Teaching · For Teachers · Research and data

Do the two
go together, or
is it chance?

Type a table of counts from a survey or a tally. The calculator works out what each cell would hold if the two variables were unrelated, adds up the gaps, and tells you how strong and how reliable the association is.

Run the testWhat you get
$12one-time · every device you sign in on
Buy · $12

Included with Caveat Classroom and Whole-school licenses. Or get it in the For Teachers toolkit, $79 for 72 items.

The chi-square calculator

The worked example is made up: 205 students in three grades asked how they prefer to review. Nothing you type leaves this browser.

Loading the calculator. If nothing appears, turn on JavaScript.

What you get

Teaching · For Teachers$12 · included with Classroom and Whole-school licenses

What you finish with
Chi-square, degrees of freedom, the p-value and Cramér’s V, expected counts and row percents for every cell, the cell that contributes most and a warning about small expected counts. It prints as a summary and downloads as a spreadsheet.
Who it is for
Teachers doing action research, school survey and data teams, counselors analyzing surveys and graduate students in education.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Up to 12 rows and 4 columns. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
$12 one-time, yours on every device you sign in on; the tool opens once you are signed in with it. Included with Caveat Classroom and Whole-school licenses. Also in the For Teachers toolkit ($79) and the Teaching Suite pass ($199), and 1 more bundle. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The For Teachers space in Caveat Teaching.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Say what the table shows and name the columns.
  2. Add a row for each category with its counts.
  3. Read p together with Cramér’s V and the expected counts.
  4. Look at the cell contributing most to see where the association lies.
  5. Print the summary or download the spreadsheet.

Run the test

How the test works

Observed against expected, cell by cell.

The worked example, one cell at a timeGrade 11, practice tests35 seenof 65 grade 11 studentsIf grade made no difference27.9 expected65 × 88 ÷ 205This cell’s share1.81(35 − 27.9)² ÷ 27.9All nine cellsχ² = 8.89df 4, p = .064The worked example, one cell at a timeGrade 11, practice tests35 seenof 65 grade 11 studentsIf grade made no difference27.9 expected65 × 88 ÷ 205This cell’s share1.81(35 − 27.9)² ÷ 27.9All nine cellsχ² = 8.89df 4, p = .064
Each cell compares what was counted with what would be expected if review method had nothing to do with grade; the nine shares add up to chi-square, 8.89.

Expected counts

If the two variables were unrelated, each row would split across the columns in the same proportions as the whole table. That gives each cell an expected count: its row total times its column total divided by the grand total. Chi-square adds, over every cell, the squared gap between observed and expected divided by expected.

When to be careful

The test needs counts of separate people or events, not percents or repeated answers from the same person. The chi-square approximation is unreliable when many expected counts are below 5; combine thin categories or use an exact test. A significant result in a large survey can come with a tiny Cramér’s V, so report both.

Sources

  1. NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5.15 and 7.4: chi-square tests (itl.nist.gov).
  2. Cochran, W. G. (1954). Some methods for strengthening the common χ² tests. Biometrics, 10(4), 417–451: the expected-count guideline.
  3. Cramér, H. (1946). Mathematical Methods of Statistics. Princeton University Press: the V coefficient.
  4. National Center for Education Statistics. NCES Statistical Standards (nces.ed.gov): reporting tests on categorical survey data.

The worked example is made up. Your counts stay in this browser. Support: team@caveatacademic.com.