Summarise categorical data in a cross-tab with row, column and total percentages, or run a chi-square goodness-of-fit test against expected proportions — all client-side.
Paste your categorical data and press Calculate to build the cross-tab or run the goodness-of-fit test.
You have two yes/no or category questions and want to know if they move together. Enter the lab to build the cross-tab and test whether the categories are related.
For a cross-tab, paste two columns of category labels where row 1 of each belongs to the same item. For goodness-of-fit, paste one column of counts and (optionally) the percentages you expect.
The calculator counts how often each category combo appears and figures out percentages (by row, by column, or overall). For goodness-of-fit, it also calculates how many you'd expect in each category if your specified pattern were true.
It compares what you actually got to what was expected, and turns the size of that gap into a p-value — telling you whether your data genuinely differs from the expected pattern, or is close enough to be normal variation.
Cross tabulation is the standard way to summarise the relationship between two categorical variables. Add a chi-square goodness-of-fit test and you can also check whether a single set of category counts matches the proportions you expected — turning a simple table into a statistical conclusion.
A cross tabulation (or contingency table) counts how many observations fall into each combination of two categorical variables — for example shift (day/night) against outcome (pass/fail). Adding row, column or total percentages turns raw counts into comparable proportions, making patterns and associations easy to read at a glance.
The cross-tab simply tallies how many times each combination of labels occurs, then adds up row, column and grand totals and turns them into percentages so you can compare groups fairly. The goodness-of-fit test goes further: it compares the counts you observed against the counts you expected from a target split, and measures the gap as a chi-square statistic. A small p-value (below 0.05) means your observed counts do not match the expected pattern — something is different from what you assumed.
A supervisor counts rework jobs for three assembly teams over a month. Team A: 12 rework out of 100. Team B: 25 out of 100. Team C: 8 out of 100. A Chi-Square test on the table gives p = 0.001.
Team B's rate is more than three times higher than Team C's — and the test confirms it's not chance.
What to do with this: Share Team C's best practices with Team B and track whether the rework rate drops over the next month.
Categorical data is everywhere — pass/fail, defect type, shift, supplier, region. Cross tabulation organises it so you can compare groups fairly, while goodness-of-fit tells you whether an observed mix departs from a target or historical pattern. Together they turn tallies into decisions about where to act.
Build a cross-tab whenever you want to compare the distribution of one category across the levels of another. Use goodness-of-fit when you have one categorical variable and a clear expectation — equal proportions, a published benchmark, or last year's mix — and want to test whether this period's counts still fit it.
Cross tabulation is a core Measure and Analyse tool for attribute data. It feeds Pareto analysis, stratification, and chi-square tests of independence, helping teams find which categories drive defects and whether differences between groups are real or just noise.
If the goodness-of-fit test is significant, identify which categories contribute most to χ² and target them for investigation. Combine cross-tabs with a Pareto chart to prioritise, and with a chi-square test of independence when you want to test the association between two variables rather than fit to fixed proportions. Document the table in your Analyse phase as evidence for the vital few causes.
Pair cross tabulation with chi-square tests, Pareto analysis, and a DMAIC project structure to find and prove the vital few causes.
A cross tabulation (cross-tab) is a summary table that shows the counts of observations for every combination of two categorical variables, usually with row, column and total percentages. It is purely descriptive — it organises and displays the data. A chi-square test goes a step further and tests whether the pattern in the table is statistically significant, comparing observed counts to the counts expected under independence. You typically build the cross-tab first to see the picture, then run a chi-square test of independence to confirm whether an apparent association is real.
A chi-square goodness-of-fit test checks whether a single set of observed category counts matches a set of expected proportions. You supply the observed counts and the proportions you expect (for example equal proportions, or a historical mix), and the test computes χ² = Σ(O−E)²/E with degrees of freedom equal to the number of categories minus one. A low p-value means the observed counts depart significantly from the expected proportions — the data does not fit the expected pattern.
A row percentage expresses each cell as a proportion of its row total, so the percentages across each row add to 100% — useful for comparing the distribution of the column variable within each row. A column percentage expresses each cell as a proportion of its column total, so each column adds to 100% — useful for comparing rows within each column. A total (or overall) percentage expresses each cell as a proportion of the grand total. Choose the direction that matches the question you are asking.
In a goodness-of-fit test the expected count for a category is the total number of observations multiplied by its expected proportion. In a contingency-table chi-square test it is (row total × column total) / grand total. Expected counts matter because the chi-square approximation works well only when they are reasonably large — the common rule of thumb is that expected counts should be at least 5. If several expected counts fall below 5, combine categories, collect more data, or use an exact test instead.
A cross-tab shows where the differences lie; a goodness-of-fit test confirms they are real. Structured training shows you how to act on what the categories reveal.
More calculators for statistics, quality, and improvement.
Want to test relationships between categorical variables inside a structured improvement project? The Black Belt course covers advanced statistics, hypothesis testing, and the full analytical toolkit.
View Black Belt →