyway button, see Troubleshooting for the one-line fix. The desktop app (version 1.3.0, October 1, 2026) is older than this guide: it does not have the empty start, the separate distrACTION and Learn pages, the new event choices or the phone and keyboard improvements described here, so use the browser version for class.

Privacy

Your data stays on your computer. The app has no server. It opens with an empty table unless your browser remembers data of your own. Your browser (local storage) remembers, on the same device:

• Your own data, with its filter and the types you set by hand: a file you opened; data you pasted, typed or simulated; a table you made with Stack columns or Random sample of rows; and a sample dataset once you change it (a computed, recoded, z-score or binned column, an edited cell, a renamed or deleted column, or a type set by hand; a filter or a sort alone does not count). The bar above the table then says "remembered from your last visit".
• Two settings: the decimal places you chose and the panel width you dragged.

Not remembered: a sample dataset you only opened or sorted (open it again from Data, Sample datasets), results, and the distrACTION inputs. Clearing your browser data removes what is stored. To keep a permanent copy, use Results, Save session or Data, Download data as CSV.

A two-minute first run

1. Data, Sample datasets, pick "Our class data (40 students)", click Open.
2. Exploration, Descriptives, select GPA, click Run. A card appears in the Analyses tab.
3. Graph, Histogram, choose Hours_Sleep, click Run. The graph appears in the Graphs tab.
4. T-Tests, Independent Samples T-Test, dependent variable Hours_Sleep, grouping variable Pet_Owner (Yes or No), click Run. Read the blue interpretation box near the bottom of the card.

2. The screen

Variable types

The app guesses a type for each column when data loads. The type decides which menus can use the column.

If a guess is wrong (a numeric code that is really a category, or a numeric column that was read as text because one cell contains a word), click the type under the column name and pick Continuous, Ordinal, Nominal or ID, the same job as a data setup panel in other tools. A type you set by hand stays set, even after you edit cells. Data, Set variable type does the same thing from the menu.

3. Getting data in

Open CSV file

Data, Open CSV file. Any comma-separated file with one row of column names at the top. Exports from Excel, Google Sheets, Canvas, Qualtrics and survey tools all work. Quoted text with commas inside is handled. Dates stay as text.

Paste data

Data, Paste data. Copy a block from a spreadsheet (including the header row), paste it in, give it a name. Tabs and commas both work.

Sample datasets

Data, Sample datasets. Real and course datasets that ship with the app, listed in section 13. They also work offline in the installed app. A sample dataset is not remembered for your next visit until you change it (see Privacy).

New data table

Data, New data table. Type column names separated by commas and how many rows you want. Then click cells to type values. Good for a small in-class exercise.

Editing cells

Click any cell, type, then click away or press Tab. Enter moves down a row, the arrow keys move between cells, and Escape puts back the value the cell had. Types are re-guessed after each edit. Column names can be changed with Data, Rename or delete column.

Download data as CSV

Saves the current table (including computed, recoded and z-score columns) as a CSV file you can open in Excel or load again later.

4. Preparing data

Filters

Data, Filters, or the filter box above the table. Write a condition using column names exactly as written. Rows that fail the condition are greyed out and left out of every analysis and graph until the filter is cleared. Join conditions with and and or in any spelling (AND, &&, &, OR, ||, |), the habits of Python, R and spreadsheets; a single = is read as ==. A condition that cannot be read is explained under the box (in the dialog, under its field), and all rows stay in use until it is fixed.

Year == "Freshman"
Commute_Minutes < 30
Year == "Senior" and GPA >= 3.5
Major == "Biology" or Major == "Nursing"
Year == "Freshman" && GPA > 3
Employed != "Full-time"

Operators: == equal, != not equal, < <= > >=, AND, OR. Text values go in quotes. A single = is accepted as equal.

Compute a new variable

Data, Compute. Name the new column and write a formula using existing columns.

Hours_Study * 7                       weekly hours
Commute_Minutes / 60                  minutes to hours
(GPA - mean(GPA)) / sd(GPA)           z-score by hand
log(Income)                            natural log
round(Age / 10) * 10                  decade
Hours_Sleep >= 7                       gives true or false

Functions: log (natural), log10, sqrt, abs, exp, round, floor, ceil, pow(x, k). Whole-column summaries: mean(X), sd(X), median(X), min(X), max(X), sum(X), n(X). A row with a missing value in any column used gets a blank.

