Exploring the Relationship Between Confidence Level Selection and Statistical Error Rates in Hypothesis Testing

Posted: Apr 20, 2019

• Austin Rivera
• Benjamin Cox
• Blake Henderson

Abstract

Hypothesis testing represents a cornerstone of statistical inference, providing a formal framework for making decisions about population parameters based on sample data. The selection of confidence levels, typically set at 95% or 99%, has become deeply entrenched in scientific practice across diverse disciplines. However, this conventional approach often lacks rigorous justification and fails to account for the specific contextual factors that influence statistical error rates. The relationship between confidence level selection and the resulting balance between Type I and Type II errors remains inadequately explored in the statistical literature. Traditional statistical education emphasizes the importance of controlling Type I errors at predetermined levels, typically 0.05 or 0.01, while paying comparatively less attention to the consequential impact on Type II error rates. This imbalance can lead to suboptimal decision-making in research contexts where the consequences of different types of errors vary substantially. For instance, in clinical trials for life-saving treatments, the cost of a Type II error (failing to detect an effective treatment) may far exceed that of a Type I error (falsely claiming effectiveness). This research addresses several critical gaps in current statistical practice. First, we investigate how confidence level selection interacts with sample size and effect size to influence overall error rates. Second, we develop a methodological framework for dynamically selecting confidence levels based on the specific research context and the relative costs of different error types. Third, we provide empirical evidence challenging the universal applicability of standard confidence levels across diverse research scenarios. Our approach represents a departure from conventional statistical practice by treating confidence level selection as an optimization problem rather than a matter of convention. By explicitly considering the trade-offs between different types of errors and their contextual consequences, we aim to provide researchers with a more nuanced and principled approach to hypothesis testing.