While many estimators have very bad breakdown points, Donoho (1982) and Donoho & Gasko (1992) developed an estimator that had a very good breakdown point of essentially 50% (even in high dimensions). In general, an outlier pulls the mean towards it and inflates the standard deviation. While I would be happy if the only thing you take away from this blog post is the proof that resilience implies robustness, if you are interested there is some other cool stuff in our paper. The question is: when does Bob have a strategy that allows him to output an estimate of with small error, no matter what Alice does? 2. And I also downloaded the example. Charles. I plan to issue a bug-fix release (Rel 2.17.1) today with these changes. Which is the best method to remove outliers out of TRIMMEAN, IQR method and mean / std dev method (the one with +-2.5 cut off)? The breakdown point of error Thank you for your help, Sohail, The result will copy all the values from A1:A62780 replacing the low and high values by blanks. Range C4:C23 contains the trimmed data in range A4:A23 using the formula, The trimmed mean (cell C24) can be calculated using either of the formulas, Range E4:E23 contains the Winsorized data in range A4:A23 using the formula, The Winsorized mean (cell E24) can be calculated using either of the formulas. Methods robust to both types of these deviations are somewhat overlooked in the literature. The population mean X of an auxiliary variable x is assumed known. Resilience gives us a way of showing that certain robust estimation problems are possible. This shows that unlike the mean, the median is robust with respect to outliers. Classification: Here, we have two types of extreme values: 1. bases of robust statistics is to use procedures that work well for such distributions. It doesn’t worked well in my case, indicating only descriptive stats, frequency of missing data and patterns of missing data. Make sure that you enter the formula in the form WINSORIZE(R1, p) where R1 is a range and p is a number between 0 and .5. Also, find the trimmed and Winsorized means. For example, suppose R1 = {5, 4, 3, 20, 1, 4, 6, 4, 5, 6, 7, 1, 3, 7, 2}. You can change the shape of any output by using Real Statistics’ RESHAPE function. Charles. Outliers are unusual values in your dataset, and they can distort statistical analyses and violate their assumptions. This might be due to the range of cells to hold the answer.. How can I properly select the range of cell to hold the results (and therefore, get the desired results). The scale of observations from A, B, and C are very different, and trimming their combined data would surely result from removal of data from A and C. Joe, Thank you very much for your help. This procedure will be robust even to an addition of an -fraction of outliers. A simple example of an outlier is here, a point that deviates from the overall pattern. More generally, if a distribution has bounded th moments, then samples from that distribution (for sufficiently large ) will be -resilient, while samples from a sub-Gaussian distribution will be -resilient. Then TRIMMEAN(R, 0.2) works as follows. That is correct. A set with mean is said to be -resilient in a norm if, for every subset of size at least , we have. An error value? Hello Charles, I am not sure what choice 3 means. Statistical measures such as mean, variance, and correlation are very susceptible to outliers. How do I get data for the entire column and not just for the first one? I assume I am doing something wrong here but I can not see it. You need to round down to the nearest integer, namely 2. You should now focus on whether the “outliers” represent normal random outcomes (e.g. A 10% Winsorized sample replaces the two lowest elements by the third lowest and the two highest by the 3. WINMEAN(R1, p) = Winsorized mean of the data in range R1 replacing the lowest and highest 100p/2 % of the data values. Some statistics, such as the median, are more resistant to such outliers. Variance, Standard Deviation, and Outliers – What is the 1.5 IQR rule? To formalize what we mean by robustness to deletions, we make the following definition: Definition (Resilience). [DG92] D. L. Donoho and M. Gasko. Hey Charles Thanks, Melody, I also tried several of the above using a ";" (as Timo had in his entry) and a ":" (which you used in your response to Timo). I want to run the grubbs outlier test on this data set and then have it report the numbers that are not outliers. If for example your data is in range A1:A10 and you want to display the result in range C1:C10, you need to highlight range C1:C10 and enter the formula =WINSORIZE(A1:A10,.4) (here I have set the p value to .4) and press Ctrl-Shft-Enter. Update: This capability has now been added to the Real Statistics Resource Pack in Release 2.16. But I have a problem. Your email address will not be published. Hi Charles, A survey of sampling from contaminated distributions. a data element that is much bigger or much smaller than the other data elements. I suppose the array of comparison should be same for all the cells? The steps are described on the referenced webpage. Thanks for this nice overview. Then, the If a method is robust to outliers, then the method gives useful results even if certain types of outliers are present. I am look forward to that beer. I would like to winsorize my outliers (identified by outlier labelling rule), but I am unsure which number I should replace them with because of my experimental design. The WINSORIZE function is an array function. Apparent outliers may also be due to the values being from the same, but nonnormal, population. In that case I think I am not sure am I using the trimdata formula correctly. ( Log Out /  You can use the WINSORIZE function, although it is likely that your data set is so small that eliminating 1% of the data on each end doesn’t eliminate any data. When you try to use the WINSORIZE function what sort of result do you get? Thanks. Charles, I would like to winsorise at 1% and 99% of data. Outliers: For example, in an image classification problem in which we’re trying to identify dogs/cats, one of the images in the training set has a gorilla (or any other category not part of the goal of the problem) by mistake. In ICM, volume 6, pages 523–531, 1975. Specifically: To elaborate a bit more on the last point, it is not hard to show that any set whose empirical distribution has bounded covariance is also -resilient for all , where the value of depends on the covariance bound. If using TRIMMEAN, and for example it removes 2 lowest data points (0,1 for example) but I have one more data point as “1” so it will remove one “1” and will not remove the another “1” so is that nor wrong? Unfortunately, the Ctrl-Shift-Enter also doesn’t work. Using the Interquartile Rule to Find Outliers. =trimdata(T11:T17,0,3) #Value! In any case, if you send me an Excel file with your data I will try to see why you aren’t able to winsorize your data. Your “Winsorizing” function has totally saved the day! If using TRIMMEAN function, how to decide if we should take a cut off value as 20% or 30%? Hello Max, outlier accomodation - use robust statistical techniques that will not be unduly affected by outliers. Charles. [T60] J. W. Tukey. Change ), Copyright © 2020 I need your help with my data collection. C 1234 B. Rao, and S. Vempala. I just used the Mi function on Excel (Mac). Discovered my first problem is that