# Levene Test for Equality of Variances¶ ↑

From NIST/SEMATECH: <blockquote>Levene's test ( Levene, 1960) is used to test if k samples have equal variances. Equal variances across samples is called homogeneity of variance. Some statistical tests, for example the analysis of variance, assume that variances are equal across groups or samples. The Levene test can be used to verify that assumption.</blockquote> Use:

```require 'statsample'
a=[1,2,3,4,5,6,7,8,100,10].to_scale
b=[30,40,50,60,70,80,90,100,110,120].to_scale

levene=Statsample::Test::Levene.new([a,b])
puts levene.summary
```

Output:

```Levene Test
F: 0.778121319848449
p: 0.389344552595791```

Reference:

# Levene Test for Equality of Variances¶ ↑

From NIST/SEMATECH: <blockquote>Levene's test ( Levene, 1960) is used to test if k samples have equal variances. Equal variances across samples is called homogeneity of variance. Some statistical tests, for example the analysis of variance, assume that variances are equal across groups or samples. The Levene test can be used to verify that assumption.</blockquote> Use:

```require 'statsample'
a=[1,2,3,4,5,6,7,8,100,10].to_scale
b=[30,40,50,60,70,80,90,100,110,120].to_scale

levene=Statsample::Test::Levene.new([a,b])
puts levene.summary
```

Output:

```Levene Test
F: 0.778121319848449
p: 0.389344552595791```

Reference:

### Attributes

d1[R]

Degrees of freedom 1 (k-1)

d2[R]

Degrees of freedom 2 (n-k)

name[RW]

Name of test

### Public Class Methods

new(input, opts=Hash.new()) click to toggle source

Input could be an array of vectors or a dataset

```# File lib/statsample/test/levene.rb, line 31
def initialize(input, opts=Hash.new())
if input.is_a? Statsample::Dataset
@vectors=input.vectors.values
else
@vectors=input
end
@name=_("Levene Test")
opts.each{|k,v|
self.send("#{k}=",v) if self.respond_to? k
}
compute
end```

### Public Instance Methods

f() click to toggle source

Value of the test

```# File lib/statsample/test/levene.rb, line 44
def f
@w
end```
probability() click to toggle source

Probability. With H_0 = Sum(s2)=0, probability of getting a value of the test upper or equal to the obtained on the sample

```# File lib/statsample/test/levene.rb, line 81
def probability
p_using_cdf(Distribution::F.cdf(f, @d1, @d2), :right)
end```