THE MAD TEST FOR LARGE SAMPLE COMPARISONS
Ramnath Takiar
Flat N0.11, 3rd Floor, Building # 9, 1st Khoroo,
Ulaanbaatar district, Ulaanbaatar, Mongolia- 14241, and
Scientist G – (Retired),
National Centre for Disease Informatics and Research
(NCDIR), Indian Council of Medical Research (1978-2013)
Bangalore – 562110, Karnataka, India
Email: ramnathtakiar@gmail.com,
ramnath_takiar@yahoo.co.in
Abstract
In a recent
study, a test based on the Mean Absolute Deviation (MAD)
was developed and demonstrated superior performance
compared to the t-test (Takiar R, 2024). This study aims to
extend the application of the MAD test to the large
samples. The test fundamentally utilizes the relationship
between the Range and the Mean Absolute Deviation,
proposing several critical scores associated with sample
size to assess the comparability of two samples.
The MAD test
recommends critical scores of 2, 3, and 4 for the sample
sizes of less than 50, between 50 and 99, and greater than
100, respectively. A score exceeding the suggested
threshold for the specified sample size indicates
significant differences in the distributions of the
samples. Conversely, a score equal to or less than the
threshold suggests comparable distributions among the
samples.
For the present
study, two pairs of normal populations, each consisting of
200 observations, were generated using an Excel function:
(P1, P2) and (P3, P4) with Skewness and Kurtosis values
closer to 0. From each population, 500 random samples of
sizes 30, 50, 75, 100, 125, 150, and 175 were generated
using a V-basic program and compared within each set of
(P1, P2) and (P3, P4). All sample comparisons were
conducted using both the Z-test and the MAD test, with a
focus on comparing their significant results. On average,
the MAD test resulted in 86.7% of correct decisions,
compared to 89.0% observed with the Z-test. Therefore, the
MAD test can be claimed as performing comparably to the
Z-test. Notably, the applications of the MAD test have
shown to be consistently effective, regardless of the
sample size being small (below 30) or large (above 30).
Keywords: Test
of Significance, MAD test, Z-test, Performance
