## Remove Outliers Normal Distribution

If A is a matrix or table, then filloutliers operates on each column separately. Detection of Outliers. Here is the Standard Normal Distribution with percentages for every half of a standard deviation, and cumulative percentages:. removing outliers in non-normal distributions. (f) Normal distribution is right skewed. You should now focus on whether the "outliers" represent normal random outcomes (e. More complex approaches apply multivariate tools to look for outliers through various density or distance based algorithms. The IQR (Q3 - Q1) represents 2 x. N = 185 Distribution for females Distribution for males 60 Use non-parametric descriptive statistics • Min. If a value is higher than the 1. An outlier is any value that is numerically distant from most of the other data points in a set of data. Now, after removing outliers we have minimum and maximum value. Thirdly, as stated by Cousineau and Chartier (2010), this method is very unlikely to detect outliers in small samples. Typical procedure in finance, remove public utilities or financial firms from the analysis. outliers in normal distribution look up Q1 and Q3 in the Stand. Remove Outliers with Feature Thresholds. However, these assumptions have not undergone much testing and are not elaborated upon in the original FGDC documents on NSSDA. 24-standard -- -- Table structure for table `archive` -- CREATE TABLE archive ( ar_namespace int(11) NOT NULL default '0', ar_title varchar(255) binary NOT NULL default '', ar_text mediumtext NOT NULL, ar_comment tinyblob NOT NULL, ar_user int(5) unsigned NOT NULL default '0', ar_user_text varchar(255. , and can be used as a screening tool for the initial identification of outliers. Is it dishonest to remove outliers from data? Posted by Cavtini in Uncategorized December 9, 2011 An outlier is defined as a single score in a data set that seems too distant from the normal distribution to be a valid score. That an outlier is an unlikely observation in a dataset and may have one of many causes. Normal Distribution and Outliers One of the strange things about data mining is that most of the theorems and axioms start with, "If X is a normally distributed random variable…" In this section, we are going to discuss what happens "if X is INDEED a normally distributed random variable". Do I remove outliers to make the data normally distributed for ANOVA? people remove outliers if that's the case anova normal-distribution outliers or. In an statistics assignment I had recently, we had to visualise a set without its outliers to determine the best regression model to use for the data. Whether an outlier should be removed or not. A data set n>30 will approximate a normal distribution if it is otherwise t-distributed, but you would have to look at your data to see if they approximate a normal distribution. Learn about the sources of outliers, histograms, scatterplots, the number line, and more. Can you safely remove outliers from scatter charts? If you have observations from a normal distribution, you should expect around 1 in 22 observations to be more than 2 standard deviations. Then take Q3 -Q1 and you get 1. Leptokurtic is a statistical distribution where the points along the X-axis are clustered, resulting in a higher peak, or higher kurtosis, than the curvature found in a normal distribution. Each data point contained the electricity usage at a point of time. In the ‘mean-shift’ model, which is. There are ways to deal with outliers without having to delete them, and in fact the suspicious data may not even be an outlier if the incorrect distribution has been assumed. Click Analyze from a Column data table, and then choose Identify outliers from the list of analyses for Column data. Working with Scatter Plots in Power BI. randn(100, 3)) from scipy import stats df[(np. For each iteration, Statistica removes any outliers detected in the previous iteration, recompute the statistics (mean, standard deviation), and identify any new outliers. This is a plausible outcome and is a credible result from the tests. In this plot, the actual scores are ranked and sorted, and an expected normal value is computed and compared with an actual normal value for each case. Distribution-based approaches develop statistical models from the given data and then identify outliers with respect to the model using discordance test. Another possibility is that the case did not come from the intended sample. I really don't want to remove more than small fraction of the data, and preferably only that when these are outliers. A quick and dirty implementation of this would be. 621% of the data should have a z-score larger than 2. In fact, if the outlier was taken as the mean of an alternate mechanism with similar properties to the first, its. I demonstrate why it is statistically absurd and point out how. If the data come from the normal distribution, the mean, median, mode, and the trimmed mean are all equal. I choose k=1. ) The outlier is part of the population you wanted but in the distribution it is seen as an extreme case. Morse should do to help his patient?. The names of the counties were entered as case names. Details The function can perform three tests given and discussed by Grubbs (1950). Outliers seem especially relevant for endocrinological studies, since hormonal data, such as T, typically do not conform to normal distributions. Anomaly detection. , a normal distribution. This should not surprise us, even in the ﬁrst experimental run of a new production line, be-cause the Mahalanobis distances are known to suﬀer from the masking eﬀect. Sometimes a point is so close to the lines used to flag outliers on the graph that it is difficult to tell if the point is between or outside the lines. Thus, if the mean is intended as a measure of the location of the center of the data, it is, in a sense, biased when outliers are present. 