One-sided and two-sided tests and ρ values

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Abstract
Several considerations for the use of one-sided and two-sided tests are discussed: the inferential posture of the design of a study, the level of stringency for supporting a conclusion, the style for reporting ρ values, the perspective for interpreting results in the opposite direction to the one initially expected, and the role of confidence intervals. The suggestions for addressing these issues for confirmatory biopharmaceutical studies with one-sided objectives are as follows: 1. Clear documentation of the one-sided inferential posture of a study in its protocol 2. Sufficient sample size for at least moderate power for evaluation with two-sided stringency 3. Use of one-sided ρ values to express direction of results together with distinct flags for those which are suitably extreme to support inferences for the target direction or to merit description for the opposite direction 4. Interpretation of opposite direction results in a post hoc, exploratory, descriptive way rather than inferentially 5. Provision of one-sided confidence intervals to clarify the nature of one-sided inferences Alternatively, for academic studies where publication with an inferential posture is of interest for either potential direction of findings, two-sided methods are typically useful. An underlying reason for this is the adjustment provided by two-sided methods for the multiplicity in the two complementary one-sided counterparts that they encompass.

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