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The method above for determining statistical significance actually is applying the principle of statistical equivalence. Essentially, the process outlined above for determining statistical significance could be restated as Given results data from multiple tests intended to be equivalent, the data from any one of those tests may be treated as statistically significant if that data is statistically equivalent to 80 percent or more of all the tests intended to be equivalent. Mathematical determination of equivalence using such formal methods as chi-squared and t-tests are not common on commercial software development projects. Rather, it is generally deemed acceptable to estimate equivalence by using charts similar to those used to determine statistical significance.
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Statistical Outliers
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From a purely statistical point of view, any measurement that falls outside of three standard deviations, or 99 percent, of all collected measurements is considered an outlier. The problem with this definition is that it assumes that the collected measurements are both statistically significant and distributed normally, which is not at all automatic when evaluating performance test data. For the purposes of this explanation, a more applicable definition of an outlier from a StatSoft, Inc. (http://www.statsoftinc.com) is the following:
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Outliers are atypical, infrequent observations: data points which do not appear to follow the distribution of the rest of the sample. These may represent consistent but rare traits, or be the result of measurement errors or other anomalies which should not be modeled.
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Note that this (or any other) description of outliers only applies to data that is deemed to be a statistically significant sample of measurements. Without a statistically significant sample, there is no generally acceptable approach to determining the difference between an outlier and a representative measurement. Using this description, results graphs can be used to determine evidence of outliers occasional data points that just don t seem to belong. A reasonable approach to determining if any apparent outliers are truly atypical and infrequent is to re-execute the tests and then compare the results to the first set. If the majority of the measurements are the same, except for the potential outliers, the results are likely to contain genuine outliers that can be disregarded. However, if the results show similar potential outliers, these are probably valid measurements that deserve consideration. After identifying that a dataset appears to contain outliers, the next question is, how many outliers can be dismissed as atypical infrequent observations There is no set number of outliers that can be unilaterally dismissed, but rather a maximum percentage of the total number of observations. Applying the spirit of the two definitions above, a reasonable conclusion would be that up to 1 percent of the total values for a particular measurement that are outside of three standard deviations from the mean are significantly atypical and infrequent enough to be considered outliers. In summary, in practice for commercially driven software development, it is generally acceptable to say that values representing less than 1 percent of all the measurements for a particular item that are at least three standard deviations off the mean are candidates for omission in results analysis if (and only if) identical values are not found in previous or subsequent tests. To express the same concept in a more colloquial way: obviously rare and strange data points that can t immediately be explained, account for a very small part of the results, and are not identical to any results from other tests are probably outliers. A note of caution: identifying a data point as an outlier and excluding it from results summaries does not imply ignoring the data point. Excluded outliers should be tracked in some manner appropriate to the project context in order to determine, as more tests are conducted, if a pattern of concern is identified in what by all indications are outliers for individual tests.
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