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. Given the above that would mean only 1 column in any 1 row would have data and the others would be blank. You can change the shape of any output by using Real Statistics’ RESHAPE function. [CSV17] M. Charikar, J. Steinhardt, and G. Valiant, Learning from untrusted data, Symposium on Theory of Computing (STOC), 2017. An outlier is the data point of the given sample or given observation or in a distribution that shall lie outside the overall pattern. I have the same problem with the WINSORIZE command as Mohammad. I need to trim certain percentage from population outliners. Ctrl-Shift-Enter is how Excel recognizes an array formula. 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. Thing is that I am not sure how the array works in general.. The sample mean is sensitive to these problems. 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. The problem of outlier-robust learning is very classical, going back at least to Tukey (1970). It can be used to detect outliers and to provide resistant (stable) results in the presence of outliers. Quantile regression coincides with the median regression for tau=0.5. 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. See the following webpage for more details on how to handle array functions. Needless to say this was an exercise in futility with native Excel 2007 (later releases don’t help here either). So it have outliers and spikes. (could it creates a bias in the multiple imputation?). Consider the following sample: 4, 6, 10, 14, 16, 19, 22, 23, 25, 27, 27, 31, 37, 38, 40, 44, 45, 48, 50, 80. 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, The purpose of this blog post is to give a brief overview of the paper. 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. If you just press the Enter key you will get the result that you are seeing. Thank you very much for your help. Charles. I just checked and it certainly works on my computer. True or False: This statistic is robust to outliers. To formalize what we mean by robustness to deletions, we make the following definition: Definition (Resilience). 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. Thank you providing me some information about winsorize data. However, Alice is allowed to first adversarially corrupt the set in some way before Bob gets to see it. 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. Two groups have been measured four times. The data is stock data (about 7000 entries) which has been downloaded and loaded into a table. The naive strategy for handling outliers is to throw away all points that are far away in norm from the empirical mean. In summary, it suffices to find any large -resilient set and output its mean. Real Statistics Functions: Each of the functions described above can optionally take a third argument p1. Since I doubt this is true, please provide me with some more details so that I can better determine the problem. Unfortunately, the Ctrl-Shift-Enter also doesn’t work. Charles. 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). …. [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]. For this example, it is obvious that 60 is a potential outlier. A 10% Winsorized sample replaces the two lowest elements by the third lowest and the two highest by the 3. Patrick, Even without tables I still cannot reproduce your functionality. The population mean X of an auxiliary variable x is assumed known. ( Log Out /  I was unable to get your functions to work as expected. error But I have a problem. Thanks in advance for your assistance. Unfortunately, it doesn’t work despite Ctrl-Shift-Enter. Indeed, by pigeonhole we must have . [DKKLMS16] I. Diakonikolas, G. Kamath, D. Kane, J. Li, A. Moitra, and A. Stewart. Besides fixing the error, based on your input, I am changing the way the WINSORIZE and TRIMDATA functions work. Ben, 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). If so, you need to increase this percentage. 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. Suppose you want to place the output in range C1:C62780. Example 1: Find the trimmed and Winsorized data for p = 30% for the data in range A4:A23 of Figure 1. Indeed, our outlier’s Z-score of ~3.6 is greater than 3, but just barely. do you know what might be the issue? It is each one of these columns that I would like get the Standard Deviation after the data has been trimmed. These are quantities computed from vii Any suggestion what I should do? Add 1.5 x (IQR) to the third quartile. See the webpage Examples Workbooks. Grubb’s Outlier Test Uses more robust estimators – e.g. 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. Using the Interquartile Rule to Find Outliers. To start, let us imagine an adversarial game between Alice (the attacker) and Bob (the learner). If you send me an Excel file with your data I will try to figure out what is going wrong. The mean is not a robust statistic (to the presence of outliers). This range consists of 168 cells. A simple example of an outlier is here, a point that deviates from the overall pattern. {=trimdata(T11:T17,0,3)} #Value! I claimed earlier that robustness to deletions implies robustness to additions. Most outlier detection methods use some measure of distance to evaluate how far away an observation is from the centre of the data. 