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JoEllen Turner
<br />970 - 864 -7682 p.11
<br />Borch Environmental Pollution Consuitina, LLC October 2, 2012
<br />For further details and evidence please refer to:
<br />Wolfe, R.; Hanley, J., If we're so different, why do we keep overlapping? When 1 plus I
<br />doesn't make 2. Canadian Medical Association Journal 2002, 166, 65 -66.
<br />Introduction to Statistics and Data Analysis by Roxy Peck, Chris Olsen and Jay L.
<br />Devore (Jan 1, 2011). ISBN -10: 0840054904
<br />Shaw, R. G.; Mitchellolds, T., Anova for unbalanced data - an overview. Ecology 1993,
<br />74, 1638 -1645.
<br />Cox D.R., Hinkley D.V. (1974) Theoretical Statistics, Chapman & Hall Design and
<br />Analysis of Experiments (fifth edition), Douglas Montgomery, John Wiley and Sons,
<br />2001, 684 pages.
<br />L.G. Daniels, Statistical Significance Testing: A Historical Overview of Misuse and
<br />Misinterpretation.... RESEARCH IN THE SCHOOLS, 1998, Vol. 5, No, 2, 23 -32
<br />However, we can't use the "Tukey's method ", and t -tests (ANOVA) for the reason that such
<br />methods assume a normal distribution for the sample and it is not necessarily true that the
<br />underlying distribution in this case is normal. Moreover, the sample size for each group is VERY
<br />small, which means we are not able to use the normal distribution to approximate the true
<br />distribution for each group.
<br />Statistical significance tests (SSTs) and Sample Size from L.G. Daniels, Statistical Significance
<br />Testing: A Historical Overview of Misuse and Misinterpretation.... RESEARCH IN THE
<br />SCHOOLS, 1996, Vol. 5, No. 2, 23 -32:
<br />"Mast tests of statistical significance utilize some test statistic (e.g., F, t,
<br />chi - square) with a known distribution. An SST is simply a comparison of
<br />the value for a particular test statistic based on results of a given analysis
<br />with the values that are "typical" for the given test statistic. The
<br />computational methods utilized in gene - rating these test statistics yield
<br />larger values as sample size is increased, given a fixed effect size. In other
<br />words, for a given statistical effect, a large sample is more likely to
<br />guarantee the researcher a statistically significant result than a small
<br />sample is. For example, suppose a researcher was investigating the
<br />correlation between scores for a given sample on two tests. Hypothesizing
<br />that the tests would be correlated, the researcher posited the null
<br />hypothesis that r would be equal to zero. As illustrated in Table 1, with an
<br />extremely small sample, even a rather appreciable r value would not be
<br />statistically significant (p < .05). With a sample of only 10 persons, for
<br />example, an r as large as .6, indicating a moderate to large statistical
<br />effect, would not be statistically significant; by contrast, a negligible
<br />10 I Page
<br />PLTF 002484
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