Transform (recode)

Data, Transform. Turn values into new values, one rule per line, as old = new. Numeric ranges are written 0 to 29 = short. "Everything else becomes" catches what the rules miss; leave it blank to keep the original value.

Full-time = Employed
Part-time = Employed
Not employed = Not employed

0 to 29 = short
30 to 59 = medium
60 to 300 = long

Add z-score column

Data, Add z-score column. Adds z_Variable with (x minus mean) divided by the sample SD, the same as the by-hand formula.

Bin into classes

Data, Bin into classes. Turns a numeric variable into classes of a width you choose ("60 to under 70"), starting where you say. Each class includes its left end. The new column is categorical, kept in numeric order, ready for a frequency table or bar plot.

Stack columns

Data, Stack columns. When each group sits in its own column, stacking makes one column of values and one column naming where each value came from, the layout two-sample tests, ANOVA and side-by-side graphs need. It makes a new data table (your own, so it is remembered), so download the old one first if you need it.

Simulate random data

Data, Simulate random data. Random values from a normal, uniform, discrete uniform, binomial, Poisson, exponential or yes or no distribution, any number of rows and columns (one column per sample). If the row count matches the open table the columns are added to it; otherwise a new table is made. A seed repeats the same numbers, so a whole class can work with identical data.

Random sample of rows

Data, Random sample of rows. A simple random sample from the open table, with or without replacement, with an optional seed. Uses only the rows kept by a filter. The sample becomes a new data table (your own, so it is remembered) in place of the old one.

Sorting

Click a column name: smallest first (or A to Z), again for the reverse, and a third time for the order the rows had before any sorting. Sorting changes the row order for Time Series and for the display; analyses do not depend on it.

5. Reading a result card

Every analysis produces a card with the same layout, top to bottom:

1. Title and a grey line naming the dataset, the variables and n. Three buttons: edit (reopens the same dialog with your choices filled in; change anything and Run, and the new result replaces this card in place, the StatCrunch habit), copy text (copies the card's words and tables as plain text for a report, without its buttons and graphs; the button then says Copied) and remove. Under every table, copy as CSV (for a spreadsheet) and copy as Markdown (for a report or a slide); under every graph, download PNG, so a result goes into a document without a screenshot.
2. Tables, named the way the course instructions name them (Descriptives, Independent Samples T-Test, Model Fit Measures, Contingency Tables, and so on), so the instructions transfer as written.
3. Formula box (grey, monospace): the formula that produced the statistic, with the symbols the course uses: mu and x bar for means, sigma and s for standard deviations, p and p hat for proportions. Under it, Show the numbers in the formula opens the same formula with the actual values in it, worked through to the statistic, the interval and the effect size (t-tests, z-tests, ANOVA, regression, chi-square): the step between the formula and the answer. Then Report it as (APA style), one line such as t(37.98) = −0.15, p = .878, d = −0.05, to paste into a write-up.
4. Blue box: the decision and a written conclusion in plain English, including the p-value compared with alpha.
5. Green or pink box: a condition check. Green means the condition for the method is met (for example n at least 30, or at least 10 successes and 10 failures). Pink means it is not, and says what to do instead.
6. Graphs attached to the analysis (descriptives plots, residual plots), below the text.

Decimals. Numbers are shown to the number of decimals set under Results, Decimal places shown (4 by default). Internally everything is full precision.

6. Which analysis do I need

Which test? (the button next to the filter box, or the first item of the T-Tests menu) asks three questions: what you measured (a number, a yes or no, or a category), what the question is (one group against a value, two groups, three or more, or a relationship), and for two groups whether they are the same people measured twice. It names the test as you answer and opens its dialog. With no data loaded it leaves a note naming the test instead. The table below is the same decision written out.

7. Menu by menu

Exploration

Descriptives

Pick one or more variables; optionally split by a group. Tick the statistics you want: N, missing, mean, median, mode (all modes are listed when there is a tie), sum, standard deviation (sample, n minus 1), variance, population SD, range, minimum, maximum, standard error, IQR, quartiles, fences for outliers, skewness, kurtosis, coefficient of variation, and any other percentiles you list (such as 10, 90). Tick plots: histogram, density, boxplot, dotplot, QQ plot, bar plot for categorical variables. Frequency tables appear for nominal and ordinal variables, with counts, relative frequency, percent, cumulative frequency, cumulative relative frequency and cumulative percent. Classes named by numbers ("60 to under 70") are listed in numeric order.

