
Download: tTester tdistribution calculator Go to: software & models articles & manuals reports case studies FAQ's & papers home page 
tTester graphics in accordance to data in the
above screenprint 

MATHEMATICS The tTester software uses a numerical solution of the cumulative t distribution function and from that it derives the t probability density by numerical differentiation. Numerical approximation of Student's t (probability) distribution. Using: T = reference value for the Xvariable following the tdistribution, Po = intermediate probability variable, Pc(T) = cumulative probability of T, and Pc(T) = P(X < T) , the following equations hold: N (degrees of freedom) even : Po = sin(z) [1 + cos^{2}(z) / 2 + 3 cos^{4}(z) / 8 + 15 cos^{6}(z) / 48 + 105 cos^{8}(z) / 384 + . . . ] N (degrees of freedom) uneven (odd) and >1 : Po = 2Z/pi + (2/pi)cos(z).sin(Z) [1 + 2 cos^{2}(z) / 3 + 8 cos^{4}(z) / 15 + 48 cos^{6}(z) / 105 + . . . ] N (degrees of freedom) = 1 : Po = 2z / pi where : z = arctan(T / sqrt(N) , and pi = 22 / 7 Now : when T is positive: Pc(T) = Po + (1Po) / 2 when T is negative: Pc(T) = (1Po) / 2 The number of terms between the parentheses [ ] to be used is N / 2 when N is even and (N1) / 2 when N is uneven (odd). 
The flowers are here to make the mathematics less boring. 