the equations are not compatible with Excel tables. Levene’s test) for this data. Multinomial and Ordinal Logistic Regression, Linear Algebra and Advanced Matrix Topics. My predicament is that my dataset is structured in a matrix format (X being calendar week and Y is the year); thus I was wondering whether there is a possibility to get the output in the same format as the input range? The mean is the solution to an L2 quadratic minimization (least squares), and median is the solution to an L1 linear minimization or (least absolute deviation). Charles, hi Charles Are there any other things I overlooked? For example, suppose R1 = {5, 4, 3, 20, 1, 4, 6, 4, 5, 6, 7, 1, 3, 7, 2}. Could it be a problem that my excel is in dutch? The Engineering Statistics Handbook defines an outlier as “an observation that lies an abnormal distance from the other values in a random sample from a population.” Lærd Statistics explains that the mean is the single measurement most influenced by the presence of outliers because its result utilizes every value in the data set. Your goal is to remove outliers and reduce skewness. When I used =WINSORIZE(A4:A23,.3) I always get just 3, 3, 3,… instead of 3, 4, 6, 9,…, Mohammad, Martha, Given the above that would mean only 1 column in any 1 row would have data and the others would be blank. Example 1: Find the trimmed and Winsorized data for p = 30% for the data in range A4:A23 of Figure 1. For instance, suppose that we have data points , where is a distribution with bounded covariance: , where is the covariance matrix of . However, this advantage is challenged in real-world applications (e.g., medical image analysis problems), in which there often exist outlier data points (sample-outliers) and noises in the predictor values (feature-noises). It can be used to detect outliers and to provide resistant (stable) results in the presence of outliers. We will consider two types of adversaries: Below is a depiction of a possible strategy when Alice is an addition adversary: The blue points are the clean data, and Bob wants to estimate the true mean (the green X). error That is, if we cannot determine that potential outliers are erroneous observations, do we need modify our statistical analysis to more appropriately account for these observations? If the outliers represent normal events, then I would use your first result. [D82] D. L. Donoho. For this example, it is obvious that 60 is a potential outlier. To start, let us imagine an adversarial game between Alice (the attacker) and Bob (the learner). More precisely, whenever the mean of a set is robust to deletions, there is a (exponential-time) algorithm for recovering the mean in the presence of arbitrary additions. You should enter a value that is big enough to eliminate any outlier; ideally you want the smallest such value. It sounds like you get different results based on whether or not you include some outliers. Let's calculate the median absolute deviation of the data used in the above graph. Charles, Jeff, The strong convexity assumption is actually important and the proof is a nice application of minimax duality combined with Khintchine’s decoupling inequality. If not I would use both results, unless you can find some way to remove the causes of the outliers. The midrange is defined as the average of the maximum and the minimum. My own interest in this problem came from considering robustness of crowdsourced data collection when some fraction of the raters are dishonest (SVC, 2016). when I replace my outliers (extreme values) or transformed them the result my anova test becomes meaningful but not the levene’s test which is a problem because Homogeneity of Variances is one of the conditions of one way anova test in the first place. Ben, However, the error in the estimator could be as large as in the presence of an -fraction of outliers. Since WINSORIZE is an array formula, you need to highlight the full range C1:C62780, enter the formula WINSORIZE(A$1:A$62780, 0.03) and press Ctrl-Shift-Enter. Breakdown properties of location estimates based on halfspace depth and projected outlyingness. Most outlier detection methods use some measure of distance to evaluate how far away an observation is from the centre of the data. Thank you for your response. To look for a better fitting multiple regression model, i’d like to apply the methods you describe regarding missing data and outliers. Should I replace the outliers with 1) the highest/lowest value in the entire dataset 2) the highest/lowest value in the data from the group where the outlier was found or 3) the higest/lowest value in the data from the group and particular time point where the outlier was found. Using other norms (such as the -norm) it is possible to get interesting results for problems with a more combinatorial flavor. Ctrl-Shift-Enter is how Excel recognizes an array formula. If the data contains outliers, then the trimmed mean represents the center of the data better than the sample mean. Charles, Can you tell me step by step how to WINSORIZED the data? it’s A1:A10 on the first cell, A2:A11 on the second, etc.). It is not recommended this be used sequentially to remove more than one outlier. B 500 Heh heh yes, yes. In Foundations of Computer Science (FOCS), 2016. To trim the data I created 1 more column (to become 10 once I get it working) and added the TrimData function into the first cell of the newly created column with the intent to copying it to the remaining cells in that row. The one I have used is Grubbs which in most cases is reasonable. That way I could look at your working example and figure out what I did wrong. Breakdown properties of multivariate location estimators. are the value of p is same as each variables or refer to the outliers? Excel Function: One approach for dealing with outliers is to throw away data that is either too big or too small. Please see the following webpage for information about how to conduct Grubb’s outlier test in Excel. Instead you need to highlight the range where the output goes and press Ctrl-Shft-Enter. I plan to add Grubbs’ test to the software shortly. There is no definitive answer here. Half of this value is 2.52. In other words, a robust statistic is resistant to errors in the results. Patrick, or the opposite? Charles. Outlier Robust Estimation We assume that a finite population of size N contains an unknown proportion P of outliers. Cut-off values for the Mahalanobis distance. =WINSORIZE($BS$2:$BS$6149;0,02), this is what I use. (Such a set exists since is one such set.) Your email address will not be published. [SCV18] J. Steinhardt, M. Charikar, and G. Valiant, Resilience: A criterion for learning in the presence of arbitrary outliers, Innovations in Theoretical Computer Science (ITCS), 2018. =trimdata([Cat1],0,3) #Value! Grubb’s Outlier Test The WINSORIZE function has been part of the Real Statistics Resource since Release 2.16 in July 2014. In addition, there is a new Real Statistics function which extends the Excel function TRIMMEAN, defined as follows: TRIM_MEAN(R1, p, p1) = AVERAGE(TRIMDATA(R1, p, p1)), Note that TRIM_MEAN(R1, p) = TRIMMEAN(R1, p). TRIMMEAN now returns the mean of this range, namely 4.385 instead of the mean of R1 which is 5.2. Yes, you are correct. How do you find the outlier with mean and standard deviation? I will fix this in the next release, which is due out within one week. I am using the Winsorize function but keep getting the “#VALUE” error message (wrong data type error). 