European Journal of Scientific Research - EuroJournals

321 Nadia Saeed, Muhammad Khalid Pervaiz and Muhammad Qaiser Shahbaz
2.2. Variance
Another situation exists when someone is interested to find the right variance (Birkett & Day, 1994;
Gould, 1995; Browne, 1995; Shih & Zhao, 1997) since some of the power functions usually involve
parameters unrelated to the hypotheses. Most notably, they often involve one or more variances. For
instance we need to know the residual variance of the measurements in the planned two-sample
experiments, there may be substantial uncertainty in variance estimates obtained from historical or
pilot data. There is some literature on dealing with variation in pilot data; a good starting point is
Taylor and Muller (1995). Also, Muller and Benignus (1992) and Thomas (1997) discuss various
simpler ways of dealing with these issues, such as sensitivity analyses.
2.3. Issues and Prior Information
At times the researcher has no choice about sample size. Often a study has limited budget. Sample size
determination is an important issue because not all sample-size problems are the same, nor is sample
size equally important in all studies. For example, the ethical issues in an opinion poll are very
different from those in a medical experiment, and the consequences of an over or under-sized study
also differ. Additional complications can hold for attribute data due to failures of asymptotic tests and
inability to achieve a stated size due to discreteness or unusual situations such as inferences about rare
attributes (Wright, 1997) and in case of Poisson and logistic regression (Whittemore, 1981; Hsieh,
1989; Flack & Eudey, 1993; Bull, 1993 and Signorini, 1991). There are numerous articles, especially
in biostatistics journals, concerning sample-size determination for specific tests like tests of continuous
variables (Cohen, 1969; Pearson & Hartley, 1970 and Day & Graham, 1991). The extent to which
sample size is adequate or inadequate in published studies provided by Freiman, Chalmers, Smith, and
Kuebler, (1986). They worked on the importance of beta, the type-II error and sample size in the
design and interpretation of the randomized controlled trial. Sample size determination can be done
with the help of softwares. There is a growing amount of software for sample-size determination,
including Query Advisor (Elashoff, 2000), PASS (Hintze, 2000), UnifyPow (O’Brien, 1998), and
Power and Precision (Borenstein, 1997). Similarly Web resources include a comprehensive list of
power-analysis software and online calculators (Thomas, 1998; Lenth, 2000). Wheeler (1974) provided
some useful approximations for use in linear models; Castelloe (2000) gave an up-to-date overview of
computational methods.
Though it is an important issue with respect to Statistics, social sciences and natural sciences
but there is surprisingly small amount of published literature. One step in the sample size problem
requires eliciting an effect size of scientific interest. It is not up to statistical consultant to decide this;
however, it is his responsibility to try to elicit this information from the researchers involved in
planning the study. Boen & Zahn (1982) discussed some of the human dynamics involved in
discussing sample size (mostly as distinct from effect size). They suggested asking directly for an
upper bound on sample size, relating that most clients will respond readily to this question.
2.4. Clinical Trials
Adequate sample size can help to ensure academically interesting result, whether or not a statistically
significant difference is eventually found in the study (Eng & Siegelman, 1997). There is a need to
know that how certain study design characteristics affect sample size and how to calculate sample size
for several simple study designs, which are discussed in different scientific fields especially in clinical
trials (Eng, 2003). An inadequate sample size also has ethical implications. If a study is not designed to
include enough individuals to adequately test the research hypothesis, then the study unethically
exposes individuals to the risks and discomfort of the research even though there is no potential for
scientific gain. Although the connection between research ethics and adequate sample size has been
recognized for at least 25 years (Newell, 1978), the performance of clinical trials with inadequate