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The cumulative tdistribution of Student is used in the Ttester model calculator to test the difference between the means of data sets. 
The confidence interval of the difference of mean values of data series is shown in green color. This interval is used by Ttester model calculator in Student's ttest 
MATHEMATICS The tTester software model 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. 