Rank-permutation tests for behavior analysis, and a test for trend allowing unequal data numbers for each subject

Area of Science:

• Statistics
• Behavioral Science
• Data Analysis

Background:

• Null-hypothesis significance testing (NHST) in behavioral science often relies on methods with restrictive assumptions.
• Traditional statistical tests may require data to follow specific distributions or be measured on an interval scale.
• These assumptions can limit the applicability and validity of NHST for diverse behavioral datasets.

Purpose of the Study:

• To advocate for rank-permutation tests as a superior alternative for NHST in behavioral data analysis.
• To introduce a novel algorithm for computing exact probabilities in rank-permutation tests.
• To develop and extend rank-permutation tests for analyzing monotonic trends, accommodating unequal observations per subject.

Main Methods:

• Development of an exact-probability algorithm for rank-permutation tests, avoiding large-sample approximations or resampling.
• Application of rank-permutation tests to detect monotonic trends in behavioral data.
• Extension of the rank-permutation test to handle subjects with varying numbers of data points.

Main Results:

• The proposed algorithm enables exact-probability rank-permutation tests, enhancing precision.
• A rank-permutation test for monotonic trend is presented, suitable for behavioral data.
• An extension allows for unequal observations per subject, increasing the test's flexibility.
• An extended table of critical values and software tools are provided for practical application.

Conclusions:

• Rank-permutation tests offer a powerful and assumption-free approach to NHST for behavioral data.
• The developed algorithm and extended test provide precise and flexible tools for trend analysis.
• These methods enhance the reliability of statistical inference in behavioral research.