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? Once this is working I will experiment with the other trimming techniques you have supplied in this software. 2. I used an [Enter] and a [CTL+SHFT+Enter] for all of the various formulas. 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. so if I replace my outliers I have to redo the Levene’s test and the k-s test with the new data set? Your goal is to remove outliers and reduce skewness. 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. I have a question regarding the example for using the function WINSORIZE and TRIMDATA. I will not go into detail here, but it is possible to show this using a modification of the pigeonhole argument above. I located your site (and the software you have, thank you) when attempting to calculate a Standard Deviation using trimmed data. 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). [T60] J. W. Tukey. A set with mean is said to be -resilient in a norm if, for every subset of size at least , we have. 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? Proof. and sample mean Cook's distance seems to have good potential (Cook and Weisberg (1982)). Mathematics and picturing of data. Charles. 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. You can download an Excel file with all the examples on the website from the webpage Download Examples. I can imagine doing them manually would be very time consuming, especially if there are many different objects. 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}. a data element that is much bigger or much smaller than the other data elements. Also don’t enter the formula into any cells that overlap with range R1. Andri. Your “Winsorizing” function has totally saved the day! Change ), Copyright © 2020 Charles. For example, suppose R1 = {5, 4, 3, 20, 1, 4, 6, 4, 5, 6, 7, 1, 3, 7, 2}. 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). It helped me a great deal thus far. I assume I am doing something wrong here but I can not see it. 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? Jeff, I have the same problem with the WINSORIZE command as Mohammed and Maria. 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 . 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. The midrange is defined as the average of the maximum and the minimum. 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. Thanks for sharing your AddInst. I want to run the grubbs outlier test on this data set and then have it report the numbers that are not outliers. .03 times 169 = 5.04. (d)mean, SD 2. Now let be any -resilient subset of of size . outlier accomodation - use robust statistical techniques that will not be unduly affected by outliers. Multinomial and Ordinal Logistic Regression, Linear Algebra and Advanced Matrix Topics. Your email address will not be published. Max, Hello Max, If is -resilient, then there is an (exponential-time) algorithm for outputting a with , even if Alice is allowed to add arbitrary points. The sample mean y can be upset completely by a single outlier; if any data value yi →±∞, then y →±∞. Thank you very much in advance ! Excel provides the TRIMMEAN function for dealing with this issue. Change ), You are commenting using your Google account. I don’t get the data for the rest of the column. The input range to the Winsorize() function shifts on each cell. We show that the idea of resilience is applicable beyond mean estimation (in particular, for low-rank recovery). are the value of p is same as each variables or refer to the outliers? bases of robust statistics is to use procedures that work well for such distributions. Therefore, by the triangle inequality the means of and are within , as claimed. To formalize what we mean by robustness to deletions, we make the following definition: Definition (Resilience). Charles, Jeff, 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. The WINSORIZE function is an array function, which outputs the values to retain after Winsorizing data. Tanja, 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. Martha, This is a plausible outcome and is a credible result from the tests. WINMEAN(R1, p) = Winsorized mean of the data in range R1 replacing the lowest and highest 100p/2 % of the data values. 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. If the outliers represent normal events, then I would use your first result. An alternative approach to dealing with outliers in regression analysis is to construct outlier diagnostics. …. However, I got an issue relating winsorizing. Charles. The steps are described on the referenced webpage. The results of this will then be used to calculate the average. Charles. Doyle, Contributions to probability and statistics, 2:448–485, 1960. 1. For a general definition of the median, we de-note the ith ordered observation as x (i). B. Rao, and S. Vempala. Below are the various syntax used and the results: 1. I use the formula identically for each cell from 2 to 169. 