Texas Instruments 84PLSECLM1L1T Guidebook - Page 393

df(x, n1-1 , n2-1 ) = Ûpdf( ) with degrees of freedom df, n1-1 , and n2-1 p = reported p value 2-SampÜTest for the alternative hypothesis σ1 > σ2 . α p = ∫ f(x,n1 - 1,n2 - 1)dx F 2-SampÜTest for the alternative hypothesis σ1 < σ2 . F p = ∫ f(x,n1 - 1,n2 - 1)dx 0 2-SampÜTest for the alternative hypothesis s1 ƒ s2. Limits must satisfy the following: Lbnd ∞ p-- = 2 ∫ f(x,n1 - 1,n2 - 1)dx = ∫ f(x,n1 - 1,n2 - 1)dx 0 Ubnd where: [Lbnd,Ubnd] = lower and upper limits The Ü-statistic is used as the bound producing the smallest integral. The remaining bound is selected to achieve the preceding integral's equality relationship. 2-SampTTest The following is the definition for the 2-SampTTest. The two-sample t statistic with degrees of freedom df is: t = x---1----------x---2S where the computation of S and df are dependent on whether the variances are pooled. If the variances are not pooled: S = S----x---1--2- + -S---x---2--2n1 n2 ⎛ ⎜ S----x---1--2- + -S---x---2--2-⎟⎞ 2 df n----1 n----2 ------1-------n1 - 1 ⎛ ⎜ ⎝ S---n-x---11--2-⎠⎟⎞ 2 + -n---2--1-------1 S---n-x---22--2-⎠⎟⎞ 2 Appendix B: Reference Information 386