Environmental Engineering Reference
In-Depth Information
for outliers ( http://www.graphpad.com/quickcalcs/Grubbs1.cfm ) that is available to
identify extreme values. If the value came from a contaminated sample, then it is
appropriate to recollect the sample if possible or discard the initial observation.
Outliers cause considerable problems with most statistical analyses that are based
on a particular sampling distribution (e.g., normal) and associated assumptions
(e.g., constant variance). If the extreme values were actually recorded and represent
a legitimate data point, then the investigator must decide how to handle the value by
either removal from the data set, consider data transformation to meet statistical
assumptions, or conduct the analyses with techniques robust to outliers (i.e.,
nonparametric and multivariate methods, or use of generalized linear models linked
to a non-normal sampling distribution).
1.11 Sample Size and Effect Size
Although usually an afterthought during study formulation, one must consider the
magnitude of a treatment difference or effect size that is biologically meaningful in
addition to statistically significant results. Biological significance is defined by the
investigator but based on a firm understanding of the system being studied and
associated literature relative to the system. There is no replacement for sound,
extensive biological knowledge of the system that generated the data. If an investi-
gator or reviewer of proposed study design lacks this knowledge, discussions with
experienced biologists/ecologists regarding the system and interpretation of results
is just as important as use of proper statistical techniques. Not all statistically
significant results have biological meaning and, at times, biologically significant
differences may not be found to be statistically different. Frequently, the latter is
attributed to lack of sample size as an explanation, a situation that would be avoided
with proper design prior to collecting the first sample in a study.
Central to a scientific study is the ability to detect a biologically meaningful
effect and measure the size of the effect. The primary controlling element for
detecting an effect of interest is sample size, where the general rule is “more is
better.” Increasing sample size decreases the overall variability of the data around a
mean for a given treatment, which increases the power of statistical tests (i.e., the
probability of finding a difference due to treatment when one truly exists). There-
fore, one of the most important aspects of study design is the determination of the
appropriate sample size necessary to detect a specified effect. Under classical
hypothesis testing (i.e., true experiments), the required sample size to realize a
level of power to detect a treatment effect of desired magnitude should be
estimated. Calculation of the appropriate sample size primarily depends on the
underlying distribution (i.e., variation) of the sample values for the dependent
variable, significance level (i.e.,
), and minimum effect size to be detected. The
concept of effect size is part of study design considerations prior to sampling and
after analyzing the collected data. In the effort to determine appropriate sample size
prior to conducting a study, investigators need to determine the minimum effect
α
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