Quartile method. "Textbook halves" (default) finds Q1 and Q3 as the medians of the lower and upper halves with the overall median excluded, which is what the course teaches by hand. "Type 7" is what R and Excel use by default; the two can differ for small n. Boxplots use the same rule as the descriptives.

Scatterplot

Quick scatterplot with an optional group colour and regression line; the Graph menu version has more options.

Graph

All graphs land in the Graphs tab. Every graph follows the honest-graph rules, and says so under the picture. Every graph dialog has an Appearance section (title, axis labels, color), and the edit button on the card reopens it with your choices filled in. A group (Group by, or Color by on the scatter plot) is a categorical column. A numeric column with 10 or fewer different values works too: each value is a group, in numeric order. With more values, or with an ID column, a message under the box asks for a categorical grouping variable instead; Data, Bin into classes turns a numeric column into classes you can group by. The same holds for Split by in Descriptives.

T-Tests

The One Sample and Independent Samples t-test dialogs (and both Z-Tests) have a Data switch: from the data table, or "from summary statistics" (type the mean, SD and N from a textbook problem). With no data loaded they open in summary mode. If a summary box is empty, a message says what to type, and no card is made. The Paired Samples T-Test works from two columns of data. Options: mean difference with confidence interval, effect size (Cohen's d), descriptives, descriptives plots.

One Sample T-Test

Tests whether the population mean equals a test value. Reports t, df, p, mean difference, the confidence interval, and the condition check (n at least 30, or a normal-looking QQ plot when n is smaller). The formula box shows t = (x bar minus mu0) / (s / sqrt(n)).

Independent Samples T-Test

Compares two group means. Welch's version (no equal-variance assumption) is the default; untick it for Student's. Hypothesis can be two-sided, group 1 greater, or group 1 less. If the grouping variable has more than two levels, name the two you want, for example Full-time, Not employed; left blank, the first two levels are compared and the card says so. Summary-statistics mode takes mean, SD and N for each group (each SD above 0, each N at least 2).

One Sample Z-Test and Two Sample Z-Test

Only for problems that give the population standard deviation sigma. You type sigma (one, or one per group); the card gives z, the p-value, and the interval x bar plus or minus z* sigma / sqrt(n). If only the sample SD s is known, use the t-test: the card says so.

Paired Samples T-Test

Two columns measured on the same subjects (before and after). The test is a one-sample t on the differences; tick "Histogram of differences" to see them.

ANOVA

One-Way ANOVA

Three or more group means. Fisher's (equal variances) and Welch's F are both available; the homogeneity check compares the largest SD with the smallest (ratio under 2 passes), and Levene's test (deviations from the median, the Brown-Forsythe version) is available as a formal check. Tukey post-hoc tests tell which pairs differ, with adjusted p-values. Descriptives table and plot (means with confidence intervals) are optional.

Two-Way ANOVA

Two factors, with or without their interaction (Type II sums of squares, as R's car::Anova). Main effects, interaction, cell means table and interaction plot: non-parallel lines in the plot are the interaction.

ANCOVA

One factor plus one or more numeric covariates. The ANCOVA table (Type II) tests the factor after the covariates and each covariate after the factor, with partial eta squared; the adjusted means are each group's predicted value at the covariate mean, with standard errors, so the groups are compared as if they had the same covariate value; Holm-adjusted pairwise comparisons of the adjusted means; the homogeneity-of-slopes check (the group by covariate interaction) says whether one adjustment serves every group; and a scatterplot with the parallel fitted lines.

Repeated Measures and Mixed ANOVA

Wide data, one column per condition, with an optional between-subjects factor. Mauchly's sphericity test, Greenhouse-Geisser and Huynh-Feldt corrections, Holm-adjusted pairwise paired t-tests, the ICC and a profile plot.

MANOVA

One factor, two or more outcomes tested at once. Pillai's trace, Wilks' lambda, the Hotelling-Lawley trace and Roy's largest root, each with its F approximation (as R's summary.manova), the group means, a follow-up one-way ANOVA on each outcome with a Bonferroni line, and a profile plot of the standardized group means. Pillai's trace is the one to read when the groups are unequal in size or spread. Checked against R on the iris data.

