This article is about the statistical term. An outlier can cause serious problems in statistical analyses. Outlier points can therefore indicate faulty data, erroneous procedures, or areas where a outliers the story of success pdf free download theory might not be valid. However, the sample maximum and minimum are not always outliers because they may not be unusually far from other observations.
Naive interpretation of statistics derived from data sets that include outliers may be misleading. C but the mean temperature will be between 35. However, the mean is generally more precise estimator. 1 in 370 will deviate by three times the standard deviation.
If the sample size is only 100, however, just three such outliers are already reason for concern, being more than 11 times the expected number. Outliers can have many anomalous causes. A physical apparatus for taking measurements may have suffered a transient malfunction. There may have been an error in data transmission or transcription. Outliers arise due to changes in system behaviour, fraudulent behaviour, human error, instrument error or simply through natural deviations in populations. A sample may have been contaminated with elements from outside the population being examined.
Alternatively, an outlier could be the result of a flaw in the assumed theory, calling for further investigation by the researcher. There are various methods of outlier detection. The principle upon which it is proposed to solve this problem is, that the proposed observations should be rejected when the probability of the system of errors obtained by retaining them is less than that of the system of errors obtained by their rejection multiplied by the probability of making so many, and no more, abnormal observations. How it works: First, a data set’s average is determined. Next the absolute deviation between each data point and the average are determined.
Student t distribution with n-2 degrees of freedom, n is the sample size, and s is the sample standard deviation. Rejection Region, the data point is an outlier. Rejection Region, the data point is not an outlier. Meaning, if a data point is found to be an outlier, it is removed from the data set and the test is applied again with a new average and rejection region. This process is continued until no outliers remain in a data set.
Instance hardness provides a continuous value for determining if an instance is an outlier instance. The choice of how to deal with an outlier should depend on the cause. Even when a normal distribution model is appropriate to the data being analyzed, outliers are expected for large sample sizes and should not automatically be discarded if that is the case. The application should use a classification algorithm that is robust to outliers to model data with naturally occurring outlier points.
Rejection of outliers is more acceptable in areas of practice where the underlying model of the process being measured and the usual distribution of measurement error are confidently known. An outlier resulting from an instrument reading error may be excluded but it is desirable that the reading is at least verified. Trimming discards the outliers whereas Winsorising replaces the outliers with the nearest “nonsuspect” data. Even a slight difference in the fatness of the tails can make a large difference in the expected number of extreme values.