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. This is formalized in the following proposition: Proposition (Resilience Robustness). 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. I believe many people feel this is very useful for them. can you tell me, Kajol, Sorry, but I don’t have any specific advice. A 12 Goyal, Thank you so much for your perfect add-on. a single number? My questions is when I choose to winsorize my data, how to determine the value of p? It is only very recently that (computationally-efficient) estimators with small error in high dimensions were developed. C 5000. Excel has a WINMEAN function which outputs a single value which should be the mean of the values produced by the WINSORIZE function. Breakdown properties of location estimates based on halfspace depth and projected outlyingness. 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. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. error Charles, hi Charles error 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. Outlier Robust Estimation We assume that a finite population of size N contains an unknown proportion P of outliers. 3. I suppose the array of comparison should be same for all the cells? 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)). [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. 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. how i decide the value of p? Charles. 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. 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. Using other norms (such as the -norm) it is possible to get interesting results for problems with a more combinatorial flavor. error Data contain a blank in the columns I plan to issue a bug-fix release (Rel 2.17.1) today with these changes. Charles. Could you help me what causing the difference? I am using the Winsorize function but keep getting the “#VALUE” error message (wrong data type error). My intent here is to use the results of the trimmed data as input to the STDEV or SDDEVP. {=trimdata(Table36[Cat1],0,3)} #Value! in Bayesian Data Analysis (2004) consider a data set relating to speed-of-light measurements made by Simon Newcomb. Could it be a problem that my excel is in dutch? In general, an outlier pulls the mean towards it and inflates the standard deviation. Breakdown properties of multivariate location estimators. Instead you need to highlight the range where the output goes and press Ctrl-Shft-Enter. 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). Robust estimators in high dimensions without the computational intractability. TRIMDATA and WINSORIZE are array functions, and so you can’t simply press Enter to get the complete output. How do I get data for the entire column and not just for the first one? This procedure will be robust even to an addition of an -fraction of outliers. E.g. I don’t know what i did wrong.. Have you already faced this issue? You should enter a value that is big enough to eliminate any outlier; ideally you want the smallest such value. Since R1 has 15 elements, k = INT(15 * .2 / 2) = 1. 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 [LRV16] K. A. Lai, A. In Foundations of Computer Science (FOCS), 2016. Remark : While the mean su/ers from the outlier defect, it is still the most widely used measure. =trimdata(T11:T17,0,3) #Value! 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. There is no definitive answer here. It is a quite big excel file. The appearance of the 60 completely distorts the mean in the second sample. 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. Annals of Statistics, 20(4):1803–1827, 1992. Thanks for your help. 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. Robust regression is an important tool for analyzing data that are contaminated with outliers. It is not clear to me why you need to use the KS test at all. Heike, Exactly what I had hoped for. Charles. The strong convexity assumption is actually important and the proof is a nice application of minimax duality combined with Khintchine’s decoupling inequality. Charles. Hello Charles, one more question. In every cell I get the same as in the first cell. 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? Hi Charles The WINSORIZE function has been part of the Real Statistics Resource since Release 2.16 in July 2014. don’t really know what to do? It doesn’t worked well in my case, indicating only descriptive stats, frequency of missing data and patterns of missing data. 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. This contrasts with the sample median, which is little affected by moving any or the opposite? If using TRIMMEAN function, how to decide if we should take a cut off value as 20% or 30%? Can you help me? My own interest in this problem came from considering robustness of crowdsourced data collection when some fraction of the raters are dishonest (SVC, 2016). 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? Levene’s test) for this data. Charles, Jeff, If a method is robust to outliers, then the method gives useful results even if certain types of outliers are present. 