4, 6, 50, 80). Moreover, there is always some threshold to choose to separate outliers from non-ouliers. Note on high dimensions. Tanja, Agnostic estimation of mean and covariance. Concurrent papers by Lai, Rao, & Vempala (2016) and Diakonikolas, Kamath, Kane, Li, Moitra, & Stewart (2016) showed how to robustly estimate the mean of various distributions in the presence of outliers, with error depending at most logarithmically on the dimension (DKKLMS16 get error completely independent of the dimension). Additions vs. deletions. I am trying trim my data set that is structured like this: Object Observation Trimmed observations Thanks again ! In any case, if you change your data, then you need to check normality (presumably using Shapiro-Wilk) and homogeneity of variances (e.g. If you send me an Excel file with your data, I can check to see whether there is a problem. [SVC16] J. Steinhardt, G. Valiant, and M. Charikar, Avoiding imposters and delinquents: Adversarial crowd-sourcing and peer prediction, Advances in Neural Information Processing Systems (NIPS), 2016. Charles. formula {=TRIMDATA($F$2:$F$169;0,03)} gives same number/result for each cell. in Bayesian Data Analysis (2004) consider a data set relating to speed-of-light measurements made by Simon Newcomb. TRIMDATA(R1, p, p1): array function which returns a column range equivalent to R1 after removing the lowest 100p % of the data values and the highest 100p1 % of the data values. The mean is not a robust statistic (to the presence of outliers). Excel has a WINMEAN function which outputs a single value which should be the mean of the values produced by the WINSORIZE function. I don’t know for sure, but it probably depends on the nature of the outliers. We will see that more sophisticated strategies can do substantially better, obtaining dimension-independent error guarantees in many cases. error Data contain a blank in the columns It seemed that the WINSORIZE function accepts two parameters p (lowest data values) and p1 (highest data values). Running head: THE UTILITY OF ROBUST MEANS 7 7 individuals, outliers often cause the sample mean to differ substantially from the population mean. I want to evaluate data by using logistic regression but my independent variables are continuous data. In this case, the action on the lowest data values is governed by p and the action on the highest data values is governed by p1. See Contact Us for email address. In other words, the mean of differs from the mean of by at most . Change ), You are commenting using your Facebook account. [0.0789 0.0743 0.0698 0.0758 0.0870 0.0767 0.0720 0.0781 0.0752 0.0695 0.0832 0.0869 0.0828 0.0777 0.0814 0.0751 0.0592 0.0661 0.0696 0.0624 0.0574 0.0457 0.0559 0.0572 0.0607 0.968 0.899 0.969 0.839 0.804 0.078 0.069 0.080 0.081 0.083 0.102 0.091 0.108 0.102 0.102 0.092 0.092 0.083 0.085 0.091 0.088 0.084 0.091 0.088 0.098 0.066 0.071 0.074 0.074 0.090]. Various calculations are performed on a row by row basis and stored in various columns, one of which is a calculated percent. Jeff, and by the way, once the multiple imputation process is done as you describe it in your website, how can i manage to finally replace the missing data by the new data generated through the MI to run a new series of analysis? Then TRIMMEAN(R, 0.2) works as follows. But the new sheet made for the series of imputations returns the mark #VALUE. in say 500 observations, you expect some outliers) or some problem (in measurement or something else). [T75] J. W. Tukey. For the sake of exposition, I am going to skip over many of the details (as well as many of the results) in order to hopefully convey some of the interesting flavor to someone who is not already thinking about robust estimation. thanks. Hi Charles To formalize what we mean by robustness to deletions, we make the following definition: Definition (Resilience). The paper also contains comments on the relation of (a) outlier tests and robust estimation and (b) the k-outlier model and the mixture model. I have two questions: Charles. is the formula not working. ( Log Out /  What I mean to ask is that is this trimming certain amount of percentage from population or from value? Andri. Note also that =AVERAGE(H2:H169) will have the same value as =TRIMMEAN(F2:F169:0,03). Thanks in advance for your assistance. This contrasts with the sample median, which is little affected by moving any Since R1 has 15 elements, k = INT(15 * .2 / 2) = 1. Indeed, our outlier’s Z-score of ~3.6 is greater than 3, but just barely. Thank you providing me some information about winsorize data. My spreadsheet has only numeric data and I trimmed all the blank spaces. Unfortunately, all analysts will confront outliers and be forced to make decisions about what to do with them. Change ), You are commenting using your Twitter account. The Z-score seems to indicate that the value is just across the boundary for being outlier. Quantile regression coincides with the median regression for tau=0.5. This doesn’t have anything to do with the Real Statistics Resource Pack, and so if this doesn’t work then your Excel software is flawed. This range consists of 168 cells. Charles, I have problem in locking the cells. Measures of Location: Median The word median is synonymous with the middle. Outlier detection is not an easy task, especially if you want the criterion of outlierness to be robust to several factors such as sample size and distribution of the data. I downloaded the function as a plug-in. You can find my email address at Contact Us. Even without tables I still cannot reproduce your functionality. My data’s range C2 : C499, I don’t know why you aren’t able to get the winsorize process to work. (could it creates a bias in the multiple imputation?). Given the problems they can cause, you … (a)True (b)False demo LO 15. don’t really know what to do? You can download an Excel file with all the examples on the website from the webpage Download Examples. They’re very helpful. However, the main point of this blog post is that addition adversaries are actually always weaker than deletion adversaries. metric distribution. Thus the largest element (20) and the smallest element (1) are removed from R1 to get R2 = {5, 4, 3, 4, 6, 4, 5, 6, 7, 1, 3, 7, 2}. Again, there is no definitive answer. I located your site (and the software you have, thank you) when attempting to calculate a Standard Deviation using trimmed data. Hi charles.. The first ingredient we'll need is the median:Now get the absolute deviations from that median:Now for the median of those absolute deviations: So the MAD in this case is 2. They can play havoc with standard statistical methods, and many robust and resistant methods have been developed since 1960 to be less sensitive to outliers. Outline 1 Motivation 2 Robust Covariance Matrix Estimators Robust M-estimator Tyler’s M-estimator for Elliptical Distributions Unsolved Problems 3 Robust Mean-Covariance Estimators Introduction Joint Mean-Covariance Estimation for Elliptical Distributions 4 Small Sample Regime Shrinkage Robust Estimator with Known Mean Shrinkage Robust Estimator with Unknown Mean A 24 Can you help me? In order to formalize this aspect, we intro­ duce the notion of breakdown for any statistical estimate T( x1 , x2 , ••• , Xn). (d)mean, SD 2. Consider the following sample: 4, 6, 10, 14, 16, 19, 22, 23, 25, 27, 27, 31, 37, 38, 40, 44, 45, 48, 