Kruskal-Wallis and Friedman

The rank-based versions of one-way and repeated measures ANOVA, for ordinal, skewed or small data. Kruskal-Wallis compares three or more independent groups (H on chi-square). Friedman ranks each row across the conditions: the chi-square with the tie correction, Kendall's W as the agreement between rows, median and mean rank per condition, and Holm-adjusted pairwise Wilcoxon signed-rank tests. Both are also under Nonparametric.

Regression

Correlation Matrix

Two or more numeric variables. Pearson (linear) and Spearman (rank) correlations, with p-values if requested, and a grid of scatter plots. r near 0 means no linear relationship, not no relationship.

Linear Regression

One dependent variable and one explanatory variable (covariate). Reports the coefficients table (intercept, slope, SE, t, p, confidence interval), r (with the sign of the slope) and r squared, the residual plot and QQ plot of residuals, and predictions at one or several x values (comma separated). Each prediction comes with a confidence interval for the mean response and a prediction interval for one new value, and a warning when x is outside the data. Tick "Show confidence and prediction bands" to draw both bands around the line. The slope interpretation sentence is written for you.

Sensitivity to a lurking variable (Cinelli-Hazlett benchmark)

After "correlation is not causation", the honest next step. Pick an outcome, a treatment (the cause being studied, a number or a 0/1 column), the covariates you adjust for, and a benchmark covariate. The card fits the regression and reports the robustness value: the share of the remaining variation of both the treatment and the outcome that an unobserved confounder (a lurking variable) would have to explain to bring the estimate to zero, and the smaller share that would make it not significant at alpha. The partial R2 of the treatment is the floor: a lurking variable explaining less than that of the outcome cannot explain the estimate away whatever its link to the treatment. Benchmarking asks what a lurking variable 1, 2 or 3 times as strong as the chosen covariate would do: its R2 with the treatment and the outcome, the adjusted estimate, SE and t. The contour plot shows the adjusted estimate for every strength, with the dashed red line where it reaches zero and the benchmark points marked. Formula, worked numbers and an APA-style sentence follow, as on every card. Cinelli and Hazlett (2020), Journal of the Royal Statistical Society B; the sample dataset Darfur survey is the paper's example (peacefactor on directlyharmed, benchmark female), and the card reproduces its Table 2.

Frequencies

2 Outcomes: Binomial test

One proportion against a test value. The exact binomial p-value is always given; its two-sided p adds every outcome as unlikely as the one observed, the same rule as R and jamovi. Tick "Also show the z test" for the course's by-hand method with the success and failure check (n p0 and n (1 minus p0) both at least 10). Summary mode: successes and n. Interval method: standard (Wald, the by-hand formula, default), plus four, Agresti-Coull, Wilson score, or exact Clopper-Pearson. When there are fewer than 10 successes or failures, the card points you to one of the small-sample methods instead of the standard interval.

N Outcomes: chi-square Goodness of fit

Do observed counts across categories match expected proportions? Choose Equally likely (every level gets 1 / k, the default) or type your own proportions or counts in the level order shown. The card states which null was used, shows the expected counts and the check that all are at least 5.

Contingency Tables: Independent Samples

Two categorical variables, or a typed table of counts. Chi-square test of independence with expected counts, row, column and total percentages; for a 2 by 2 table also Fisher's exact test, the odds ratio and the relative risk with confidence intervals. Fisher's Hₐ, shown when Fisher's exact test is ticked, picks the alternative: two-sided, greater (row 1 has a larger share of the first column, right tailed) or less (left tailed), where row 1 and the first column are the first ones in the Contingency Tables result (a typed table keeps the order you typed); for Ana with 8 makes and 2 misses and Ben with 3 makes and 7 misses, greater gives "Hₐ: Ana has a larger share of make than Ben (right tailed)" with exact p-value 0.0349. Each cell shows whatever you tick under Cells and Percentages, separated by vertical bars. If you untick all of them the table falls back to the observed counts and says so, rather than printing empty cells.

