Comparisons of continuous and discrete methods for combining probability values associated with matched-pairs t-test...

Area of Science:

• Statistics
• Biostatistics
• Probability Theory

Background:

• Fisher's continuous method is widely used for combining independent probability values.
• The method assumes continuous probability distributions, which may not apply to discrete data.
• Assessing the suitability of Fisher's method for discrete distributions is crucial for accurate statistical inference.

Purpose of the Study:

• To compare Fisher's continuous method with an exact discrete analog for combining probability values from discrete distributions.
• To evaluate the adequacy of Fisher's method when applied to discrete data, particularly in the context of matched-pairs t-test data.
• To determine if the discrete analog method offers improved detection of effects compared to the continuous method.

Main Methods:

• Utilized matched-pairs t-test data to simulate discrete distributions.
• Applied Fisher's continuous method for combining probability values.
• Developed and applied an exact discrete analog method for combining probability values.
• Compared the sensitivity and accuracy of both methods in detecting a known effect.

Main Results:

• Fisher's continuous method demonstrated inadequacy when applied to discrete probability values due to its inherent continuity assumption.
• The exact discrete analog method successfully detected a well-documented effect that was missed by Fisher's continuous method.
• The continuity assumption of Fisher's method leads to a loss of statistical power for discrete distributions.

Conclusions:

• Fisher's continuous method is not suitable for combining probability values from discrete distributions.
• The exact discrete analog method provides a more accurate and sensitive approach for analyzing discrete probability data.
• Employing discrete-specific methods is essential for robust statistical analysis when dealing with discrete distributions.