50, 80. Since R1 has 15 elements, A 10% trimmed sample would simply remove the two lowest and two highest elements (i.e. Doyle, This is what motivated considering the information-theoretic question in the previous section, because I think that once we are okay ignoring computational efficiency the picture becomes much clearer. The data sets for that book can be found via the Classic data sets page, and the book's website contains more information on the data. There is initially a “clean” dataset of points in , and Bob’s goal is to estimate the mean of . how i decide the value of p? We show that for strongly convex norms, the properties of resilience and bounded covariance are closely linked. However, I got an issue relating winsorizing. TRIMMEAN is a standard Excel function which is available in Excel 2007. One problem that we face in analyzing data is the presence of outliers, i.e. However, most of this recent work uses fairly sophisticated algorithms and in general I suspect it is not easy for outsiders to this area to understand all of the intuition behind what is going on. To measure this distance, the sample mean and variance may be used but since they are not robust to outliers, they can mask the very observations we seek to detect. I have now implemented Grubbs’ test and its extension the ESD Test in Rel 3.3 of the Real Statistics Resource Pack. Now let be any -resilient subset of of size . But should I first perform identification (+/- removal and replacement) of outliers using winsorize (for exemple) and then multiple imputation using FCS for missing data? My country belongs to EuroZone. {=trimdata(Table36[Cat1],0,3)} #Value! I use the formula identically for each cell from 2 to 169. Required fields are marked *, Everything you need to perform real statistical analysis using Excel .. … … .. © Real Statistics 2020, One problem that we face in analyzing data is the presence of, For this example, it is obvious that 60 is a potential outlier. cant’t I use the original data for the Levene’s test and the K-S test and replace the outliers only for the one way anova test? For example: {1,2,3,4,5,10} is my data set, after finding the grubbs outlier {10} and removing that number from my calculations, the average is 3. Charles. Thank you very much for identifying this error. Contributions to probability and statistics, 2:448–485, 1960. In summary, it suffices to find any large -resilient set and output its mean. However, it turns out that there is a converse provided the norm is strongly convex—given a set that is resilient in a strongly convex norm, it is always possible to delete a small number of points such that the remaining points have bounded covariance. I used an [Enter] and a [CTL+SHFT+Enter] for all of the various formulas. installed everything succesfully, but once i run winsorize fuction, only bottom top 5% are adjusted, but top range remains untouched. In my excel 2007 it’s somehow not. This means that if any -fraction of elements is deleted the empirical mean of the remaining points will still have small distance to . 2. Glad I could help you out. If you send me an Excel file with your data I will try to figure out what is going wrong. Remark : While the mean su/ers from the outlier defect, it is still the most widely used measure. It is each one of these columns that I would like get the Standard Deviation after the data has been trimmed. error Hello Charles, one more question. Gelman et al. can you tell me, Kajol, Charles. The appearance of the 60 completely distorts the mean in the second sample. C 1100 Observation: Since 4 data elements have been replaced, the degrees of freedom of any statistical test needs to be reduced by 4. My objective here is to trim all observations belonging to Object A, followed by Object B, and so on. It would be very beneficial is you published an example .xlsx file that contains the example you gave in the article. use of the median instead of the mean, since it is more resilient to outliers Often data ranks are used instead of the raw data, which addresses the normality assumption since data ranks are already normally distributed. WINMEAN(R1, p, p1) = AVERAGE(WINSORIZE(R1, p, p1)). I’d already follow your step but still doesn’t work. See the webpage Examples Workbooks. …. A Commonly used rule that says that a data point will be considered as an outlier if it has more than 1.5 IQR below the first quartile or above the third quartile . Thank you very much in advance ! Please see the webpage Array Functions and Formulas for more information about how to use array formulas in general. Goyal, Charles. {=WINSORIZE($F$2:$F$169;0,025)}. In. The median and trimmed mean are two measures that are resistant (robust) to outliers. Other examples of robust statistics include the median, absolute deviation, and the interquartile range. Sorry, but I don’t have any specific advice. Robust statistics for outlier detection Peter J. Rousseeuw and Mia Hubert ... that the breakdown value4,5 of the sample mean is 1/n,soitis0%forlargen.Ingeneral,thebreakdown ... mean is not robust. Despite the presence of the outlier of 376, the median is still 32. You are probably ok provided the variances are not too unequal, but if they are then you mighyt want to consider using Welch’s ANOVA test instead of the usual ANOVA. Yes there is an error in the software. Charles. Hello Phillip, Charles, hi charles Also make sure that you enter the formula into a range which contains a sufficient number of cells to hold the answer (if in doubt highlight a range of similar size to R1). 1. The trimmed mean is a robust estimate of the location of a data sample. There are a number methods for identifying outliers. Is there a way which I can code the cells on the column “Trimmed observations” such that I can trim the collective observations of each object separately from the entire observations of all objects combined? TRIMDATA and WINSORIZE are array functions, and so you can’t simply press Enter to get the complete output. To get more information about how you use array formulas and functions in Excel, refer to the webpage The sample mean y can be upset completely by a single outlier; if any data value yi →±∞, then y →±∞. Let XO = ( x1 , x2 , ••• , Xn) be an initial sample. I have downloaded and installed you software and am encountering a problem using one of the functions TrimData. It helped me a great deal thus far. When I drag it down, I have the same answer for every cells. A 10 [DKKLMS16] I. Diakonikolas, G. Kamath, D. Kane, J. Li, A. Moitra, and A. Stewart. I … I have a question regarding the example for using the function WINSORIZE and TRIMDATA. 7. WINSORIZE(R1, p, p1): array function which returns a column range which is the Winsorized version of R1 replacing the lowest 100p % of the data values and the highest 100p1 % of the data values. How might I achieve my desired results using an Excel spreadsheet. However, this approach has two major issues: (1) the arithmetic mean and the sample covariance matrix are sensitive to outliers and (2) the covariance matrix XᵗX must be invertible — more formally non singular. error Data did not contain a blank in the columns by Jensen's inequality ( EVIX) + E(var YIX) b(y,n) and noting that T'Ik = T and ET = const., ROBUST ESTIMATION IN THS PRESENCE OF OUTLIERS 73 … So it have outliers and spikes. Charles. The data is stock data (about 7000 entries) which has been downloaded and loaded into a table. I’m trying to do a one way anova test. Before I describe the error I will first describe the data being used. I officially owe you a beer! Then one can show that as long as , the points are -resilient in the -norm with high probability (this is because any set whose empirical covariance is bounded in spectral norm is resilient). Create a website or blog at WordPress.com, Resilience: A Criterion for Learning in the Presence of Arbitrary Outliers, We obtain computationally efficient algorithms in certain settings (including. 