ANOVA
``Analysis of Variance.'' A Statistical Test for heterogeneity of Means by analysis of groupVariances. To apply the test, assume random sampling of a variate 
with equalVariances, independent errors, and a Normal Distribution. Let 
be the number ofReplicates (sets of identical observations) within each of 
Factor Levels(treatment groups), and 
be the 
th observation within Factor Level 
. Also assume that the ANOVA is ``balanced'' by restricting to be the same for each Factor Level.
Now define the sum of square terms
 |  |  | (1) |
 |  | (2) | |
 | |  | (3) |
 | |  | (4) |
|  | (5) |
which are the total, treatment, and error sums of squares. Here,
is the mean of observations within FactorLevel , and 
is the ``group'' mean (i.e., mean of means). Compute the entries in the following table,obtaining the P-Value corresponding to the calculated F-Ratio of themean squared values | (6) |
| Category | SS | °Freedom | Mean Squared | F-Ratio"> F-Ratio |
| Treatment | SSA |  |  |  |
| Error | SSE |  |  | |
| Total | SST |  |  |
If the P-Value is small, reject the Null Hypothesis that all Means are the same for thedifferent groups.
See also Factor Level,Replicate, Variance- Sphere Point Picking
- Sphere-Sphere Intersection
- Sphere with Tunnel
- Spherical Bessel Differential Equation
- Spherical Bessel Function
- Spherical Bessel Function of the First Kind
- Spherical Bessel Function of the Second Kind
- Spherical Bessel Function of the Third Kind
- Spherical Cap
- Spherical Coordinates
- Spherical Design
- Spherical Excess
- Spherical Frustum
- Spherical Geometry
- Spherical Hankel Function of the First Kind
- Spherical Hankel Function of the Second Kind
- Spherical Harmonic
- Spherical Harmonic Addition Theorem
- Spherical Harmonic Closure Relations
- Spherical Harmonic Tensor
- Spherical Helix
- Spherical Point System
- Spherical Polygon
- Spherical Ring
- Spherical Sector