# class Statsample::Test::BartlettSphericity

## Bartlett's test of Sphericity.¶ ↑

Test the hyphotesis that the sample correlation matrix comes from a multivariate normal population where variables are independent. In other words, the population correlation matrix is the identity matrix.

## Reference¶ ↑

• Dziuban, C., & Shirkey E. (1974). When is a correlation matrix appropriate for factor analysis? Some decision rules. Psychological Bulletin, 81(6), 358-361.

## Bartlett's test of Sphericity.¶ ↑

Test the hyphotesis that the sample correlation matrix comes from a multivariate normal population where variables are independent. In other words, the population correlation matrix is the identity matrix.

## Reference¶ ↑

• Dziuban, C., & Shirkey E. (1974). When is a correlation matrix appropriate for factor analysis? Some decision rules. Psychological Bulletin, 81(6), 358-361.

df[R]
name[RW]
ncases[R]
nvars[R]
value[R]

### Public Class Methods

new(matrix,ncases) click to toggle source

Args

• matrix: correlation matrix

• ncases: number of cases

```# File lib/statsample/test/bartlettsphericity.rb, line 21
def initialize(matrix,ncases)
@matrix=matrix
@ncases=ncases
@nvars=@matrix.row_size
@name=_("Bartlett's test of sphericity")
compute
end```

### Public Instance Methods

compute() click to toggle source

Uses SPSS formula. On Dziuban & Shirkey, the minus between the first and second statement is a *!!!

```# File lib/statsample/test/bartlettsphericity.rb, line 32
def compute
@value=-((@ncases-1)-(2*@nvars+5).quo(6))*Math::log(@matrix.determinant)
@df=(@nvars*(@nvars-1)).quo(2)
end```
probability() click to toggle source
```# File lib/statsample/test/bartlettsphericity.rb, line 36
def probability
1-Distribution::ChiSquare.cdf(@value,@df)
end```