5 and add it to. The outlier airports cause the external ripples of this distribution. You can see few outliers in the box plot and how the ozone_reading increases with pressure_height. In normally distributed data a outlier is not always caused by a special cause. continuous distributions. As other writers wisely advised, you should only remove outliers for a good reason and you should document what was removed and the rationale. ” When you simulate data, you know the data-generating distribution. We do not require any assumptions on the distribution of the outlier points; our simulations in the next section consider a uniform distribution and a half-normal. That is, even if there were a group of outliers (here, deformed diaphragm parts),. A particular procedure for rejecting outliers, and also a particular procedure for modifying outliers, are considered for samples of size three, supposed drawn from a common normal population except that one of the three readings may have an added bias. If the data come from the normal distribution, the mean, median, mode, and the trimmed mean are all equal. A data set n>30 will approximate a normal distribution if it is otherwise t-distributed, but you would have to look at your data to see if they approximate a normal distribution. Outliers are extreme, or atypical data value(s) that are notably different from the rest of the data. 05 for them to be considered outliers. The Normal Distribution Assumption and Outliers - blogspot. , mean, variance) Number of expected outliers (confidence limit) Grubbs’ Test Detect outliers in univariate data Assume data comes from. We wish to reset points deemed outliers to a. kstest_normal lilliefors. 68 or greater than 2. The function lme, a linear mixed effects model from the package nlme [30] , was used with channel as a random effect to analyse the effects of the treatment on final body length, body mass, and percentage of body fat for the trapping experiments. However, consider a single outlier value, say an extremely high price. It appears that this is not what you are trying to do. See the section Normal Distribution for details, and see Example 4. However, outliers will always exist in research, that is why I feel it is not necessarily unethical to take them out. Outliers have also been shown to detrimentally impact testing for mean differences using ANOVA through biasing group means where they are present (Osborne and Overbay, 2004). Sometimes in regression analysis, a few data points have disproportionate effects on the slope of the regression equation. Probability of getting an outlier in a normal distribution. Is it dishonest to remove outliers from data? Posted by Cavtini in Uncategorized December 9, 2011 An outlier is defined as a single score in a data set that seems too distant from the normal distribution to be a valid score. They provide reliable estimates of the distribution of variables on the basis of the observed data through random sampling procedures. For example, due to its skewed distribution, T usually contains multiple outliers when defining outliers based on a normal distribution (Fig. Example 7: Detecting Outliers. If they exist, the distribution is skewed in the direction of the outlier(s). These points are often referred to as outliers. That is, one should first verify that the data can be reasonably approximated by a normal distribution before applying the Grubbs test. 5 or less than -2. Re: Numpy outlier removal. distribution of the data (e. If the outliers represent normal events, then I would use your first result. We will use a gaussian (normal) model to detect anomalous examples in our dataset. By definition, outliers are at a distance of at least є from the end points of the main distribution. There are multiple ways to detect and remove the outliers but the methods, we have used for this exercise, are widely used and easy to understand. NOTABCONTENTS. These are the ones that skew the distribution into the F-shape shown earlier. The test sta-tistic is defined as: max. Learn vocabulary, terms, and more with flashcards, games, and other study tools. The Outliers fall above the Upper Limit and fall below the Lower Limit of the observations. The new test statistics based on the superior estimators for the population parameters are given. We simply require a BLUE Estimator (Best Linear Unbiased Estimator). Re: Numpy outlier removal. It has been proven that predictions from the model will be increasingly biased. all(axis=1)]. It is usually assumed that the response errors follow a normal distribution, and that extreme values are rare. Many variables in biology have log-normal distributions, meaning that after log-transformation, the values are normally distributed. The statistical analyses were performed with R, v. Which of the following statements are true? Check all that apply. The Normal Distribution Assumption and Outliers - blogspot. edu ABSTRACT Defining outliers by their distance to neighboring examples is a popular approach to finding unusual examples in a data set. Novelty and