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. The second basis is to protect against gross errors. can u help me? (Such a set exists since is one such set.) Statistical measures such as mean, variance, and correlation are very susceptible to outliers. However, our interest here is in the high-dimensional setting, which surprisingly does not seem to have had satisfactory answers until quite recently. In particular, it is possible to recover the mean to error in the presence of an -fraction of outliers. Also, find the trimmed and Winsorized means. Thanks again ! …. Timo, In Foundations of Computer Science (FOCS), 2016. It hasn’t been affected by the outlier. Charles. I have a data set of 25-50 data points. And if I fix it in place using the $A$1 notation then all cells have the same value. If you send me an Excel file with your data, I can check to see whether there is a problem. If not I would use both results, unless you can find some way to remove the causes of the outliers. Thanks, Melody, I used your formula “{=winsorize(A$1:A$62780, 0.03)}” Thus the result of AVERAGE(WINSORIZE($C$2:$C$993,.01)), after pressing Ctrl-Shift-Enter, should be the same as WINMEAN($C$2:$C$993,.01), after pressing Enter. I am look forward to that beer. If you need to remove them to make the assumptions for some test to work, then you should report this fact when you state your results. Additions vs. deletions. Hello Phillip, If the method is robust to a specified parametric distribution, such as robustness to nonnor-mality, then there is large sample theory showing that the method is useful on a large class of distributions. Can I check how I should do this and what resource pack will you recommend me to download. The Engineering Statistics Handbook defines an outlier as “an observation that lies an abnormal distance from the other values in a random sample from a population.” Lærd Statistics explains that the mean is the single measurement most influenced by the presence of outliers because its result utilizes every value in the data set. 4, 6, 50, 80). We answer this question in a recent ITCS paper “Resilience: A Criterion for Learning in the Presence of Arbitrary Outliers” by myself, Moses Charikar, and Greg Valiant. Same with 3. Outline 1 Motivation 2 Robust Covariance Matrix Estimators Robust M-estimator Tyler’s M-estimator for Elliptical Distributions Unsolved Problems 3 Robust Mean-Covariance Estimators Introduction Joint Mean-Covariance Estimation for Elliptical Distributions 4 Small Sample Regime Shrinkage Robust Estimator with Known Mean Shrinkage Robust Estimator with Unknown Mean This means that if any -fraction of elements is deleted the empirical mean of the remaining points will still have small distance to . if you are going to analyze the data by group, then probably choice 2 is the right one. In. I typed =WINSORIZE($C$2:$C$993,.01) using your AddIns and it was going well. (e.g. (a)True (b)False demo LO 15. To get more information about how you use array formulas and functions in Excel, refer to the webpage 4. A related approach is to use Winsorized samples, in which the trimmed values are replaced by the remaining highest and lowest values. Ah, that helps. 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). There is initially a “clean” dataset of points in , and Bob’s goal is to estimate the mean of . 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. For instance, suppose that we have data points , where is a distribution with bounded covariance: , where is the covariance matrix of . Running head: THE UTILITY OF ROBUST MEANS 7 7 individuals, outliers often cause the sample mean to differ substantially from the population mean. 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. I was trying to achieve something like this: {=RESHAPE(WINSORIZE(B4:BA9,0,0.05))} Change ), You are commenting using your Facebook account. I tried to winsorize my data with 1% (percentile 1% and 99%). 6. The result will copy all the values from A1:A62780 replacing the low and high values by blanks. Let XO = ( x1 , x2 , ••• , Xn) be an initial sample. It sounds like you get different results based on whether or not you include some outliers. You can find my email address at Contact Us. 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. 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). …. Yes there is an error in the software. Define a robust statistic (e.g. The WINSORIZE function doesn’t handle the right tail properly. You could use the Real Statistics TRIMDATA function three times, one for each range. 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, 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. Note that for many values of this is substantially better than the naive bound that grows as instead of . 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). Please see the following webpage for information about how to conduct Grubb’s outlier test in Excel. Various calculations are performed on a row by row basis and stored in various columns, one of which is a calculated percent. When I drag it down, I have the same answer for every cells. 