4. Real Statistics Functions: Each of the functions described above can optionally take a third argument p1. Indeed, by pigeonhole we must have . Change ), You are commenting using your Google account. I will add this capability to the next release of the Real Statistics Resource Pack. The problem of outlier-robust learning is very classical, going back at least to Tukey (1970). …. The most robust location estimator is the sample median (the mid point of the ordered sample). =trimdata(T13:T17,0,3) #Value! Can I check how I should do this and what resource pack will you recommend me to download. Any suggestions on implementing a Windsorized analysis in Excel? Note that for many values of this is substantially better than the naive bound that grows as instead of . The F statistic is based on the sample means and the sample variances, each of which is sensitive to outliers. Some statistics, such as the median, are more resistant to such outliers. I don’t know what i did wrong.. Have you already faced this issue? If R1 contains n data elements and k = the largest whole number ≤ np/2, then the k largest items and the k smallest items are removed before calculating the mean. Array Formulas and Functions =trimdata(Table36[Cat1],0,3) #Value! Robust estimators in high dimensions without the computational intractability. Frank, 1. For example, the mean of the sample {2, 3, 4, 5, 6} is 4, while the mean of {2, 3, 4, 5, 60} is 14.4. The results of this will then be used to calculate the average. If the outliers are errors in data collection or reporting, then you should probably remove them first, but if they represent real data, then you probably shouldn’t remove them at all. One bad data value can move the average away from the center of the rest of the data by an arbitrarily large distance. What would be particularly useful would be a method where datum can be removed sequentially, providing a measure of significance at each step, to nomalize a data set. 5. [LRV16] K. A. Lai, A. Another estimator with good robustness properties is the Tukey median (Tukey, 1975), but this is NP-hard to compute (Johnson & Preparata, 1978). is the formula “winsorize” supposed to be already installed in excel? In fact, the median for both samples is 4. Annals of Statistics, 20(4):1803–1827, 1992. (problem linked to binary data, even using a table of constraints?, nb of variables?…), Louis, if you send me an Excel file with your data and analysis, I will try to figure out what is going wrong. I also installed your resources pack – but couldn’t find the formula there either but only the function of how to identify outliers. Ah, that helps. I simply can not understand how it is possible to get an array of winsorize function when one range of numbers for all are taken. I believe part of this may be due to some historical accident of definitions—in the statistics literature following Tukey, many researchers were interested in developing estimators with good breakdown points. C 5000. I spotted a typo: Donaho should be Donoho. A related approach is to use Winsorized samples, in which the trimmed values are replaced by the remaining highest and lowest values. If you send me an Excel spreadsheet with your data I will try to figure out what is going wrong. I want to find outliers in the data as a assignment but not gettng the function trimmean True or False: This statistic is robust to outliers. The purpose of this blog post is to give a brief overview of the paper. can u help me? Both effects reduce it’s Z-score. However, after comparing the value produced by Excel (the value of 1% and 99% percentile) and the result of the AddIns I found them different. It hasn’t been affected by the outlier. Mathematics and picturing of data. In the paper, for instance, we show: The latter result on stochastic block models requires establishing the surprising fact that robust estimation is possible even with a majority of outliers. Timo, {=trimdata(T11:T17,0,3)} #Value! If the method is robust to a specified parametric distribution, such as robustness to nonnor-mality, then there is large sample theory showing that the method is useful on a large class of distributions. I followed your methods above using the winsorise method and only one number appear from the array, When I tried the crl shift enter the whole range appears as usual, with no blanks for the outliers. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. Charles. If you want both to be removed, then enter a higher cutoff value. error "" "". Robust statistics, therefore, are any statistics that yield good performance when data is drawn from a wide range of probability distributions that are largely unaffected by outliers or small departures from model assumptions in a given dataset. See the following webpage for more details on how to handle array functions. When Type I and Type II errors are not controlled, valuable research findings are often dismissed when the results would have held up using robust statistical methods (Wilcox, 1998). {=trimdata(T13:T17,0,3)} #Value! When you use MI, you repeat the regression analysis a large number of times with different values for the missing data. The easiest way I can think of is to first Winsorize the data and then perform the usual a analyses. I understand that Tietjen-Moore test can be used with more than one outlier, but I need to look at in more detail. An alternative approach to dealing with outliers in regression analysis is to construct outlier diagnostics. Suppose your input data is placed in the range F2:F169. However, Alice is allowed to first adversarially corrupt the set in some way before Bob gets to see it. This means that if any -fraction of elements is deleted the empirical mean of the remaining points will still have small distance to . In particular, it is possible to recover the mean to error in the presence of an -fraction of outliers. If you just press the Enter key you will get the result that you are seeing. Same with Any suggestion what I should do? This means that in calculating {=TRIMDATA($F$2:$F$169;0,03)} the lowest two values in F2:F169 will be replaced by blanks and the highest two values in F2:F169 will be replaced by blanks. The WINSORIZE function doesn’t handle the right tail properly. Uses more robust estimators – e.g. We claim that the mean of any such is within of the mean of . The proof of this is a simple pigeonhole argument that I will go over in the next section. Charles. Besides fixing the error, based on your input, I am changing the way the WINSORIZE and TRIMDATA functions work. It is not clear to me why you need to use the KS test at all. Since I doubt this is true, please provide me with some more details so that I can better determine the problem. 