Dictionary of Evidence-based Medicine.pdf

F
Factor cost (see under Gross domestic product)
Fail-safe number
For a variety of reasons, notably the preference of authors to submit studies
with positive results rather than negative results for publication, studies in
the former group are more likely to be published. Therefore estimates of
effect based on the results of studies in the public domain may be biased.
Therefore when undertaking meta-analyses, a critical assessment of the
potential threats to the validity of the estimates of effect is necessary.
Rosenthal suggested calculating the number of studies needed to nullify
any effect observed (Rosenthal R (1979) The 'file drawer problem' and
tolerance of null results. Psychological Bulletin. 86: 638-41) and Cooper
suggested calling this number the 'fail-safe sample size' (Cooper H (1979)
Statistically combining independent studies: a meta-analysis of sex differences
in conformity research. Journal of Personality and Social Psychology. 37:
131^46). This number, which is now generally referred to as the fail-safe
number, is calculated as follows:
Suppose that there are k published studies and the significance level for
these studies are p v p v py-,p^ Postulate the null hypothesis that the mean
effect is zero and that each p i is uniformly distributed on [0,1]. Let Z ; be the
standard normal variate associated with each p { . Z { is then given by Z ; = O" 1
(1 - p.) where O is the standard normal cumulative distribution function.
Let S k = Zj + Z 2 + ... + Z n and z a be the critical value for a one-sided test at
a significance level of a for a normally distributed mean effect. The failsafe
N is then calculated by solving the following equation.
Fallacy of composition
The fallacy of composition is the error made by wrongly generalizing to
groups the results which apply to individuals. In economic theory, two