This book covers some recent developments in statistical inference. The author's main aim is to develop a theory of generalized p-values and generalized confidence intervals and to show how these concepts may be used to make exact statistical inferences in a variety of practical applications. In particular, they provide methods applicable in problems involving nuisance parameters such as those encountered in comparing two exponential distributions or in ANOVA without the assumption of equal error variances. The generalized procedures are shown to be more powerful in detecting significant experimental results and in avoiding misleading conclusions.