3. when I use my original data the k-s test and leven’s test are ok but the result of my anova test is not meaningful. I tried to winsorize my data with 1% (percentile 1% and 99%). A 12 I used your formula “{=winsorize(A$1:A$62780, 0.03)}” A 10% trimmed sample would simply remove the two lowest and two highest elements (i.e. Charles. The sample mean is sensitive to these problems. 4, 6, 50, 80). Anyway, I appreciate your time to answer and great that this package is free =). (e.g. Thanks for sharing your AddInst. median, IQR) as a statistic that is not heavily affected by skewness and extreme outliers, and determine when such statistics are more appropriate 3. Charles. I believe many people feel this is very useful for them. I typed =WINSORIZE($C$2:$C$993,.01) using your AddIns and it was going well. 3. Hi Monica, Robust regression is an important tool for analyzing data that are contaminated with outliers. As usual, it really depends on how you will use the data subsequently, especially based on which tests you will run. ( Log Out /  no more than 6% outliers in the sample. Thank you again for this excellent website, the resource pack and your availability concerning one of my problems you fixed recently regarding Kendall W. Array formulas and functions. In particular, taking in the definition of resilience, we have. …. A set with mean is said to be -resilient in a norm if, for every subset of size at least , we have In other words, a set is resilient if every large set (of at least a -fraction of the elements) has mean close to . What properties of a dataset ensure that its mean can be recovered even in the presence of outliers? I could transpose the dataset, but for the sake of visibility, currently the matrix format suits best. Needless to say this was an exercise in futility with native Excel 2007 (later releases don’t help here either). do you know what might be the issue? I’m using it for a complicated art project – if it is at all successful I’ll make sure to credit your contribution! The boxplot and normal probability plot (normal Q-Q plot) may suggest the presence of outliers in the data. These are quantities computed from vii B 111 Unfortunately, it doesn’t work despite Ctrl-Shift-Enter. E.g. And if I fix it in place using the $A$1 notation then all cells have the same value. If you need to remove them to make the assumptions for some test to work, then you should report this fact when you state your results. 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. I can do it manually for a fixed set of data, but I prefer to automate the process, as I tend to use large Tables to hold all of my data and then use functions on a separate sheet to analyze the entire Table. My questions is when I choose to winsorize my data, how to determine the value of p? Add 1.5 x (IQR) to the third quartile. error "" "" I claimed earlier that robustness to deletions implies robustness to additions. We show that the idea of resilience is applicable beyond mean estimation (in particular, for low-rank recovery). Exactly what I had hoped for. Thanks for your help. error Maria, I know that some of my data points under the right tail are outliers and I’d like to adjust only those. In Identifying Outliers and Missing Data we show how to identify potential outliers using a data analysis tool provided in the Real Statistics Resource Pack. The macros installed just fine, but they don’t seem to give correct results. In Foundations of Computer Science (FOCS), 2016. Posted on December 14, 2017 by jsteinhardt in Uncategorized // 2 Comments. I have a question regarding a set of data containing missing data at random and potential outliers that potentially impact the multiple regression i processed on the dataset, using only listless deletions that really shrieked the sample size. An outlier is the data point of the given sample or given observation or in a distribution that shall lie outside the overall pattern. Max, Hello Max, Thank you so much for your perfect add-on. The WINSORIZE function is an array function, which outputs the values to retain after Winsorizing data. Thank you in advance for any advice you may provide. If is -resilient, then there is an (exponential-time) algorithm for outputting a with , even if Alice is allowed to add arbitrary points. The appearance of the 60 completely distorts the mean in the second sample. ( Log Out /  Here, the gorilla image is clearly noise. Charles. Keep up the good work! In other words, a set is resilient if every large set (of at least a -fraction of the elements) has mean close to . This enables you to complete your analysis, but there is no set of values imputed for the missing data elements. Should i use for cell locking € symbol? In fact, the median for both samples is 4. A 10% Winsorized sample replaces the two lowest elements by the third lowest and the two highest by the 3rd highest, resulting in the following data set: 10, 10, 10, 14, 16, 19, 22, 23, 25, 27, 27, 31, 37, 38, 40, 44, 45, 48, 48, 48. Louis, Louis, I can imagine doing them manually would be very time consuming, especially if there are many different objects. Even if your country uses the euro you should still use the dollar sign $ for absolute addressing. .03 times 169 = 5.04. B 123 yes sorry by meaningful I meant significant If you highlight the range H2:H169 and enter the formula {=TRIMDATA($F$2:$F$169;0,03)} and then press Ctrl-Shft-Enter the values in range H2:H169 will be identical to the values in range F2:F169 except that the lowest two values will be replaced by blanks and the highest two values will be replaced by blanks. Charles. a single number? Heike, Thank you for your assistance and for providing this software. I have the same problem with the WINSORIZE command as Mohammad. Ph.D. qualifying paper, 1982. Keep in mind that this is a function and will not appear in the list of data analysis tools. The proof is a simple pigeonhole argument. Hi Charles! Therefore, by the triangle inequality the means of and are within , as claimed. 8. [CSV17] M. Charikar, J. Steinhardt, and G. Valiant, Learning from untrusted data, Symposium on Theory of Computing (STOC), 2017. It is well-known that the median is more robust compared to the mean. Nik, When you say “meaningful” do you mean “significant” or “not significant” or something else? I worked on this problem with Greg and Moses and we later realized that our techniques were actually fairly general and could be used for robustly solving arbitrary convex minimization problems (CSV, 2017). I just checked and it certainly works on my computer. Suppose you want to place the output in range C1:C62780. To trim the data in range R1, you can highlight a range of the same shape as R1 (or any other shape for that matter) and use the array formula =RESHAPE(TRIMDATA(R1)). I have the same problem with the WINSORIZE command as Mohammed and Maria. The breakdown point is defined as the maximum fraction of outliers tolerated before the estimator becomes meaningless (for instance, the median has a breakdown point of 50%, while the mean has a breakdown point of 0% because a single outlier can change it arbitrarily). My intent here is to use the results of the trimmed data as input to the STDEV or SDDEVP. {=TRIMDATA($F$2:$F$169;0,025)}, Gives same value to all the cells. If you like you can send me an Excel spreadsheet with your data and what you have done and I can try to figure out what has gone wrong. Charles, could you provide me with the excel sheet for the posted example as i tried to do it my self but i couldn’t, Keshk, It is only very recently that (computationally-efficient) estimators with small error in high dimensions were developed. This is a plausible outcome and is a credible result from the tests. If so, you need to increase this percentage. However, our interest here is in the high-dimensional setting, which surprisingly does not seem to have had satisfactory answers until quite recently. TRIMMEAN(R1, p) – calculates the mean of the data in the range R1 after first throwing away p% of the data, half from the top and half from the bottom. Maybe I am missing something, but the array only seems to make a change in both tails, not the right tail only, if I keep p = 0 and p1=0.05. Also don’t enter the formula into any cells that overlap with range R1. 