How do I calculates the noncentrality parameter from the noncentral t-distribution.

[Snuffy Dog]

Hi all,

 

Is there a way for me to calculate the noncentrality parameter from the lower (and upper) cumulative distribution function of the noncentral t-distribution.

For example, given:

 

cumultive distribution = 8.2219

percentile = .975

degrees of freedom = 9

 

Given these values above I need to work out the noncentrality parameter?  (the solution should give a value of 3.96 lower and 12.39 upper)

 

I need a spss function or syntax to work this out?

 

Any help is greatly appreciated.

 

Kind regards,

 

Jack Thomas

[MaxJasper]

You can use Normal dist approximation to non-central t-dist to get its inverse for calculating delta=non-central parameter:

P(t | df, delta) =~ P(x) = Normal dist

where:

x=[t*(1-1/4df)-delta]/sqrt[1+t^2/2df]