Outlier Detection¶. Identify and remove outliers with SAS Deepanshu Bhalla 16 Comments SAS, Statistics. Data sets may follow normal or Poison distribution. Details The function can perform three tests given and discussed by Grubbs (1950). Online statistical calculator which helps you to calculate outlier probability distribution by entering set of values. When it comes to psychological testing there are many occasions when outliers occur. Can we say that the data points that lie outside the 2nd or 3rd standard deviation is an outlier?. If the test for Normal distribution reports 'reject Normality' the outlier detection methods may be invalid since they assume that the data follow an approximately normal distribution. The very purpose of this diagram is to identify outliers and discard it from the data series before making any further observation so that the conclusion made from the study gives more accurate results not influenced by any extremes or abnormal values. If successful, the technique could be used to predict animal use areas, or those. On the boxplot shown here outliers are identified, note the different markers for "out" values (small circle) and "far out" or as SPSS calls them "Extreme values" (marked with a star). test for normal distribution of residuals. Example 1: Identify potential outliers for the three data samples on the left side of Figure 1 (range B3:D16). We use multivariate normal distribution to detect servers with very low probabilities and hence can be considered anomalous (outliers). Rather than remove outliers, an alternative approach is to fit all the data (including any outliers) using a robust method that accommodates outliers so they have minimal impact [2,3]. What to do with outliers in data? What is a normal distribution?. 96 standard deviations from the mean. The question is whether they are nearly normally distributed, and free of outliers. Figure 1 illustrates the standard normal probability distribution and a bimodal. Detect outliers using the four. The statistical analyses were performed with R, v. With this equation, the kurtosis of a normal distribution is 0. 1 Univariate methods. has a normal distribution; and the raw variables correlate strongly (r>. Mining Distance Based Outliers in Near Linear Time with Randomization and a Stephen D. , mean, variance) – Number of expected outliers (confidence limit). If you use the above equation, the kurtosis for a normal distribution is 3. Outliers can corrupt such surrogate models because they do not follow this assumed distribution. its usally 1. In an statistics assignment I had recently, we had to visualise a set without its outliers to determine the best regression model to use for the data. Is there a specific way of removing outliers from a data set that has a non-normal distribution? not to remove much of the outliers. Negative values indicate a flat (platykurtic) distribution, positive values indicate a peaked (leptokurtic) distribution, and a near-zero value indicates a normal (mesokurtic) distribution. The result is a distribution of the statistic (e. There isn't a set method to identify/remove outliers so you'll have to be more specific. Morse should do to help his patient?. Let's replace the outliers with minimum and maximum value. • Range = Max. We therefore conclude that the observations with ages 74 and 80 should be flagged as extreme outliers in the distribution of ages. Because of this, every analysis should begin with either a graphical or statistical check about the possibility of outliers. In this plot, the actual scores are ranked and sorted, and an expected normal value is computed and compared with an actual normal value for each case. First test (10) is used to detect if the sample dataset contains one outlier, statistically different than. In our example, we will use the hsb2 data set and we will investigate the distribution of the continuous variable write , which is the scores of 200 high school students on a writing test. For example, in a normal distribution, outliers may be values on the tails of the distribution. These I feel are unethical to remove. q-q plots for normal data with general mean and scale. Also you want to be convinced that the people you eliminate for sleeping would not have very different reaction times compared to the ones that remain. Outside 2 standard deviations. Multivariate Model Approach. Figure 1 – Identifying potential outliers and missing data. 5×IQR" as being a "step". There are many outlier tests available which allow analysts to inspect suspect data and if necessary correct or remove erroneous values. It is usually better to focus more on violations of the other assumptions and/or the influence of a few outliers (which may be mainly responsible for violations of normality anyway) and to look at a normal probability plot or normal quantile plot and draw your own conclusions about whether the problem is serious and whether it is systematic. ratcliff (1993) investigated the effect of these methods by using Monte carlo simulations on rt data. Mild outliers are observations that are between an inner and outer fence. , normal distribution) Apply a statistical test that depends on – Data distribution – Parameter of distribution (e. The Government Printing Office (GPO) processes all sales and distribution of the CFR. Outliers have also been shown to detrimentally impact testing for mean differences using ANOVA through biasing group means where they are present (Osborne and Overbay, 2004). is not possible to remove random errors. Both do not show the original distribution, however. The median of a normal distribution to outlier as lu An outlier can be very large or small. Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. 5 times of Interquartile. A deeper discussion of this approach is outside the scope of this article. Standardization, or mean removal and variance scaling¶. Typical procedure in finance, remove public utilities or financial firms from the analysis. This method is also known as Tukey’s method. I would consider trimming/Winsorizing if I think that my data are from a contaminated normal distribution. -Removing an outlier from a data set will cause the standard deviation to increase. R's mahalanobis function provides a simple means of detecting outliers in multidimensional data. However, consider a single outlier value, say an extremely high price. Outliers are individual values that fall outside of the overall pattern of the rest of the data. 3 ways to remove outliers from your data. 90) Criterion for outliers Outliers are not what SPSS calls "extreme values", just so that is clear. Now, after removing outliers we have minimum and maximum value. I applied this rule successfully when I had to clean up data from millions of IoT devices generating heating equipment data. Robust fitting can find reasonable best-fit values of the model's parameters but cannot be used to compare the fits of alternative models. That the interquartile range can be used to identify outliers in data regardless of the distribution. sensitive to outliers if the summary statistic is greatly affected by the removal of outliers. 5) shows that the quantiles of the unselected observations fall along a straight line, indicating that those observations appear to be normally distributed. It is usually assumed that the response errors follow a normal distribution, and that extreme values are rare. (g) Mean is more robust to outliers. Each data point contained the electricity usage at a point of time. Written by Peter Rosenmai on 25 Nov 2013. The process of identifying outliers has many names in data mining and machine learning such as outlier mining, outlier modeling and novelty detection and anomaly. Apart from normal distribution assumption, the additional assumption that two metrics come from a population of equal variance can be a big disadvantage for this method. Moreover, the Tukey’s method ignores the mean and standard deviation, which are influenced by the extreme values (outliers). Both the pre-period and post-period costs are converted to natural logarithm values and assumed to be distributed as log-normal. Here, di is the difference between the performance metrics of two algorithms. How do I remove or deal with outliers? Removing outliers can cause your data to become more normal but contrary to what is sometimes perceived, outlier removal is subjective, there is no real objective way of removing outliers. DOE Analyze Graph Tools View Window Help Quantiles M aments More Moments Class Data- Distribution of Siblings Distributions Display Options Histogram Options Normal Quantile Plot Outlier sox Plot Quantile sox Plot Stem encl Leaf CDF Plot Test Mean Test Std Dev. The logarithm function tends to squeeze together the larger values in your data set and stretches out the smaller values. This article takes a look at the four techniques to detect and optionally remove outliers from delays against the density of a standard normal distribution. Basically, I am wondering about taking the (it is large) sample, resampling, building a distribution of the bootstrap mean or median and then building a confidence interval (using percentile method, Bca what ever). How to check and remove outliers when it is Learn more about outlier, mapstd, z-score, transformation, preprocessing, normalization Deep Learning Toolbox. –The normal distribution is theoretical. What we do here, we replac the outliers with some representative values like mean, median, minimum or maximum values etc. For example, in a normal distribution, outliers may be values on the tails of the distribution. Grubbs' Outlier Test Introduction It is well known that outliers (extreme points) often distort the results of an analysis. 4-5 -3 -1 1 3 5 Bimodal Distribution The t-test and ANOVA (Analysis of Variance) compare group means, assuming a variable of interest follows a normal probability distribution. An outlier in a distribution is a number that is more than 1. In a mathematical way of thinking, to detect outliers one has to take into consideration the shape/structure of the data set. Looking at distributions in n-dimensional spaces can be very difficult for the human brain, that is why we need to train a model to do it for us. Finding Outliers in a Graph. Statistical Analysis Outliers - Free download as Powerpoint Presentation (. These approaches are based on the assumption of normal distribution of data. See the article Detecting outliers in SAS: Part 3: Multivariate location and scatter - The DO Loop for some SAS code to do this. If you want to identify them graphically and visualize where your outliers are located compared to rest of your data, you can use Graph > Boxplot. If there are no outliers and the distribution is normal, then the mean and median are the same. or fax your order to 202-512-2250, 24 hours a day. An outlier is a value looking for its distribution - no sorry that is an attempt at being funny. 