One-Way ANOVA Calculator & Post-Hoc Test (Summary Data)

Enter a name and the summary statistics (n ≥ 2, x̄, s ≥ 0) for each group. ANOVA requires at least 3 groups.

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How to Use the One-Way ANOVA Calculator

Follow these four simple steps to perform your One-Way ANOVA and Tukey HSD Post-Hoc analysis using summary data.

  1. Enter Group Data: For each treatment group (a minimum of three are required), enter a descriptive name, the Sample Size (n), the Sample Mean (x̄), and the Sample Standard Deviation (s).
  2. Add Groups: Use the "Add Group" button to add more treatment levels if necessary. Remember, One-Way ANOVA requires at least three groups.
  3. Run Calculation: Click the large blue "Calculate ANOVA" button to instantly generate your statistical results.
  4. Analyze Results: The output will display the Descriptive Statistics, the complete ANOVA Source Table (including SS, df, MS, and the F-Statistic), and the p-value. If the p-value is significant (p < 0.05), the Tukey HSD Test results will automatically appear below to show which specific pairs of groups have a statistically significant difference.

Ready to analyze your data? Input your summary statistics into the calculator above!

One Way ANOVA Online Calculator and Theoretical Explanation

Example: One-Way ANOVA Calculation

A pharmaceutical company wants to test the effectiveness of three different doses of a new drug (Low Dose, Medium Dose, High Dose) on lowering cholesterol levels compared to a control group (Placebo).

They randomly assign 40 patients into four groups (n=10 per group). The reduction in cholesterol (in mg/dL) after one month is recorded. The summary data for the four groups is given below.

Group Name Sample Size (n) Sample Mean (x̄) Sample SD (s)
Placebo (Group 1) 10 5.2 2.1
Low Dose (Group 2) 10 8.9 2.5
Medium Dose (Group 3) 10 13.1 3.0
High Dose (Group 4) 10 12.5 2.8

Interpretation of Results (Expected)

Expected Outcome:

Initial Step: Input the 4 groups' summary data into the calculator (n, mean, sd).

ANOVA Test: The calculator will output the F-statistic and the p-value. Since the means are visually different, we expect the p-value to be less than 0.05. Therefore, we reject the null hypothesis H0: At least one dose level is significantly different from the others in reducing cholesterol.

Tukey HSD Test: Since the ANOVA is significant, the calculator will perform the Tukey HSD post-hoc test to identify *which specific pairs* are different. We expect to find:

  • Placebo (Group 1) is significantly lower than all drug groups (Groups 2, 3, and 4).
  • Low Dose (Group 2) is significantly lower than Medium and High Dose (Groups 3 and 4).
  • Medium Dose (Group 3) and High Dose (Group 4) are not significantly different from each other.

How to Do This in Statistical Software

The same cholesterol-reduction example can be reproduced in the most widely used statistical packages. These examples assume you have the raw data per patient rather than just the summary statistics used above.

RStudio

R's built-in aov() function handles one-way ANOVA directly, with Tukey's HSD available via TukeyHSD():

model <- aov(cholesterol_reduction ~ group, data = mydata)
summary(model)

TukeyHSD(model)

SPSS

Analyze → Compare Means → One-Way ANOVA. Move your outcome (cholesterol reduction) into the Dependent List and your group variable into the Factor box. Click Post Hoc and check Tukey to get the same pairwise comparisons this calculator provides.

JASP

ANOVA → ANOVA. Move your outcome into the Dependent Variable box and your group variable into Fixed Factors. Under Post Hoc Tests, move the factor in and check Tukey. JASP also generates the F-statistic, p-value, and effect size (η²) automatically.

jamovi

ANOVA → ANOVA. Drag your outcome into Dependent Variable and your group variable into Fixed Factors. Under Post-Hoc Tests, move the factor into the right box and select Tukey. jamovi is free and open-source, making it a popular classroom alternative to SPSS.

Other tools such as Stata (oneway or anova commands, with pwmean for Tukey comparisons) and JMP (Analyze → Fit Y by X → Means/ANOVA) can also perform this analysis, though their workflows differ from the packages above.

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