Two proportions: z test

Compares a success proportion between two groups using the pooled z test taught in the course, with the confidence interval for the difference and the success-failure check in each group. Type the success level exactly as in the data (Yes, not yes); if it is not one of the levels, the message under the box lists them. Summary mode takes successes and n per group.

distrACTION

Calculators, no data needed (Custom can also read two columns of the open dataset). Each one opens on the distrACTION page and works out its answer from the starting values at once, so a card is there before you type anything. The probability calculators draw the distribution and shade the probability.

How the page works

• The inputs card holds the parameters (for example Mean and SD) and a Find box: the Compute list, then x1, and x2 when the event is a "between" one. x2 is hidden for every other choice. Uniform (continuous) and Exponential open with x1 empty, and Custom opens with empty boxes: type a value and the answer appears.
• The result updates as you change anything: the parameters, the Compute list, x1 or x2. You never need to press Run to see it. If an input is empty, a grey note under the inputs says what to type; if it is impossible (an SD that is not positive, x2 below x1, a p outside 0 to 1 for a quantile), the note is red. Until the inputs make sense again the card fades and says "Out of date: see the message under the inputs".
• Run (or Enter) keeps the current result: the card shows Kept for a moment, and your next change starts a new card above it, so you can stack results and compare them. Pressing Run again with nothing changed makes no copy. edit on any card puts its values back in the inputs card and marks the card "Editing this result"; changes then update that card in place.
• When you open another calculator, a card the last one made by itself (one you never changed or kept) goes away, so browsing does not pile up cards.
• Every card starts with the answer in large type. For an event it is the event in symbols, words and percent, for example "P(X ≤ 67) = 0.8849, about 88.5%. The probability that X is at most 67." For t*, a p-value, a critical value, a sample size or power it is that number, for example "t* = 2.086 for 95% confidence". With "none, just the mean and SD" (Poisson, Geometric, Hypergeometric, Discrete Uniform and Custom) it is the mean and the SD, for example "mean = 3, SD = 1.7321". The tables and formula follow. On the probability cards the graph is shaded and its title states what is shaded, for example "Shaded: P(X ≤ 67) = 0.8849"; with "none" nothing is shaded and the title gives the mean and SD.
• A probability too small to show at the decimals chosen prints as "< 0.0001", never a bare 0, and the words give it the way a calculator writes it (for example 3.17E-5). One too close to 1 prints as "> 0.9999".
• On a phone or an iPad in portrait, the inputs card also repeats the current answer under the Find box, with a See the full result button.

Events you can find

Every calculator lists these events in this order (T-Distribution and Chi-square and F list their t*, p-value and critical value choices first). Binomial opens on P(X = x1); the continuous calculators open on "probability: P(X at most x1)". On the continuous calculators the same choices start with "probability:" (for example "probability: P(X at most x1)"), and the card adds the note "For a continuous variable, < and <= give the same area; P(X = a) = 0." For a discrete variable the strict and inclusive choices differ, and the app computes each one exactly. Example, Binomial with n = 4 and p = 1/6: P(X < 1) = 0.4823, P(X ≤ 1) = 0.8681, P(X = 1) = 0.3858, P(X > 3) = 0.0008, P(X ≥ 3) = 0.0162.

The calculators

• Binomial: number of trials and probability of success, then any event above, plus the mean, variance and SD of the distribution and a full table. Up to 100 trials the graph and the full table show every value. For more trials they show the values where the probability is, with a note giving the total probability of the values left out; the answer itself is always exact, for any number of trials.
• Poisson, Geometric, Hypergeometric, Discrete Uniform: the same layout as Binomial, with "none, just the mean and SD" as an extra choice, a full table and a shaded bar graph. Geometric lets you choose whether X counts the trials up to the first success (1, 2, 3, ...) or the failures before it (0, 1, 2, ...), since textbooks use both.
• Custom (discrete x and P(x)): any discrete probability distribution. Either put x in one column and P(x) in another (columns named x and p(x) are picked automatically), or type both lists separated by commas. The two boxes open empty, with grey examples; while you type, a grey note keeps count of the values so far. Gives the mean (expected value), variance and SD, a work table with x P(x) and (x minus mean)^2 P(x) to match the hand method, and any event above. The bar graph shades that probability and marks the mean. It stops with a red message if the two lists have different lengths, if a probability is not between 0 and 1, or if the probabilities do not add to 1. When they add to between 0.99 and 1.01 it says that is usually rounding and uses the values as typed.
• Normal: any event above, or the value for a given percentile (quantile). Type z scores by using mean 0 and SD 1. A between event shows both z scores, "z for x1" and "z for x2".
• Uniform (continuous) and Exponential: any event above and percentiles, with mean and SD and the shaded area. Exponential takes the mean; if you are given a rate lambda, the mean is 1/lambda.
• T-Distribution: the critical t* for a confidence level and df (type the level as a decimal, such as 0.95), the p-value for a t statistic (two-sided, upper or lower tail), or any event above for a t variable with that df. It opens on t* for 95 percent confidence with df = 20, and the graph shades the middle 95 percent.
• Chi-square and F: the right-tail p-value for a statistic (the Statistic box), the critical value for alpha (the alpha box, 0.05 to start), or any event above for that distribution.
• Sample size for a margin of error: for a proportion (with a guess for p, 0.5 if unknown) or a mean (with a guess for s). Only the guess that applies shows.
• Power and sample size for a test: the Advanced power calculator, on the distrACTION page, titled Power and Sample Size. Only the boxes the chosen test uses show.