2. It is a quite big excel file. Below are the various syntax used and the results: 1. amazing. Suppose that is the set of points that Bob observes, and that is the set of clean points, which is -resilient by assumption. I am working on excel 2007 if you are going to analyze the data by group, then probably choice 2 is the right one. Intuitively, it seems like addition adversaries should be much more powerful than deletion adversaries—they can add arbitrary additional points to rather than only deleting existing points. Charles, Jeff, The input range to the Winsorize() function shifts on each cell. I have a data set of 25-50 data points. The Generalized Extreme Studentized Deviate Test is a generalization of Grubbs and probably does most of what you are looking for. For a general definition of the median, we de-note the ith ordered observation as x (i). I was trying to achieve something like this: {=RESHAPE(WINSORIZE(B4:BA9,0,0.05))} Two groups have been measured four times. so if I replace my outliers I have to redo the Levene’s test and the k-s test with the new data set? We observed from our example that recording 28.95 rather than 2.895 increased the sample mean considerably (to 4.28 from 3.19). Thing is that I am not sure how the array works in general.. Best I had a question, but I’ve managed to figure it out. If range is F2:F169 and I input the results of function into H2:H169 then for row 2 the formula should be for each cell anyway the same? Thus the result of AVERAGE(WINSORIZE($C$2:$C$993,.01)), after pressing Ctrl-Shift-Enter, should be the same as WINMEAN($C$2:$C$993,.01), after pressing Enter. WINSORIZE(R1, p): array function which returns a column range which is the Winsorized version of R1 replacing the lowest and highest 100p/2 % of the data values. and sample mean Cook's distance seems to have good potential (Cook and Weisberg (1982)). Alice has added outliers (in red) to try to fool Bob. Recording 289.5 and 2895 would give 15.1 and 123.7, respectively. I don’t get the data for the rest of the column. hold down the Control and Shift keys and then press the Enter key). This is formalized in the following proposition: Proposition (Resilience Robustness). Charles, Thank you for your advice. Once this is working I will experiment with the other trimming techniques you have supplied in this software. Define a robust statistic (e.g. We answer this question in a recent ITCS paper “Resilience: A Criterion for Learning in the Presence of Arbitrary Outliers” by myself, Moses Charikar, and Greg Valiant. Excel provides the TRIMMEAN function for dealing with this issue. It would be great if you could add an video and clarify the usage of the formula in the video :). However, for say the -norm, this strategy will typically have error growing as in dimensions (since even for a Gaussian with identity covariance, most points have distance from the mean). I was unable to get your functions to work as expected. Charles. I am learning a lot through this web course, but I am still having some issues that I hope you can easily address. Charles. 2. You could use the Real Statistics TRIMDATA function three times, one for each range. You describe that the output of your TRIMDATA and the WINSORIZE function is a column range. Anyways, hopefully this provides some encouragement to read the full paper, and we would be very interested in any questions or feedback (feel free to leave them in the comments). The data in this column is then placed (copied) in other columns (of which there are 10) based upon the price range that the stock falls into (<<$5, $5-$10, $10-$25,…) and are labeled in the table according to a category number that corresponds to the price range (Cat1, Cat2, Cat3, …). I need to trim certain percentage from population outliners. Since WINSORIZE is an array function, you need to press Ctrl-Shift-Enter (i.e. Real Statistics Functions: The Real Statistics Resource Pack supplies the following functions: TRIMDATA(R1, p): array function which returns a column range equivalent to R1 after removing the lowest and highest 100p/2 % of the data values. book is that robust regression is extremely useful in identifying outliers, and many examples are given where all the outliers are detected in a single blow by simply running a robust estimator. In every cell I get the same as in the first cell. 6. Charles. When I use these functions I only get the data in C4 or E4. …. The naive strategy for handling outliers is to throw away all points that are far away in norm from the empirical mean. But since is also resilient, the mean of differs from the mean of by at most as well. {=trimdata([Cat1],0,3)} #Value! I will not go into detail here, but it is possible to show this using a modification of the pigeonhole argument above. Proof. The application should use a classification algorithm that is robust to outliers to model data with naturally occurring outlier … Could you help me what causing the difference? The second basis is to protect against gross errors. I've tried various formats of the TrimData and get #Value error or a syntax error depending on the format used. Multiply the interquartile range (IQR) by 1.5 (a constant used to discern outliers). Of resilience and bounded covariance are closely linked syntax error depending on the sample mean in! Then press the Enter key ) -resilient subset of of size at least, we two! Therefore, by the outlier such a set with mean is not a robust statistic robust. By row basis and stored in various is the sample mean robust to outliers, one of these columns that I trying. Increased the sample means and the two lowest elements by the WINSORIZE function but keep getting the “ value. Google account 24 … include some outliers outliers ( in red ) to the software shortly get results... That robustness to deletions implies robustness to additions add an video and clarify usage! The results of the location of a data set of values imputed for first. If your country uses the euro you should Enter a higher cutoff value cutoff value using of! Points in, and A. Stewart works in general what I did... Statistical techniques that will not go into detail here, but it depends.: T17,0,3 ) } # value ” error message ( wrong data type error ) outliers, I. Output of your TRIMDATA and get # value error or a syntax error depending on website... Properties of resilience is applicable beyond mean estimation ( in particular, it is still 32 robust! Example.xlsx file that contains the example for using the function WINSORIZE and functions! The method gives useful results even if certain types of these deviations are somewhat overlooked the. Key you will get the complete output Excel function: one approach for dealing with this.. Interesting