Skip to main content
Calcimator

ANOVA Calculator

Perform a one-way ANOVA (Analysis of Variance) to compare means across three groups and determine if differences are statistically significant.

Inputs

Results

F-Statistic

10.58

P-Value (approx)

0

df Between Groups2
df Within Groups72
Mean Square Between (MSB)1,058.33
Mean Square Within (MSW)100
Grand Mean78.33
Significant at α=0.05 (1=Yes)1
How to Use This Calculator
  1. Enter the mean and sample size for each of the three groups being compared, plus the pooled within-group variance (MSW), the average of each group's variance.
  2. One-way ANOVA tests the null hypothesis that all group means are equal against the alternative that at least one differs.
  3. The F-statistic = (Between-group variance) / (Within-group variance); a larger F indicates greater between-group variation relative to noise.
  4. The approximate p-value is derived from the F-distribution with k−1 and N−k degrees of freedom (k = number of groups, N = total observations).
  5. If p < your significance level (typically 0.05), reject the null hypothesis — at least one group mean is significantly different.
  6. Use a post-hoc test (e.g., Tukey's HSD) after a significant ANOVA to determine which specific groups differ.

How the result changes with Group 3 Mean

Group 3 MeanF-StatisticP-Value (approx)
-800,00053,343,333,804.330
-300,0007,503,750,4710
300,0007,496,250,4710
800,00053,323,333,804.330

What each input means

Group 1 Mean
The mean value for the first group.
Group 1 Sample Size
Number of observations in the first group.
Group 2 Mean
The mean value for the second group.
Group 2 Sample Size
Number of observations in the second group.
Group 3 Mean
The mean value for the third group.
Group 3 Sample Size
Number of observations in the third group.
Pooled Variance (MSW)
The pooled within-group variance (mean square within). Average of group variances.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Group 1 Mean = 72, Group 1 Sample Size = 25, Group 2 Mean = 78, Group 2 Sample Size = 25 = 7 input(s) provided
  2. Calculate F-Statistic
    F-Statistic
    10.5833 = 10.5833
  3. Calculate P-Value
    P-Value
    0 = 0
  4. Calculate df Between Groups
    df Between Groups
    2 = 2
  5. Calculate df Within Groups
    df Within Groups
    72 = 72

Engine last updated . Checked against 2 independently-derived tests — how we verify calculators.

Related Calculators

The questions that sit next to this one — chosen by subject, including calculators filed under a different category.

Statistics

Kruskal-Wallis Test Calculator

Perform a Kruskal-Wallis H test to compare rank distributions across multiple independent groups.

Statistics

T-Test Calculator

Calculate the t-statistic, degrees of freedom, and approximate p-value for a one-sample t-test.

Statistics

Z-Score Calculator

Calculate the z-score (standard score) for any value in a normal distribution. Find the percentile ranking and probability associated with your data point.

More in Math & Statistics.