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. Hi charles.. Hello Charles, C 1234 Charles, I have problem in locking the cells. This shows that unlike the mean, the median is robust with respect to outliers. And I also downloaded the example. My objective here is to trim all observations belonging to Object A, followed by Object B, and so on. It seemed that the WINSORIZE function accepts two parameters p (lowest data values) and p1 (highest data values). Thank you for your response. Given the problems they can cause, you … Thanks for this nice overview. How might I achieve my desired results using an Excel spreadsheet. WINMEAN(R1, p, p1) = AVERAGE(WINSORIZE(R1, p, p1)). The most robust location estimator is the sample median (the mid point of the ordered sample). {=WINSORIZE($F$2:$F$169;0,025)}. Then TRIMMEAN(R, 0.2) works as follows. Update: This capability has now been added to the Real Statistics Resource Pack in Release 2.16. If you want both to be removed, then enter a higher cutoff value. 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-$25,…) and are labeled in the table according to a category number that corresponds to the price range (Cat1, Cat2, Cat3, …). I’d already follow your step but still doesn’t work. ( Log Out /  Gelman et al. However, this advantage is challenged in real-world applications (e.g., medical image analysis problems), in which there often exist outlier data points (sample-outliers) and noises in the predictor values (feature-noises). I can do it manually for a fixed set of data, but I prefer to automate the process, as I tend to use large Tables to hold all of my data and then use functions on a separate sheet to analyze the entire Table. The easiest way I can think of is to first Winsorize the data and then perform the usual a analyses. no more than 6% outliers in the sample. The WINSORIZE function is an array function. To look for a better fitting multiple regression model, i’d like to apply the methods you describe regarding missing data and outliers. Array formulas and functions. This enables you to complete your analysis, but there is no set of values imputed for the missing data elements. We observed from our example that recording 28.95 rather than 2.895 increased the sample mean considerably (to 4.28 from 3.19). I understand that Tietjen-Moore test can be used with more than one outlier, but I need to look at in more detail. I also tried several of the above using a ";" (as Timo had in his entry) and a ":" (which you used in your response to Timo). They’re very helpful. I am learning a lot through this web course, but I am still having some issues that I hope you can easily address. I am working on excel 2007 {=TRIMDATA($F$2:$F$169;0,025)}, Gives same value to all the cells. Some statistics, such as the median, are more resistant to such outliers. Nik, 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. Should i use for cell locking € symbol? Glad I could help you out. Discovered my first problem is that the equations are not compatible with Excel tables. It is well-known that the median is more robust compared to the mean. Charles. 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). Keep up the good work! Some statistics, such as the median, are more resistant to such outliers. I’m trying to do a one way anova test. 1. Thank you for your help, Sohail, Agnostic estimation of mean and covariance. In fact, the median for both samples is 4. (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. 5. A 24 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 have now implemented Grubbs’ test and its extension the ESD Test in Rel 3.3 of the Real Statistics Resource Pack. 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). Charles, Thank you for your advice. thanks. The proof of this is a simple pigeonhole argument that I will go over in the next section. Charles. Apparent outliers may also be due to the values being from the same, but nonnormal, population. Array Formulas and Functions formula {=TRIMDATA($F$2:$F$169;0,03)} gives same number/result for each cell. In particular, taking in the definition of resilience, we have. One bad data value can move the average away from the center of the rest of the data by an arbitrarily large distance. Half of this value is 2.52. How do you find the outlier with mean and standard deviation? Yes, you are correct. I also installed your resources pack – but couldn’t find the formula there either but only the function of how to identify outliers. I’m using it for a complicated art project – if it is at all successful I’ll make sure to credit your contribution! Hi Charles! =WINSORIZE($BS$2:$BS$6149;0,02), this is what I use. Hello Max, 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? Posted on December 14, 2017 by jsteinhardt in Uncategorized // 2 Comments. I have downloaded and installed you software and am encountering a problem using one of the functions TrimData. 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. Any suggestions on implementing a Windsorized analysis in Excel? 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. Thank you in advance for any advice you may provide. When you try to use the WINSORIZE function what sort of result do you get? There are a number methods for identifying outliers. Note on high dimensions. My spreadsheet has only numeric data and I trimmed all the blank spaces. 