Teaching · For Teachers · Research and data

Three groups, one test,
and how much
the grouping explains.

Paste each group’s scores. The calculator runs a one-way analysis of variance, shows the source table and every step, and reports how much of the spread lies between the groups, so a significant F comes with its size.

Run the ANOVAWhat 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 ANOVA calculator

The worked example is made up: fluency gains under three practice schedules. Use codes, not names. 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
F with its degrees of freedom, the p-value, eta squared and omega squared, the ANOVA source table, group summaries and the steps. It prints as a summary and downloads as a spreadsheet.
Who it is for
Teachers doing action research, data teams and instructional leaders, school psychologists and graduate students in education.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Two to five groups of up to 2,000 scores. 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. Name the measure.
  2. Name each group and paste its scores, one score per person.
  3. Read F and the p-value together with eta squared.
  4. If the note asks for it, check the result with Welch’s ANOVA; if F is significant, plan a post hoc test.
  5. Print the summary or download the spreadsheet.

Run the ANOVA

How the test works

Variation between the groups set against variation inside them.

The worked example: three practice schedulesBetween groupsSS 121.33÷ 2 df = 60.67Within groupsSS 98.00÷ 21 df = 4.67F13.0060.67 ÷ 4.67p< .001F(2, 21)The worked example: three practice schedulesBetween groupsSS 121.33÷ 2 df = 60.67Within groupsSS 98.00÷ 21 df = 4.67F13.0060.67 ÷ 4.67p< .001F(2, 21)
ANOVA splits the spread of every score into the part between the group means and the part inside the groups; F is how many times larger the first is, per degree of freedom.

What F measures

Every score sits some distance from the grand mean. Part of that distance is the gap between its group’s mean and the grand mean; the rest is how far it sits from its own group’s mean. Dividing each sum of squares by its degrees of freedom gives two mean squares. If the groups truly had the same mean, their ratio, F, would hover around 1.

Reading the result

A small p says the means are not all equal; it does not say which ones differ. Follow a significant F with Tukey’s HSD or planned comparisons. Eta squared is the share of variation between groups in this sample; omega squared corrects its upward bias. ANOVA assumes independent scores and similar spreads; when the largest SD is more than about twice the smallest, use Welch’s ANOVA.

Sources

  1. NIST/SEMATECH e-Handbook of Statistical Methods, section 7.4.3, Are the means equal? One-way ANOVA (itl.nist.gov).
  2. Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863.
  3. Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3–4), 330–336.
  4. Institute of Education Sciences, What Works Clearinghouse. Procedures and Standards Handbook, Version 5.0 (2022).

The worked example is made up. Use student codes, not names. Your scores stay in this browser. Support: team@caveatacademic.com.