The advantage of trimmed and winsorized means is that they are not influenced by one or a few very high or low values. Maybe it doesnt matter as much when we are talking outliers. Dear statalisters, i want to set the top and bottom 1% of the sample to rp1 rp99 respectively winsorize the data. The winsorized mean is similar to the trimmed mean, and both are described in the documentation for proc. The most common outlier treatments in finance are winsorizing, trimming, and dropping. This module should be installed from within stata by typing ssc install winsor2.
If the data are from a symmetric population, the winsorized mean is a robust unbiased estimate of the population mean. Three observations are replaced because, and three is the smallest integer greater than 2. This page describes stata programs developed by the ucla idre statistical consulting. This transformation is named after the biostatistician. If you choose to winsorize your data i suggest you check out the command winsor2. The trimmed and winsorized means for systolic are displayed in output 4. Winsorizedvariancelist, f1, f2 gives the variance when the fraction f1 of the smallest elements and the fraction f2 of the largest elements are replaced by the remaining extreme values. To obtain the winsorized mean, you sort the data and replace the smallest. The analyst must specify the percentages to winsorize in each tail. In addition, researchers sometimes winsorize to give the distribution more desirable statistical properties. Nick, winsorizing is one way of removing outliers, nick. Percent bias was used to judge the performance of the bootstrap approach with or without winsorization in estimating inestimable standard errors of population pharmacokinetic parameters. Among the many robust estimates of central tendency, some recommend the winsorized mean.
This is done to limit the effect of abnormal extreme values. Winsorizedmeanlist, f1, f2 gives the mean when the fraction f1 of the smallest elements and the fraction f2 of the largest elements are replaced by the remaining extreme values. It involves the calculation of the mean after replacing given parts of a probability distribution or sample at the high and low end with the most extreme remaining values, typically doing so for an equal amount of both extremes. Outliers and robustness real statistics using excel. A winsorized mean is a winsorized statistical measure of central tendency, much like the mean and median, and even more similar to the truncated mean. The winsorized mean is similar to the trimmed mean, and both are described in the documentation for proc univariate. Home site map site search free online software descriptive statistics central tendency winsorized mean home up arithmetic mean weighted mean comparison 1 geometric mean. Ywinsorisingx,w x data matrix or vector for vectors, winsorisingx is the winsorized x array. Find the trimmed and winsorized data for p 30% for the data in range a4. A scalar or vector of winsorized scores or winsorized means, sds, or variances depending upon the call. There is a module for stata called winsor that will winsorize a variable in. Trimmed, windsorized and harmonic mean graphpad software. However, instead of discarding the values outside the range, they are set to the highest or lowest value.
It involves the calculation of the mean after replacing given parts of a probability distribution or sample at the. Function winsor inputs data vector x and 21 vector of cutoff percentiles p, and replaces nonnan values of x that are below percentile p1 with the smallest remaining value, and xvalues above percentile p2 with the largest remaining value. For the mixed chisquare distribution described in chapter 1, the 20% winsorized mean is approximately. But for the first, the data is changed and is regarded as real observations. This free online software calculator computes the following statistics. The wonderful world of user written commands in stata the. As you know, this means that all the observations with values 95 percentile take the value of the 95% percentile, and all observations with value less than the 5% percentile take the value of the 5th percentile. Definition of the winsorized mean central tendency winsorized mean. Descriptive statistics central tendency winsorized mean.
Stack overflow for teams is a private, secure spot for you and your coworkers to find and share information. Winmeanr1, p winsorized mean of the data in range r1 replacing the lowest and highest 100p2 % of the data values. English wikipedia the free encyclopedia winsorized mean a winsorized mean is a winsorized statistical measure of central tendency, much like the mean and median, and even more similar to the truncated mean. The idea of trimmed or winsorized means is to not let the largest and smallest values have much impact. For details, see help winsor if installed, and help trimmean if installed. What is a little confusing looking at their pseudocode is that they call it winsorized mean, but then they use a median function. Winsorizedvariancelist, f gives the variance of the elements in list after replacing the fraction f of the smallest and largest elements by the remaining extreme values. Hello, i have several hundreds of variables that i need to winsorize at some level, let us say at the 95% and 5%. Further to johns question regarding trimming, i would like to raise the following question to seek your help. Technically a commercial software package software you have to pay for cannot be. The winsorized mean is a robust estimate of location. The stata plugin interface has only limited support for strl variables.
Thus a winsorized mean is not the same as a truncated mean. Then sigma clipping is applied using these winsorized mean and sigma. I would like to create a winsorized mean across variable and store it as a new variable in the original data set. Consider the following scatter plot and correlation. As an alternative to winsorizing your data, sas software provides. I guess im the authority on what i said, but regardless of that the part of my post which you cite in your first paragraph bears almost no resemblance to what you report. It makes sense to use the quadratic mean when the set of squares of the data form a symmetrical approximately gaussian distribution. I and testing cointegration and causality for daily return of share indices time series first log difference data based on var model. Estimating inestimable standard errors in population.
To compute the harmonic mean, first transform all the values to their reciprocals. The quadratic mean is also called the root mean square. Stata module to winsorize data, statistical software components s457765, boston college department of economics, revised 22 dec 2014. Statistical software components from boston college department of economics. Getwinsorizedmean method methods numericalvariable. As is evident, winsorization results in a measure of location that is. Based on that definition stata, spss and sas are not open source. The wincorr command is designed for situations in which a few observations appear to be distorting the correlation between two variables. The top graph shows the distribution of the original data set. The only thing that is asked in return is to cite this software when results are used in publications. This is all new to me, and i profess no knowledge of this software just learning. The initial part of the computation is to calculate the median and sigma of the data set, then winsorize the data set and compute the winsorized mean and winsorized sigma from that.
Identifying and treating outliers in finance papers in the ssrn. It reports what i personally prefer for boxplot cutoffs, and says nothing about what is usual in winsorizing. Winsorized mean is a method of averaging that initially replaces the smallest and largest values with the observations closest to them. For instance, the 10% trimmed mean is the average of the 5th to 95th percentile of the data, while the 90% winsorized mean sets the bottom 5% to the 5th percentile, the top 5% to the 95th percentile, and then averages the data. Winsorized mean parameters and their standard errors were computed and compared with their true values as well as the non winsorized estimates. To winsorize, one converts the values of data points that are outlyingly high to the value of the highest data point not considered to be an outlier. Technically a commercial software package software you have to pay for cannot be open source. The wonderful world of user written commands in stata. Recently a sas customer asked how to winsorize data in sas. The winsorized option computes a winsorized mean that replaces three observations from the tails with the next closest observations. Winsorizing data means to replace the extreme values of a data set with a certain percentile value from each end, while trimming or truncating involves removing those extreme values i always see both methods discussed as a viable option to lessen the effect of outliers when computing statistics such as the mean or standard deviation, but i have not seen why one might pick one.
The mean of this new set of numbers is called the winsorized mean. For example, the winsorized mean at 5% is calculated by setting all values smaller than the 5th percentile equal to the 5th percentile, and all values larger than the 95th percentile equal to the 95th percentile. Winsorization is best known as a way to construct robust univariate statistics. This transformation is named after the biostatistician c.
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