5×IQR or greater than Q3 + 1. There are now many fields where the outliers / anomalies are the objects of greatest interest. More commonly, the outlier affects both results and assumptions. Every data analyst/data scientist might get these thoughts once in every problem they are. 3 ways to remove outliers from your data. In many parametric statistics, univariate and multivariate. See How do I transform variables? for more information. If the outliers represent normal events, then I would use your first result. Kurtosis is a measure of peakedness for a distribution. However, not all researchers feel that way (c. In the data view of your SPSS window, click on Analyze. , ROA of -25,000) and distort the sample distribution heavily. 621% of the data should have a z-score larger than 2. You should now focus on whether the "outliers" represent normal random outcomes (e. , correlation coefficient > with dependent variable) Code:. One of the best features is it's statistical capabilities So you can find outliers in Excel easily with simple statistics formulas. The outliers can then be formally tested with the Dixon or Rosner test but both assume the underlying data is from a normal distribution. Morse is a psychologist whose current patient wants to become less introverted and more confident. logical scalar indicating whether to remove missing values from x. The above code will remove the outliers from the dataset. NOTABCONTENTS. all(axis=1)]. module5_jobsatis. For a Normal distribution, you’d expect roughly 5% of your observations to be beyond the 2 SD mark. However, with your small samples, note that 100 and 800 are not considered outliers in Ex 3. 5 Methods for Multivariate Outlier Detection. Delete outliers from analysis or the data set There are no specific commands in Stata to remove from analysis or the , you will first have to find out what observations are outliers and then remove them. One of the best features is it's statistical capabilities So you can find outliers in Excel easily with simple statistics formulas. However, in order to decide whether it is dishonest to remove outliers or transform data, it should first be understood what outliers are and why they come about. Five Number Summary; The Five Number Summary is a method for summarizing a distribution of data. But don't we need to remove the outliers to compute good estimates of location and dispersion? No, we don't. Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. in say 500 observations, you expect some outliers) or some problem (in measurement or something else). I am trying to test my Y to find whether its normal or not. You can also construct a normal probability plot. This could be considered as a preliminary step for data analysis. How to Calculate Outliers. These approaches are based on the assumption of normal distribution of data. This way we would see the original distribution where the density is the highest, while at the same time getting a feel for the number of outliers. One of the simplest methods for detecting outliers is the use of box plots. This chapter also describes the central limit theorem, which is frequently invoked in an attempt to deal with nonnormal probability curves. - Normal data objects follow a (known) distribution and occur in a highNormal data objects follow a (known) distribution and occur in a high probability region of this model - Outliers deviate strongly from this distribution Kriegel/Kröger/Zimek: Outlier Detection Techniques (SDM 2010) 17. ppt), PDF File (. Re: Numpy outlier removal. If they don’t hold context, it’s fine to remove them from your dataset so that your histogram displays more normality. The outliers (marked with asterisks or open dots) are between the inner and outer fences, and the extreme values (marked with whichever symbol you didn't use for the outliers) are outside the outer fences. Localization of autonomous underwater vehicles (AUVs) is a very important and challenging task for the AUVs applications. I think a common way of defining an outlier (if normal distribution of data is assumed) is to first find the initial mean and standard deviation of your data. Basically, when a web page is viewed by human users, the IP address has very few hits (1 to 3). In an statistics assignment I had recently, we had to visualise a set without its outliers to determine the best regression model to use for the data. If this is the case you do not need a statistical technique to identify and remove the outliers. Note: This page explains how to identify an outlier from a stack of values in a data table formatted for Column data. remove-circle Share or Embed This Item. Figure 1 – Identifying potential outliers and missing data. A look at how outliers effect the shape and mean of data. Use promo code ria38 for a 38% discount. Which of the following statements are true? Check all that apply. Outliers are extreme values that fall a long way outside of the other observations. Multivariate outliers can be found in a n-dimensional space (of n-features). You can see few outliers in the box plot and how the ozone_reading increases with pressure_height. Mining Distance Based Outliers in Near Linear Time with Randomization and a Stephen D. Outliers revealed in a box plot [72] and letter values box plot [36]. kstest_normal lilliefors. Some regulators like for you to use the Sprent Outlier Test as described in - Peter Sprent, Nigel. You can use defined tests and statistical intervals to discuss your data. Note that since