Nonparametric

Rank-based alternatives for skewed data, ordinal scores or small samples.

• Mann-Whitney U: two independent groups (alternative to the independent t-test). Reports U, the p-value and the group medians.
• Wilcoxon signed-rank and sign test: paired data, or one column against a constant. Both tests are shown; the sign test uses only the direction of each difference.
• Kruskal-Wallis: three or more groups (alternative to one-way ANOVA). Follow a significant result with Mann-Whitney tests on the pairs that matter.
• Friedman: the same people measured under three or more conditions (alternative to Repeated Measures ANOVA). Ranks within each row, Kendall\'s W, Holm-adjusted pairwise Wilcoxon tests. Also under ANOVA.

Learn

Teaching tools that show where the theory comes from. Nine of them need no data and open on the Learn page, so they work on a projector in a room where no one has a file open: everything except bootstrap and permutation. The Central Limit Theorem, the sampling distribution simulator and Bayesian can still use a column of the open dataset. Bootstrap and permutation work from your data and stay with the table.

• Coin flips and the law of large numbers: one coin, two coins, three coins, a die, two dice, or any probability you choose. It shows the first fifty outcomes, a table of the proportion after 10, 25, 50, 100, 250 and more trials, and the running proportion settling toward p. A second plot shows the count drifting further from the expected count even while the proportion settles, which is the answer to "19 percent, so 2 of the next 10 will be priority 1" and to "tails is due."
• The Central Limit Theorem: pick a population shape (right-skewed, normal, uniform, two humps, yes or no, or a column of your data) and several sample sizes at once. The sampling distributions are drawn on the same axes, with a table comparing the simulated SD against sigma / sqrt(n) and the skewness falling as n grows. The point students miss: the center never moves, the spread shrinks by sqrt(n), and only the shape is the theorem.
• What a confidence interval means: draws many samples from a population only you can see, builds an interval from each, and plots them with the true value as a fixed vertical line. It reports the actual capture rate against the stated level. The truth never moves; the interval does. Uses t with n - 1 degrees of freedom for a mean, and warns when n p or n (1 - p) falls under 10 for a proportion.
• What a p-value is: forces H0 to be true, draws thousands of fresh samples from that world, and counts how many land at least as far out as your result. For a proportion it prints the simulated p, the exact binomial p and the z formula p side by side, and explains the gap when the normal approximation is off.
• Mean versus median: click the number line to add values, click a dot to remove one. Or type a value from 0 to 100 and press Add; Remove the last value takes one off. A long tail or one far value drags the mean and barely moves the median.
• Regression: outliers and influence: click to add points to a scatterplot, or type x and y (each 0 to 12) and press Add point, and watch the least-squares line, r and the slope refit against the starting line. Remove the last point takes one off. A point far out in x and off the pattern is influential; an outlier in the middle of the x range is not.
• Guess the correlation: a fresh scatterplot each time; type your guess for r, press Enter or check it, and keep a running average of how far off you are.
• Sampling distribution simulator: pick a population (a column of your data; a normal population, mean 50 and SD 10; a right-skewed one, exponential with mean 8; a uniform one from 0 to 100; or a yes or no population with a chosen p), a statistic, a sample size and a number of samples. For a sample proportion from a column, type the success level (that box shows only for a proportion); a column with no numbers for a mean, or a level that is not in the data, gets a message under its box and nothing is drawn. It draws the population, then the distribution of the sample statistic, and compares its SD with the formula (sigma / sqrt(n) or sqrt(p(1 minus p)/n)). Watch it turn normal as n grows.
• Bootstrap: a confidence interval with no formula. Resample with replacement, recompute the statistic thousands of times, take the middle 95 percent.
• Permutation: what a p-value is. Shuffle the group labels, recompute the difference, count how often the shuffled world beats the real one.
• Bayesian: prior, data, posterior on one picture, for a proportion or a mean, from a column of your data or from numbers you type. The same tool is under Advanced, Bayesian Inference.