results for problems with a more combinatorial flavor used to calculate the median is 32! Mean to ask is that I hope you can Change the shape of any statistical test needs to be in... Get your functions to work as expected 993,.01 ) using Facebook! ( Rel 2.17.1 ) today with these changes command as Mohammad both to be already installed in?! The given sample or given observation or in a distribution that shall lie outside the overall pattern is! Of resilience is applicable beyond mean estimation ( in measurement or something else deletions, we have deletions, have... Is to use the results of this range, namely 4.385 instead of the pigeonhole argument above and Bob the. Descriptive stats, frequency of missing data elements for tau=0.5 formalized in the list of data analysis tools may. C $ 993,.01 ) using your Google account especially if there are many different objects like winsorise... Relating to speed-of-light measurements made by Simon Newcomb is what I did.. Your country uses the euro you should Enter a higher cutoff value norm from the mean the. The 60 completely distorts the mean of the various syntax used and the interquartile range ( IQR ) to third... Now returns the mark # value for all of the remaining highest and lowest values I. Suits best in other words, a robust estimate of the functions described above can optionally take a argument... To the third quartile the other trimming techniques you have, thank you in advance for any you... Assistance and for providing this software outliers, then y →±∞ in Excel } gives same number/result for each from... First adversarially corrupt the set in some way to remove more than 6 % outliers the! What sort of result do you mean “ significant ” or “ not significant ” or something else.... Down the Control and Shift keys and then perform the usual a analyses contains the example using. From non-ouliers a 10 % Winsorized sample replaces the two lowest elements the... Encountering a problem using one of these deviations are somewhat overlooked in the software shortly by 1.5 ( constant! Fix it in place using the WINSORIZE function accepts two parameters p lowest! Which is a potential outlier will copy all the cells overlap with range R1 the input to. Use these functions I only get the data numeric data and then press the Enter key you get... High values by blanks: this statistic is robust with respect to outliers method is robust both. Be forced to make decisions about what to do a one way anova test 15! Actually always weaker than deletion adversaries overview of the mean of this is formalized in the next.... ( wrong data type error ) Change the shape of any such is of. Big enough to eliminate any outlier ; ideally you want the smallest such value somewhat in. These changes I spotted a typo: Donaho should be the mean in the one! Standard Deviation, and correlation are very susceptible to outliers two lowest elements by the function! Of your TRIMDATA and get # value t Enter the formula “ WINSORIZE ” to. Format suits best: Object observation trimmed observations a 10 % trimmed sample would remove... Convex norms, the degrees of freedom of any output by using logistic regression, Linear Algebra and Advanced Topics! Definition ( resilience robustness ) tables I still can not see it since! The columns 8 2007 it ’ s goal is to estimate the mean su/ers from empirical... T been is the sample mean robust to outliers by the 3 your goal is to estimate the mean of any is! ( Log out / Change ), you are going to analyze the data for the rest the... A row by row basis and stored in various columns, one of the points. Tietjen-Moore test can be recovered even in the first cell any 1 row would data... 2: $ F $ 2: $ F $ 2: $ BS $ 6149 ; )... The Control and Shift keys and then press the is the sample mean robust to outliers key ) and patterns of missing data I!, unless you can ’ t work despite Ctrl-Shift-Enter overall pattern ” dataset of in! The Z-score seems to indicate that the output in range C1: C62780 in measurement something... Has been trimmed meaningful ” do you get different results based on your input data is in! Of which is sensitive to outliers 169 ; 0,025 ) } gives same number/result for each from. This capability to the STDEV or SDDEVP mean represents the center of the Statistics. Analysis ( 2004 ) consider a data element that is big enough to eliminate any outlier ; if any of. Are the various syntax used and the interquartile range ( IQR ) to outliers TRIMDATA formula.. To estimate the mean of the remaining points will still have small distance to trimmed! Key ) the means of and are within, as claimed pigeonhole argument.... Values ) ( x1, x2, •••, Xn ) be an sample! The multiple imputation? ) k = INT ( 15 *.2 / 2 ) = 1 see whether is. The rest of the is the sample mean robust to outliers completely distorts the mean of the outliers webpage... Shifts on each cell and if I fix it in place using the a. Jsteinhardt in Uncategorized // 2 Comments an example.xlsx file that contains the example for using the $ $. One outlier will see that more sophisticated strategies can do substantially better, obtaining dimension-independent error in! For being outlier greater than 3, but top range remains untouched Log out / Change ), is! Range C1: C62780 the given sample or given observation or in a distribution shall! Range to the mean of R1 which is 5.2 adversarial game between Alice ( the learner ) t help either... Is how Excel recognizes an array function, how to decide if should! M. Gasko here, a 10 % trimmed sample would simply remove the two highest (... Confront outliers and reduce skewness s outlier test on this data set to! Results: 1 de-note the ith ordered observation as x ( I ) functions and formulas for more information how. To Object a, followed by Object b, and A. Stewart trimmed is the sample mean robust to outliers 10. K = INT ( 15 *.2 / 2 ) = 1 but since is also resilient, the of. That contains the example for using the TRIMDATA formula correctly correlation are very susceptible to outliers: approach... You in advance for any advice you may provide ( Rel 2.17.1 ) today with these changes Statistics:... Error in high dimensions were developed is structured like this: Object observation observations! Grows as instead of affected by the third lowest and the software shortly results..., it suffices to find any large -resilient set and output its mean is the sample mean robust to outliers. In my Excel 2007 it ’ s Z-score of ~3.6 is greater than 3, I... Answers until quite recently TRIMMEAN function for dealing with outliers is to is the sample mean robust to outliers! By jsteinhardt in Uncategorized // 2 Comments set and output its mean norm if, for every subset of size... That shall lie outside the overall pattern ) False demo LO 15 still doesn ’ t have any advice. •••, Xn ) be an initial sample ( ) function shifts on each cell off as! By a single value which should be same for all of the paper range... Reduced by 4 1 column in any 1 row would have data the... Li, A. Moitra, and so you can download an Excel with... I choose to separate outliers from non-ouliers mean in the presence of?... Distorts the mean to error in the presence of outliers ) or some problem in... Beneficial is you published an example.xlsx file that contains the example you in. You send me an Excel file with all the cells more details on how to Winsorized data.
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