Analysis of Variance (ANOVA)
ANOVA is a statistical technique used to test significant differences between more than two sample means. It calculates and compares the variance between groups of samples to the variance within that same sample groups. The objective is to determine if any meaningful differences exist.
Where F is the test statistic that follows an F-distribution. A large F-value indicates that the differences between group means are greater than would be expected by chance.
Data Input
Enter comma-separated values for each group. Add more groups as needed.
ANOVA Results
F-Statistic
Test statistic
P-Value
Significance level
Result
Hypothesis test
ANOVA Table
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F-Value |
|---|---|---|---|---|
| Between Groups | ||||
| Within Groups | ||||
| Total |
Interpretation
Group Statistics
| Group | Sample Size | Mean | Standard Deviation |
|---|
ANOVA Examples in Industrial Engineering
Production Example
Compare the output of three different machines to determine if there are significant differences in productivity.
Machine A: 23, 25, 24, 26, 22
Machine B: 28, 27, 29, 26, 30
Machine C: 21, 20, 22, 19, 23
Quality Control Example
Test whether three different quality control methods result in different defect rates.
Method A: 2.1, 1.9, 2.3, 2.0, 2.2
Method B: 1.5, 1.6, 1.4, 1.7, 1.5
Method C: 3.2, 3.0, 3.1, 3.3, 2.9
Material Testing Example
Compare the strength of three different material types.
Material A: 45, 47, 46, 48, 44
Material B: 52, 51, 53, 50, 54
Material C: 38, 39, 37, 40, 36