Advanced

For second courses, research methods and upper-division work. Each card still ends with a plain-English reading.

Results

• Decimal places shown: 2, 3, 4 (default) or 6. It applies to new results, and your browser remembers the choice.
• Notation: symbols or words. Formulas, hypotheses, APA lines and table headers use the textbook's symbols by default (x̄, σ, μ, α, χ², H₀, Hₐ, ±, ≠, √). Choose words (x bar, sigma, chi-square, H0) if you use Read Aloud or a screen reader. Menu names and card titles never change, so the companion guides still match.
• Share link (data + analyses): one address that carries the setup: the dataset (a sample dataset by name, or a table of your own inside the link when it is small enough), the filter, the choices behind every card on the Analyses and Graphs tabs, and the course profile if one is set. Press Copy link and paste it into Canvas, an email or a message. Whoever opens it sees "Open the shared setup?" with what it holds and an Open button; nothing runs until it is pressed, the same data come back, and the same analyses run again on them. Nothing is sent anywhere: the whole setup is in the address after #s=. An instructor can hand a class a link that opens the app already set up for the day's activity; a student can send exactly what they ran.
• Course profile: a small set of defaults an instructor shares: the two-sample t-test offered first (Welch's or pooled), the quartile rule in Descriptives, decimal places, the alpha and confidence level offered first, and which menus show (Data and Results always do, so Advanced can be hidden from a first course). Apply uses it on this computer; the profile name shows above the table. The same dialog downloads it as a .sww-profile.json file or copies a link that sets it; Open a profile file reads the file. A link made with Share link carries the profile too. Remove the profile from the same dialog.
• Print or save as PDF: prints only the results of the page you are on (data table, menus and the distrACTION inputs are hidden). Use your browser's Save as PDF.
• Export results as HTML: one file with every card and graph, including the distrACTION and Learn pages, opens in any browser, good for submitting.
• Save session: a .sww.json file with the data, the filter, the column types you set, and the cards on the Analyses and Graphs tabs and the distrACTION and Learn pages. Open a saved session brings them back, on any computer. Graphs are not stored in the file, and a card brought back this way can be copied or removed but not edited: to redraw a graph or change a choice, run the analysis again from its menu. Opening a session file never runs anything in it, even one from someone else: its cards come in as plain content, and a saved filter is applied only when it is made of column names, numbers, text in quotes and operators.
• Clear analyses and Clear graphs: on the data page, Clear analyses empties the Analyses tab and Clear graphs empties the Graphs tab. On the distrACTION or Learn page both clear that page only, the same as Clear this page, and Undo clear brings the cards back. Individual cards have their own remove button.

8. Honest graphs

Statistics software will happily draw a misleading picture. Stats Without Walls refuses to, and prints the rules it followed under each graph so students learn them.

• The count axis starts at zero and cannot be zoomed on bar plots and histograms. A difference of two students can never be stretched to look like a cliff.
• Equal bins with nice edges. Histogram bins are all the same width, chosen from 1, 2, 2.5, 5, 10 times a power of ten, with tick marks on the edges. Each class includes its left edge; the last class also includes the maximum, so every value is counted once. When you group by a variable, all groups share the same bins so their shapes can be compared.
• Ordered scales stay in order. Freshman to Senior, Never to Always, Strongly disagree to Strongly agree, 1 to 5 and similar scales are drawn in their natural order. Sorting them tallest first hides the shape of the distribution.
• Same width for every bar; only height carries information. No 3D, no pictograms.
• Pies are flat and carry their percent and count, so nobody judges angles by eye.
• Numbers are on the picture. The count or percent is printed above each bar and bin by default, and a frequency table can sit under the graph.

