One-Way ANOVA Generator
Calculate the Analysis of Variance table and visualize group differences using Box Plots.
Data Input
Enter data for each group. Separate values with commas or spaces. One group per line.
ANOVA Table
Reject Null
| Source | SS (Sum Sq) | df | MS (Mean Sq) | F | P-value |
|---|---|---|---|---|---|
| Between Groups | — | — | — | — | — |
| Within Groups | — | — | — | ||
| Total | — | — |
Waiting for data…
Group Box Plots
IQR Range
Median
Understanding One-Way ANOVA
Analysis of Variance (ANOVA) is a statistical method used to test differences between two or more group means. The “One-Way” ANOVA compares groups based on one independent variable (factor).
Decomposition of Variance
ANOVA splits the total variation in the data into two parts:
- Between-Group Variability ($SS_{Between}$): Measures how much the group means differ from the overall (grand) mean. If this is large, it suggests the groups are different.
- Within-Group Variability ($SS_{Within}$): Measures the spread of data inside each group (error/noise). If this is large, it’s harder to detect differences between groups.
The F-Ratio
The test statistic $F$ compares these two variances: $$ F = \frac{\text{Variance Between Groups}}{\text{Variance Within Groups}} = \frac{MS_{Between}}{MS_{Within}} $$ A large F-value implies that the difference between groups is significant relative to the noise within them.
FAQ
What are the assumptions of ANOVA?
1. Independence: Samples are independent of each other.
2. Normality: Data in each group should be roughly normally distributed.
3. Homogeneity of Variance: Groups should have roughly equal variances (standard deviations).
2. Normality: Data in each group should be roughly normally distributed.
3. Homogeneity of Variance: Groups should have roughly equal variances (standard deviations).
Why not just do multiple T-tests?
Doing multiple T-tests (e.g., A vs B, B vs C, A vs C) increases the Type I Error rate (false positives). ANOVA performs a single global test to see if any difference exists while controlling the error rate.
What if my P-value is low?
If $P < \alpha$, you reject the null hypothesis. This means there is a statistically significant difference between at least two of the group means. You would then need a "Post-Hoc Test" (like Tukey's HSD) to find exactly which groups differ.