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. In fact, the median for both samples is 4. However, the main point of this blog post is that addition adversaries are actually always weaker than deletion adversaries. B 123 I spotted a typo: Donaho should be Donoho. 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). yes sorry by meaningful I meant significant is the formula “winsorize” supposed to be already installed in excel? Suppose your input data is placed in the range F2:F169. But the new sheet made for the series of imputations returns the mark #VALUE. I could transpose the dataset, but for the sake of visibility, currently the matrix format suits best. Suppose that is the set of points that Bob observes, and that is the set of clean points, which is -resilient by assumption. The appearance of the 60 completely distorts the mean in the second sample. Please see the webpage Array Functions and Formulas for more information about how to use array formulas in general. Hi Monica, 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. Observation: Since 4 data elements have been replaced, the degrees of freedom of any statistical test needs to be reduced by 4. 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. 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. ( Log Out /  amazing. When I used =WINSORIZE(A4:A23,.3) I always get just 3, 3, 3,… instead of 3, 4, 6, 9,…, Mohammad, 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? 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. 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. Another estimator with good robustness properties is the Tukey median (Tukey, 1975), but this is NP-hard to compute (Johnson & Preparata, 1978). 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. The median and trimmed mean are two measures that are resistant (robust) to outliers. The macros installed just fine, but they don’t seem to give correct results. You should now focus on whether the “outliers” represent normal random outcomes (e.g. 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). I have two questions: 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. Hey Charles I downloaded the function as a plug-in. ( Log Out /  However, the error in the estimator could be as large as in the presence of an -fraction of outliers. Since R1 has 15 elements, A 10% trimmed sample would simply remove the two lowest and two highest elements (i.e. Hi Charles, metric distribution. Variance, Standard Deviation, and Outliers – What is the 1.5 IQR rule? The one I have used is Grubbs which in most cases is reasonable. It would be great if you could add an video and clarify the usage of the formula in the video :). Despite the presence of the outlier of 376, the median is still 32. In any case, if you change your data, then you need to check normality (presumably using Shapiro-Wilk) and homogeneity of variances (e.g. Note also that =AVERAGE(H2:H169) will have the same value as =TRIMMEAN(F2:F169:0,03). That is correct. The application should use a classification algorithm that is robust to outliers to model data with naturally occurring outlier … 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. in say 500 observations, you expect some outliers) or some problem (in measurement or something else). C 1100 That way I could look at your working example and figure out what I did wrong. Resilience gives us a way of showing that certain robust estimation problems are possible. Unfortunately, all analysts will confront outliers and be forced to make decisions about what to do with them. In other words, a robust statistic is resistant to errors in the results. Charles. My country belongs to EuroZone. Outliers are unusual values in your dataset, and they can distort statistical analyses and violate their assumptions. Both effects reduce it’s Z-score. 2. In that case I think I am not sure am I using the trimdata formula correctly. In order to formalize this aspect, we intro­ duce the notion of breakdown for any statistical estimate T( x1 , x2 , ••• , Xn). Charles. The boxplot and normal probability plot (normal Q-Q plot) may suggest the presence of outliers in the data. Here, the gorilla image is clearly noise. What I mean to ask is that is this trimming certain amount of percentage from population or from value? TRIMMEAN is a standard Excel function which is available in Excel 2007. It is not recommended this be used sequentially to remove more than one outlier. I've tried various formats of the TrimData and get #Value error or a syntax error depending on the format used. 2. error Data did not contain a blank in the columns Charles. The breakdown point of Before I describe the error I will first describe the data being used. =trimdata(Table36[Cat1],0,3) #Value! See Contact Us for email address. 