9. Writing up a result

Use the "copy text" button, then write one paragraph with these parts: what was compared, the statistic with its degrees of freedom, the p-value, the decision at alpha, and what it means in context. The blue box gives you most of this sentence. The three examples below come from "Our class data (40 students)", so you can run them and compare.

Run it with T-Tests, Independent Samples T-Test: Coffee_Cups_Daily by Employed, with Full-time, Not employed typed as the two levels to compare.

Run it with Frequencies, Contingency Tables: Independent Samples: rows Employed, columns Pet_Owner.

Run it with Regression, Linear Regression: dependent variable GPA, covariate Hours_Study.

Always report the condition check. If it failed, say so and report the nonparametric or exact result instead.

10. Saving and sharing work

• Your browser remembers your own data (with its filter and the types you set), the decimal setting and the panel width between visits on the same device. A sample dataset counts as your own once you change it. A sample dataset you have not changed and the distrACTION inputs are not remembered. Results are not kept through a reload either, but the choices behind the cards on the Analyses and Graphs tabs are: after a reload, a bar above the tabs says Restore your last session? with the count, the dataset and the time. Restore opens the same data (a sample dataset included) and runs the same analyses again, graphs and edit buttons included; No thanks forgets them. This is a convenience, not a backup.
• For homework, Results, Export results as HTML or Print or save as PDF and upload the file.
• To hand someone exactly what you have open, Results, Share link: the address carries the data (a sample by name, or your own small table), the filter and the analyses, and opens with an Open button.
• To continue later or on another computer, Results, Save session and keep the .sww.json file.
• To share a dataset with a classmate, Data, Download data as CSV.

11. How it differs from other tools

Menus, option names and table names match the course instructions, so they work as written. Where common statistics software and the course textbook disagree, Stats Without Walls follows the textbook:

12. Troubleshooting

13. Sample datasets

A codebook for the real-world datasets is in the app's data folder (README_real_world_datasets).

14. How the numbers were checked

Every procedure was run on the same data in R (and the jmv package where it exists) and compared to four decimals: t-tests, proportion tests, ANOVA and Tukey, chi-square, regression coefficients and intervals, nonparametric tests, multiple and logistic regression with diagnostics, two-way and repeated measures ANOVA, count, multinomial and ordinal models, power calculations, time-series decomposition and autocorrelation, PCA, factor analysis and varimax rotation, Cronbach's alpha, k-means, Kaplan-Meier, log-rank, Cox regression and the Bayesian conjugate updates. Distributions come from jStat; graphs are drawn with Plotly.

The distribution calculators (binomial, custom discrete, Poisson, geometric, hypergeometric, discrete uniform, uniform, exponential) were checked against R's d, p and q functions, and on 2026-10-14 the strict, inclusive, equal-to, between and quantile events again (binomial, normal, uniform, Poisson, geometric, hypergeometric, t, chi-square and F against pbinom, dbinom, qbinom, pnorm, qnorm, punif, ppois, qpois, pgeom, phyper, pt, pchisq and pf); the z tests, the exact binomial test p-value (against binom.test, on 2026-10-15, for n from 5 to 100,000), the five proportion intervals (against prop.test and binom.test), the variance tests (against var.test), Levene's test (against car::leveneTest), kurtosis, percentiles and the regression confidence and prediction intervals (against predict) the same way. Simulated data were checked by their mean and SD against the distribution they came from. On 2026-10-14 every distrACTION calculator and event (967 cases) was checked again against scipy. Binomial probabilities use the same method as R (Loader's saddle point), so they stay right for any number of trials; this was checked for n up to 10,000.

The Learn demonstrations are checked the same way. The simulated sampling distributions are compared against sigma / sqrt(n); the confidence interval demo is checked by its capture rate against the stated level, which also falls below that level on purpose when the success-failure condition fails; and the p-value demo is checked against the exact binomial, computed independently. Where the z formula and the exact answer disagree, the app prints both and says why rather than hiding the gap.

Stats Without Walls was built by Safaa Dabagh for students at Santa Monica College, West Los Angeles College and Loyola Marymount University, and is free for anyone to use.