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Data analysis techniques that rely on standard statistical tools and algorithms often encounter problems when dealing with data sets that have large sample sizes. In this study, two statistical tests done in conducting simple linear regression analysis were revisited. In particular, the study simulated the effects of large sample sizes and amount of contamination in the data due to non-sampling errors on the false positive rate of the Kolmogorov-Smirnov (K-S) test in testing for normality of error terms. The study also characterized the effects of varying sample size and amount of contamination in the data on the false negative rate of the t-test in testing the significance of a regression coefficient. Lastly, an optimality index was developed to determine the sample sizes and the values of the percent noise at which both the false positive rate of the K-S test and the false negative rate of the t-test are minimized. [ABSTRACT FROM AUTHOR]

Suppose we have k samples X 1 , 1 , ... , X 1 , n 1 , ... , X k , 1 , ... , X k , n k with different sample sizes n 1 , ... , n k and unknown underlying distribution functions F 1 , ... , F k as observations plus k families of distribution functions { G 1 (· , ϑ) ; ϑ ∈ Θ } , ... , { G k (· , ϑ) ; ϑ ∈ Θ } , each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not (F 1 , ... , F k) belongs to the parametric family { (G 1 (· , ϑ) , ... , G k (· , ϑ)) ; ϑ ∈ Θ }. New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions. [ABSTRACT FROM AUTHOR]