umber of the case expressions, ݔ௜ is the i control expression and

k^th sorted case expression,

ܢൌሺݔଵ, ݔଶ, ⋯, ݔ௡, ݕଵᇲ, ݕଶᇲ, ⋯, ݕ௠ᇲሻ

(6.32)

mulative S statistic is defined as below,

ܵ௥ൌ෍ݖ௜

௥

௜ୀଵ

(6.33)

d on the S statistic, the likelihood ratio statistic is defined as below,

ߣൌ

max

௡ழ௜ழ௡ା௠

݅ܵ௡ା௠ሺ݊൅݉ሻ

⁄

െܵ௜

ඥ݅ሺ1 െ݅/2ሻ

(6.34)

proximate significance level will be calculated for the likelihood

, 2008].

e bimodality index test approach

odality index test approach assumes that the expressions of a

gene follow a mixture of two Gaussians. It also joins the control

and the case replicates together into one vector for the test. The

model for the bimodality index test is shown below, where ݖ௜

r the i^th expression in z, ߤଵ and ߤଶ stands for the mean values of

sians, ߪଵ

ଶ and ߪଶ

ଶ stand for the variances of two Gaussians,

ܢ~ߨ࣡ሺߤଵ, ߪଵ

ଶሻ൅ሺ1 െߨሻ࣡ሺߤଶ, ߪଶ

ଶሻ

(6.35)

imodality index simplifies the model using a uniform variance,

ൌߪଵ

ଶൌߪଶ. Therefore a standardised distance is defined by the

ty index by which the null hypothesizes is ࣢଴: ߜൌ0

ߜൌ

|ߤଵെߤଶ|

ߪ

(6.36)