Nonparametric comparison of two histograms

Area of Science:

• Statistics
• Nonparametric Statistics
• Statistical Tests

Background:

• The Anderson-Darling k-sample test is a nonparametric statistic used for grouped data.
• Scholz and Stephens (1987) introduced a version of this test for grouped data.
• Existing methods may lack power when testing for alternatives beyond location shifts.

Purpose of the Study:

• To introduce and evaluate a partition-of-chi 2 method as an alternative nonparametric test for grouped data.
• To demonstrate the superior power of this new method compared to the Anderson-Darling statistic, especially for complex alternatives.
• To provide a practical example motivating the use of the proposed statistical test.

Main Methods:

• Comparison of a partition-of-chi 2 method with the nonparametric k-sample Anderson-Darling statistic.
• Evaluation of statistical power under various alternative hypotheses, focusing on non-location shift alternatives.
• Application of the methods to a taste-test example for illustrative purposes.

Main Results:

• The partition-of-chi 2 method demonstrates greater statistical power for nonparametric k-sample tests on grouped data.
• This enhanced power is particularly evident when the alternative hypothesis involves deviations other than a simple location shift.
• The taste-test example effectively illustrates the practical advantages of the partition-of-chi 2 approach.

Conclusions:

• The partition-of-chi 2 method represents a more powerful nonparametric statistical test for grouped data.
• This method is recommended when testing for general alternatives, not limited to location shifts.
• The findings suggest a valuable alternative for statistical analysis in various fields using grouped data.