“What data will show the truth?” is a fundamental question emerging early in any empirical investigation. From a statistical perspective, experimental design is the appropriate tool to address this question by ensuring control of the error rates of planned data analyses and of the ensuing decisions. From an epistemological standpoint, planned data analyses describe in mathematical and algorithmic terms a pre-specified mapping of observations into decisions. The value of exploratory data analyses is often less clear, resulting in confusion about what characteristics of design and analysis are necessary for decision making and what may be useful to inspire new questions. This point is addressed here by illustrating the Popper-Miller theorem in plain terms and using a graphical support. Popper and Miller proved that probability estimates cannot generate hypotheses on behalf of investigators. Consistently with Popper-Miller, we show that probability estimation can only reduce uncertainty about the truth of a merely possible hypothesis. This fact clearly identifies exploratory analysis as one of the tools supporting a dynamic process of hypothesis generation and refinement which cannot be purely analytic. A clear understanding of these facts will enable stakeholders, mathematical modellers and data analysts to better engage on a level playing field when designing experiments and when interpreting the results of planned and exploratory data analyses.

“什么数据能证明真相？” 是任何实证调查早期出现的一个基本问题。从统计的角度来看，实验设计是通过确保控制计划数据分析和随后决策的错误率来解决这个问题的合适工具。从认识论的角度来看，计划数据分析用数学和算法术语描述了预先指定的观察到决策的映射。探索性数据分析的价值通常不太明确，导致人们混淆了哪些设计和分析特征对于决策制定是必要的，哪些可能有助于激发新问题。此处通过以简单的术语说明波普尔-米勒定理并使用图形支持来解决这一点。波普尔和米勒证明，概率估计不能代表调查人员产生假设。与 Popper-Miller 一致，我们表明概率估计只能减少对仅可能假设的真实性的不确定性。这一事实清楚地表明，探索性分析是支持假设生成和改进的动态过程的工具之一，而这种动态过程不能纯粹是分析性的。清楚地了解这些事实将使利益相关者、数学建模者和数据分析师在设计实验以及解释计划和探索性数据分析的结果时更好地参与公平竞争。我们表明概率估计只能减少对一个可能的假设的真实性的不确定性。这一事实清楚地表明，探索性分析是支持假设生成和改进的动态过程的工具之一，而这种动态过程不能纯粹是分析性的。清楚地了解这些事实将使利益相关者、数学建模者和数据分析师在设计实验以及解释计划和探索性数据分析的结果时更好地参与公平竞争。我们表明概率估计只能减少对一个可能的假设的真实性的不确定性。这一事实清楚地表明，探索性分析是支持假设生成和改进的动态过程的工具之一，而这种动态过程不能纯粹是分析性的。清楚地了解这些事实将使利益相关者、数学建模者和数据分析师在设计实验以及解释计划和探索性数据分析的结果时更好地参与公平竞争。