The simplest statistical test: how to check for a difference between treatmentsBMJ 2006; 332 doi: https://doi.org/10.1136/bmj.332.7552.1256 (Published 25 May 2006) Cite this as: BMJ 2006;332:1256
All rapid responses
Beyond Chi-square test
Professor S.J.Pocock1 in an excellent article describes in details a very
useful, simple test. As he points out later in the same article, when
events relate to a fixed follow-up time, for any trial publication one
needs to apply Chi-square test (though this is a distribution, usual form
is referred here) which is a very versatile, useful, popular and most
frequently used test of significance. However, unfortunately in few
situations this test (i) has very less power (e.g. testing the effect of
time series analysis of qualitative data i.e. seasonality); (ii) not
appropriate (e.g. testing the effect of birth order); (iii) will not lead
to any meaningful conclusion (e.g. to evaluate the effect of any
intervention programme with respect to some categorical response variable,
data are/were arranged in a change table). In such situations a specific
test (specially developed for that specific purpose) should be used. Such
alternative specific tests are described in literature2,3.
Generally comparison of two proportions is performed using the
normality test (with continuity correction) which is equivalent to Chi-
square test (test statistic is square root of Chi-square). Nevertheless,
it is very essential to make or understand clearly whether they are from
paired samples/data. In that case a modified test should be used2. Best
way to estimate 95% Confidence Interval (by recommended method due to
Wilson for ‘paired’ samples) is to use the computer software accompanying
an excellent book by Altman et al.4 called CIA. In general, for
multichotomous outcome a best choice is Chochran’s ‘Q’ test which is a
sort of multichotomous extension of McNemar test3. Application of Q test
can also be seen at many places in literature5.
One very often has to deal with data where categories are ordered and
then Chi-square test is not desirable to be applied as it ignores the
ordering. RIDIT analysis is the best choice in such situation which is
described in details with example2 and was available in DOS version of WHO
-CDC’s popular EPI-INFO software (can be downloaded free from
Though, the material covered and the solutions offered are well known
in the literature, it is sometimes necessary, to make a point about an
otherwise well-known situation from a particular pedagogical or didactic
angle. This is not to claim that anything suggested above is new, the
purpose is just to highlight this fact as recently we have seen its
importance in practice. And as one of the very important aspects of
Medical Research is ‘use of appropriate test of significance / statistical
technique to analyze the data’. Many times in the field of medical/bio
sciences the data are collected meticulously with tremendous efforts but
finally analyzed hurriedly by wrong choice of method(s).
1. Pocock S.J. (2006). The simplest statistical test: how to check for a
difference between treatments. Br.Med.J. 332:1256-1258 (27 May),
2. Sarmukaddam S.B. (2006). Fundamentals of Biostatistics. Jaypee Brothers
Medical Publishers Ltd., New Delhi, India.
3. Indrayan A., and Sarmukaddam S.B. (2001). Medical Biostatistics. Marcel
Dekker, Inc., New York, USA.
4. Altman, D.G., Machin, D., Bryant, T.N., and Gardner, M.S. (2000).
Statistics with confidence. BMJ Books, London, U.K.
5. Parlikar V., Sarmukaddam S., Agashe M., and Weiss M. (2007). Diagnostic
concordance of neurasthenia spectrum disorders in Pune, India. Soc
Psychiatry Psychiatr. Epidemiol., 42: 561-572.
Sanjeev B. Sarmukaddam
Maharashtra Institute of Mental Health,
Sassoon Hospital Campus, Pune, India.
Competing interests: No competing interests