The Fixed Effect Variance Calculator is a statistical tool used to estimate the variability attributed to fixed factors or treatments across different groups or categories in a dataset. This calculation is essential in fields like experimental design, biostatistics, psychology, and econometrics, where researchers are interested in understanding how much variation is due to known and controlled factors rather than random error.
By calculating the variance from fixed effects, researchers can assess the influence of different treatments or group means in an analysis of variance (ANOVA) or linear model framework. This helps to determine if group differences are statistically significant and how much they contribute to the overall variability in the data.
This calculator is especially useful in controlled experiments and fixed effects models where the number and identity of groups are predefined and not randomly sampled.
formula of Fixed Effect Variance Calculator
Where:
nᵢ = Number of observations in group i
μᵢ = Mean of group i
μ̄ = Overall (grand) mean across all groups
k = Total number of groups
Alternative representation in linear models:
Fixed Effect Variance = SS_between / df_between
Where:
SS_between = Sum of Squares Between Groups = Σ [nᵢ × (μᵢ - μ̄)²]
df_between = Degrees of freedom between groups = k - 1
This formula helps calculate how much of the total variability can be explained by differences between group means, rather than within-group differences.
Fixed Effect Variance Reference Table
| Term | Description | Example |
|---|---|---|
| nᵢ | Observations in group i | 10 |
| μᵢ | Mean of group i | 75 |
| μ̄ | Overall average mean across all groups | 70 |
| k | Total number of groups | 4 |
| SS_between | Total variability between group means | See Example Below |
| df_between | Degrees of freedom between = k - 1 | 3 |
This table provides a clear summary of the common terms used in the formula so users can calculate without confusion.
Example of Fixed Effect Variance Calculator
Let’s calculate fixed effect variance using the following data from 3 groups:
Group A: Mean = 70, n = 8
Group B: Mean = 75, n = 10
Group C: Mean = 65, n = 7
Step 1: Calculate overall mean
μ̄ = (8×70 + 10×75 + 7×65) / (8+10+7)
μ̄ = (560 + 750 + 455) / 25 = 1765 / 25 = 70.6
Step 2: Calculate sum of squares between (SS_between)
SS_between = 8×(70 - 70.6)² + 10×(75 - 70.6)² + 7×(65 - 70.6)²
= 8×0.36 + 10×19.36 + 7×31.36
= 2.88 + 193.6 + 219.52 = 416
Step 3: Degrees of freedom = 3 - 1 = 2
Step 4: Fixed Effect Variance = 416 / 2 = 208
So, the Fixed Effect Variance is 208.
Most Common FAQs
Fixed effect variance is use to measure how much variability in data is explain by known groups or treatments. It is commonly use in ANOVA and regression models involving fixed effects.
Total variance includes all variability in the data, including both within-group and between-group components. Fixed effect variance isolates the portion due to differences among group means only.
No, this calculator is specifically for fixed effects. If your model includes random effects (like subject-level variability), you need a separate method like mixed effects models to estimate variance components.