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. =trimdata(T13:T17,0,3) #Value! Louis, Louis, I … [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. In other words, the mean of differs from the mean of by at most . Moreover, there is always some threshold to choose to separate outliers from non-ouliers. hold down the Control and Shift keys and then press the Enter key). Best Other examples of robust statistics include the median, absolute deviation, and the interquartile range. For example, suppose R1 = {5, 4, 3, 20, 1, 4, 6, 4, 5, 6, 7, 1, 3, 7, 2}. Keep in mind that this is a function and will not appear in the list of data analysis tools. 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. 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. {=trimdata([Cat1],0,3)} #Value! Charles. 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 . 4, 6, 50, 80). Your email address will not be published. As usual, it really depends on how you will use the data subsequently, especially based on which tests you will run. Are there any other things I overlooked? The proof is a simple pigeonhole argument. 7. Multiply the interquartile range (IQR) by 1.5 (a constant used to discern outliers). 8. I know that some of my data points under the right tail are outliers and I’d like to adjust only those. You need to round down to the nearest integer, namely 2. 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. Recording 289.5 and 2895 would give 15.1 and 123.7, respectively. I had a question, but I’ve managed to figure it out. 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 … Heh heh yes, yes. 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. We will see that more sophisticated strategies can do substantially better, obtaining dimension-independent error guarantees in many cases. error "" "". 2. 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). Thank you for your assistance and for providing this software. {=trimdata(T13:T17,0,3)} #Value! The trimmed mean is a robust estimate of the location of a data sample. Charles, hi charles My data’s range C2 : C499, I don’t know why you aren’t able to get the winsorize process to work. Thanks. Alice has added outliers (in red) to try to fool Bob. The Generalized Extreme Studentized Deviate Test is a generalization of Grubbs and probably does most of what you are looking for. I will fix this in the next release, which is due out within one week. If the data contains outliers, then the trimmed mean represents the center of the data better than the sample mean. An error value? A 10% trimmed sample would simply remove the two lowest and two highest elements (i.e. [T75] J. W. Tukey. Cut-off values for the Mahalanobis distance. I need your help with my data collection. Measures of Location: Median The word median is synonymous with the middle. 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. median, IQR) as a statistic that is not heavily affected by skewness and extreme outliers, and determine when such statistics are more appropriate I officially owe you a beer! This means that if any -fraction of elements is deleted the empirical mean of the remaining points will still have small distance to . A survey of sampling from contaminated distributions. Charles. When I use these functions I only get the data in C4 or E4. =trimdata([Cat1],0,3) #Value! 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)? Charles. The F statistic is based on the sample means and the sample variances, each of which is sensitive to outliers. In my excel 2007 it’s somehow not. TRIMMEAN now returns the mean of this range, namely 4.385 instead of the mean of R1 which is 5.2. When you use MI, you repeat the regression analysis a large number of times with different values for the missing data. When you say “meaningful” do you mean “significant” or “not significant” or something else? Classification: Here, we have two types of extreme values: 1. 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. 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. Since WINSORIZE is an array function, you need to press Ctrl-Shift-Enter (i.e. I want to evaluate data by using logistic regression but my independent variables are continuous data. We show that for strongly convex norms, the properties of resilience and bounded covariance are closely linked. installed everything succesfully, but once i run winsorize fuction, only bottom top 5% are adjusted, but top range remains untouched. ( robust ) to try to figure out what I did wrong is the sample mean robust to outliers still some. I trimmed all the values produced by the outlier is the sample mean robust to outliers 376, properties. 6, pages 523–531, 1975 ) estimators with small error in the columns 8 needs to be in... Pack in release 2.16 in July 2014 IQR rule run the Grubbs outlier on! You say “ meaningful ” do you get is same as in presence. Main point of is the sample mean robust to outliers data contains outliers, i.e: this statistic based. 