Many biostatisticians use statistical data analysis techniques to make sense of the data collected and provide responses to the issues identified in their research studies. However, it has been realized that data sets used to undertake the statistical analysis contain a multiplicity of outliers that may distort the statistical conclusions if adequate caution is not taken to check and correct them (Sheskin, 2007). For example, researchers have realized that uncomplicated computations of the mean and the standard variance of a particular public health intervention may be misrepresented due to the occurrence of grossly divergent observations in the form of outliers. In such a situation, researchers can use the extreme studentized deviate (ESD) static to detect the outliers and address them accordingly (Sheskin, 2007). This paper not only provides professional and general definitions of the ESD static but also discusses its principles and limitations.
The ESD is technically defined as a statistical test that is routinely employed “to detect one or more outliers in a univariate data set that follows an approximately normal distribution” (Natrella, 2005, p. 7). Unlike other statistical techniques (e.g., the Grubbs test and the Tietjen-Moore test) that are used to specify the exact number of outliers to avoid distorting the conclusions of statistical tests, the ESD test is more explicit as it requires researchers to only specify the upper bound for the suspected quantity of outliers by performing separate tests. When used professionally, the ESD test has the capacity to detect discordant observations and other incidences that have a low probability of being members or units of the target distribution (Sheskin, 2007). The ESD test uses a complex mathematical formula that has been made easier by computer programs such as MS Excel and InStat.
In general terms, the ESD test can be described as a statistical technique that is used to detect multiple observations that appear to be inconsistent with other observations in the data set by specifying an upper boundary on the number of outliers. The ESD underscores the fact that inconsistent observations in a data set have the capacity to entirely shift the mean score and the standard deviation in statistical calculations. For example, one biostatistician evaluating the resting heart rate (bpm) could record the data points of 80, 67, 76, 78 and 66 (mean = 73.4 and the standard deviation is 6.47), while another investigator records the data points of 80, 67, 76, 78, 66 and 120 (mean = 81.2 and standard deviation = 19.9) in the same investigation. In this example, it can be noted that the inconsistent data point of 120 in the second data set has absolutely shifted the mean score and the standard deviation. In such a scenario, the use of the ESD test can enable the second researcher to detect the upper bound outlier of 120 and remove it to achieve consistent results.
Owing to the fact that statistical tests for outliers are reliant on establishing the distribution of the data, it follows that one of the assumptions of the ESD statistic is to source data from an approximately normal distribution. Due to this assumption, statisticians are always requested to complement the ESD test with a normal probability plot to minimize the possibility of the test detecting the non-normality of the data set as opposed to identifying the presence of outliers (Natrella, 2005). Lastly, although it is assumed that the outliers being detected by the ESD test are a result of wrong measurement or recording of data scores, it is important to understand that the outliers might represent a normal disparity in the data set.
References
Natrella, M.G. (2005). Experimental statistics. Mineola, NY: Dover Publications, Inc.
Sheskin, D. (2007). Handbook of parametric and nonparametric statistical procedures. Boca Raton, FL: CRC Press.