A fortune cookie problem: A test for nominal data whether two samples are from the same population of equally likely...

Area of Science:

• Statistics
• Probability Theory
• Data Analysis

Background:

• Comparing datasets is crucial in various scientific fields.
• Determining if multiple collections share a common underlying distribution is a fundamental statistical problem.
• Existing methods may lack precision for small sample sizes or specific distribution assumptions.

Purpose of the Study:

• To develop and present a novel statistical test for assessing the uniformity hypothesis between two object collections.
• To provide a precise method for calculating the exact p-value based on observed data overlaps.
• To offer an interval estimation technique for the number of distinct objects within these collections.

Main Methods:

• The study employs a hypothesis testing framework to compare two collections.
• Exact p-values are derived from the distribution of observed overlaps.
• An interval estimation approach is utilized to quantify the number of unique objects.

Main Results:

• The proposed method allows for the exact calculation of p-values, offering a precise measure of statistical significance.
• An interval estimate for the number of distinct objects is provided, giving a range of plausible values.
• The methodology is applicable to scenarios where objects are drawn from a uniform distribution.

Conclusions:

• The presented approach offers a statistically rigorous way to test the sameness hypothesis for uniform distributions.
• The exact p-value calculation enhances the reliability of hypothesis testing in comparative studies.
• The interval estimation of distinct objects provides valuable insights into dataset composition.