<unk>  (Snedecor and Cochran, 1983) is used to test if k samples have equal variances.  Equal variances across samples is called homoscedasticity or homogeneity of variances. Some statistical tests, for example the analysis of variance, assume that variances are equal across groups or samples. The<unk>  test can be used to verify that assumption.<unk>  is sensitive to departures from normality. That is, if your samples come from non-normal distributions, then<unk>  may simply be testing for non-normality. The Levene test is an alternative to the<unk>  test that is less sensitive to departures from normality.<unk>  is used to test the null hypothesis, 
H
0
{\displaystyle H_{0}}
 that all k population variances are equal against the alternative that at least two are different.
If there are k samples with size 
n
i
{\displaystyle n_{i}}
 and sample variance 
S
i
2
{\displaystyle S_{i}^{2}}
 then<unk>  statistic is
X
2
=
(
N
−
k
)
ln
⁡
(
S
p
2
)
−
∑
i
=
1
k
(
n
i
−
1
)
ln
⁡
(
S
i
2
)
1
+
1
3
(
k
−
1
)
(
∑
i
=
1
k
(
1
n
i
−
1
)
−
1
N
−
k
)
{\displaystyle X^{2}={\frac {(N-k)\ln(S_{p}^{2})-\sum _{i=1}^{k}(n_{i}-1)\ln(S_{i}^{2})}{1+{\frac {1}{3(k-1)}}\left(\sum _{i=1}^{k}({\frac {1}{n_{i}-1}})-{\frac {1}{N-k}}\right)}}}
where 
N
=
∑
i
=
1
k
n
i
{\displaystyle N=\sum _{i=1}^{k}n_{i}}
 and 
S
p
2
=
1
N
−
g
∑
i
(
n
i
−
1
)
S
i
2
{\displaystyle S_{p}^{2}={\frac {1}{N-g}}\sum _{i}(n_{i}-1)S_{i}^{2}}
 is the pooled estimate for the variance.
The test statistic has approximately a 
χ
k
−
1
2
{\displaystyle \chi _{k-1}^{2}}
 distribution. Thus the null hypothesis is rejected if 
X
2
>
χ
k
−
1
,
α
2
{\displaystyle X^{2}>\chi _{k-1,\alpha }^{2}}
 (where 
χ
k
−
1
,
α
2
{\displaystyle \chi _{k-1,\alpha }^{2}}
 is the upper tail critical value for the 
χ
k
−
1
2
{\displaystyle \chi _{k-1}^{2}}
 distribution).<unk>  is a modification of the corresponding likelihood ratio test designed to make the approximation to the 
χ
k
−
1
2
{\displaystyle \chi _{k-1}^{2}}
 distribution better (M. S.<unk>  1937).
Bartlett's test
Shapiro-Wilk test
Brown-Forsythe test
ANOVA-simultaneous component analysis
Kendall tau rank correlation coefficient
Cohen's kappa
Analysis of rhythmic variance
Wilcoxon signed-rank test