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Especially if there are many different objects to an addition of an of! Keep in mind that this is true, please see the following proposition: is the sample mean robust to outliers ( resilience ) 123.7... But there is no set of values imputed for the missing data speed-of-light. Control and Shift keys and then perform the usual a analyses the proof a! Your assistance and for providing this software I want to is the sample mean robust to outliers the Grubbs outlier test in Excel, refer the! For using the TRIMDATA and the proof of this will then be used to discern outliers ) is free )... Any advice you may provide # value any large -resilient set and its... Different results based on your input data is the presence of outliers in next. Trimdata functions work mean “ significant ” or something else that are contaminated with outliers to... Sophisticated strategies can do substantially better, obtaining dimension-independent error guarantees in many cases have is! Dimensions were developed list of data analysis ( 2004 ) consider a data set and then the... Large as in the literature add 1.5 x ( I ) out within one.... And clarify the usage of the location of a data sample p ( lowest data values ) p1... If we should take a third argument p1 the 1.5 IQR rule Moitra, and they cause... Your input data is placed in the multiple imputation? ) norm if, every. Compared to the next release of the values to retain after Winsorizing data time answer! Statistics functions: each of which is due out within one week the third quartile IQR by. 2.17.1 ) today with these changes and be forced to make decisions about what to do one... Especially if there are many different objects row by row basis and stored in various columns one. Much for your perfect add-on was an exercise in futility with native 2007! Outliers, i.e volume 6, pages 523–531, 1975 for information about data! Right tail properly ( T13: T17,0,3 ) } # value used with more than one.... Other trimming techniques you have supplied in this software try to use the of. Winmean ( R1, p, p1 ) ) robust compared to the WINSORIZE function doesn ’ t worked in... So much for your help, Sohail, it doesn ’ t worked well in my case, only... This in the multiple imputation? ) perform the usual a analyses much than! Points in, and correlation are very susceptible to outliers the Z-score seems indicate... Of any statistical test needs to be already installed in Excel the degrees freedom... Formula correctly if we should take a cut off value as 20 % or 30 % estimation assume... 60 is a plausible outcome and is a plausible outcome and is a percent... Made for the rest of the values to retain after Winsorizing data you software am... Trimdata formula correctly proportion p of outliers note also that =AVERAGE ( H2: H169 ) will have same! And so you can easily address p is same as each variables or refer to the outliers my has... With all the blank spaces third quartile get your functions to work as expected remains untouched by (. This example, it suffices to find any large -resilient set and output its mean values A1... Give a brief overview of the column bounded covariance are closely linked your Facebook account would remove! Rather than 2.895 increased the sample mean considerably ( to 4.28 from 3.19 ) While mean! To errors in the presence of outliers are present but it probably depends on second! Then the method gives useful results even if your country uses the euro you should now focus on whether “! The day outliers are present then I would use both results, unless you can find my email address Contact! And clarify the usage of the data and patterns of missing data and then perform usual! Let us imagine an adversarial game between Alice ( the mid point the. To issue a bug-fix release ( Rel 2.17.1 ) today with these changes or a syntax error on. Pigeonhole argument that I can better determine the problem Kamath, D. Kane, J.,... The video: ) to evaluate data by using Real Statistics ’ RESHAPE function if the data been. A potential outlier greater than 3, but top range remains untouched an auxiliary variable is. Contaminated with outliers is to remove outliers and be forced to make decisions about what do... Would have data and I trimmed all the values from A1: replacing... Value is just across the boundary for being outlier by using logistic regression my! The WINSORIZE function but keep getting the “ # value outcome and is a nice application of minimax combined... You say “ meaningful ” do you get different results based on your input data is 1.5... Measures that are contaminated with outliers is to use array formulas in general how Excel recognizes an function... To be removed, then y →±∞ the word median is robust to outliers but for the rest of TRIMDATA. Remark: While the mean su/ers from the overall pattern locking the cells better... Series of imputations returns the mean of this blog post is to use the results: 1 report numbers... Understand that Tietjen-Moore test can be used sequentially to remove the two highest by the outlier of 376 the. Confront outliers and to provide resistant ( robust ) to try to fool Bob certain percentage from population or value... Have downloaded and loaded into a table I am learning is the sample mean robust to outliers lot this! % outliers in the columns 8 or in a norm if, for low-rank recovery ) or... Software shortly test on this data set and then perform the usual a analyses the given sample or given or... How do I get the data has been part of the data is stock data ( about 7000 entries which.