The authors use "conventional statistical significance tests" to
compare the baseline characteristics of the two randomised groups,
treating the two trials separately. The use of tests such as the t-test or
F-test is questionable here.
There is no indication that the initial diet-trial group of subjects
from which the two subgroups were randomly selected was itself selected
from a well-defined population.
Therefore, it is reasonable to assume that the implied model is what
Lehmann [1, page 5] calls a "Randomization Model." In this model, there
are no populations, and, consequently, there are no population means or
variances and tests about such parameters are meaningless.
Further, since the only source of randomness, in the diet and other
similar trials, is through the purported randomization, the only purpose
of testing for baseline covariate balance, is to check whether there has
truly been random allocation to the two groups. As the randomization is
actually in question in the diet trial, the use of a formal tests is
justified here.
When there is no underlying population (distribution), one is forced
to use distribution-free procedures with vague hypotheses.[see Lehmann
[1], pages 22-24
and 31-32] The issue is not one of robustness against departures from
Normality but one of the nonexistence of an underlying distribution.
References:
[1] Lehmann EL, D'Abrera HJM. Nonparametrics: Statistical Methods
Based on Ranks. Holden-Day, 1975.
Competing interests:
None declared
Competing interests:
No competing interests
24 August 2005
David Wolfson
Professor
Nora Bohossian
Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 2K6
Rapid Response:
Letter to the British Medical Journal (BMJ)
The authors use "conventional statistical significance tests" to
compare the baseline characteristics of the two randomised groups,
treating the two trials separately. The use of tests such as the t-test or
F-test is questionable here.
There is no indication that the initial diet-trial group of subjects
from which the two subgroups were randomly selected was itself selected
from a well-defined population.
Therefore, it is reasonable to assume that the implied model is what
Lehmann [1, page 5] calls a "Randomization Model." In this model, there
are no populations, and, consequently, there are no population means or
variances and tests about such parameters are meaningless.
Further, since the only source of randomness, in the diet and other
similar trials, is through the purported randomization, the only purpose
of testing for baseline covariate balance, is to check whether there has
truly been random allocation to the two groups. As the randomization is
actually in question in the diet trial, the use of a formal tests is
justified here.
When there is no underlying population (distribution), one is forced
to use distribution-free procedures with vague hypotheses.[see Lehmann
[1], pages 22-24
and 31-32] The issue is not one of robustness against departures from
Normality but one of the nonexistence of an underlying distribution.
References:
[1] Lehmann EL, D'Abrera HJM. Nonparametrics: Statistical Methods
Based on Ranks. Holden-Day, 1975.
Competing interests:
None declared
Competing interests: No competing interests