there were no suspected outliers on the low end there can be no extreme outliers on the low end of the distribution. That is, even if there were a group of outliers (here, deformed diaphragm parts),. These test statistics assume underlying a normal distribution and the test sample is relatively homogeneous. Note that є is the bin width, and choice of є controls the sensitivity of the algorithm. Is it dishonest to remove outliers from data? Posted by Cavtini in Uncategorized December 9, 2011 An outlier is defined as a single score in a data set that seems too distant from the normal distribution to be a valid score. (j) Only two parameters are required to describe the entire normal distribution. come from a certain kind of statistical distribution, e. It is easily shown that is the maximum-likelihood estimate of ,if is taken to be the common mean of normal distributions with variances , each independently sampled once. Another way to go, is to create one bin for all the outlier values. Last revised 13 Jan 2013. If the outliers are special causes it wise to filter these data points. , drop if ROA <=-5; drop if ROA>5), I would like to apply a somewhat more systematic way. Next plot the lag-1 autocorrelation plot to check for randomness. This example is based on the data file Poverty. Near Linear Time Detection of Distance-Based Outliers and Applications to Security Stephen D. In this SPSS research method, there is a tab for “Statistics”. Outliers and/or demand spikes are points in an items historical demand that are out of the normal distribution. We use multivariate normal distribution to detect servers with very low probabilities and hence can be considered anomalous (outliers). They provide reliable estimates of the distribution of variables on the basis of the observed data through random sampling procedures. Notwithstanding the decision to remove, correct or leave an outlier (for a discussion on this topic see McClelland, 2000), it is necessary to be able to detect its presence. The definitions of the yellow and red card zones are not entirely arbitrary, but not absolutely decreed either. But you'd be wrong: 61 is the only outlier in this data set. Since the quartiles for the standard normal distribution are +/-. You can read about multivariate normal distribution from Wikipedia. Data with this distribution is called log-normal. ncf is a package of programs, all related to the noncentral F distribution. This could not be a general case since determining the distribution or parameters of the underlying distribution is extremely difficult before hand or apriori. To do this, go under the option of "if a condition is satisfied" and indicate "outlier =0. While outliers can be problematic from a statistical perspective, it is not always advisable to remove them from the data. Probability plots are used for graphically displaying a data set's conformance to a normal distribution Symmetric distribution of data (bell-shaped curve), the most common distribution assumption in statistical analysis (Unified Guidance). Leptokurtic is a statistical distribution where the points along the X-axis are clustered, resulting in a higher peak, or higher kurtosis, than the curvature found in a normal distribution. Asked by J1. I developed a script to identify, describe, plot and remove the outliers if it is necessary. If they exist, the distribution is skewed in the direction of the outlier(s). Don't do this without a very good reason. (Sometimes, there are theoretical reasons to remove suspect observations. Detection of Univariate Outlier Based On Normal Distribution Data involving only one attribute or variable are called univariate data. Alternately, the distribution may be exponential, but may look normal if the observations are transformed by taking the natural logarithm of the values. 5 Methods for Multivariate Outlier Detection. the outliers probably “produced” the skewing -- so remove outliers first & recheck for skewness Certainly it isn’t always this clear, but usually one order works better than the other -- nicer distribution and fewer “outliers”. An outlier, in a distribution of data points, is a value which does not fall within three standard deviations of the mean. Outliers and/or demand spikes are points in an items historical demand that are out of the normal distribution. the decimal point is misplaced; or you have failed to declare some values. We then coded the method used to cope with outliers for which 99. If you think that your data set has more than one outlier, use the generalized extreme studentized deviate test or Tietjen-Moore test instead. The we determined a min and max value and used that to identify which values are Outliers. As other writers wisely advised, you should only remove outliers for a good reason and you should document what was removed and the rationale. Box plots use the median and the lower and upper quartiles. A great majority of statistical tests, such as t-tests, assume a normal distribution therefore if an outlier causes the distribution to become skewed, results of the data may look significant when they are in fact not. To simplify we will assume that this multivariate distribution is the Normal Distribution, so we only have to define the parameters that fit the sample (mean and covariance). 5×IQR or greater than Q3 + 1. What we do here, we replac the outliers with some representative values like mean, median, minimum or maximum values etc. Box plot diagram also termed as Whisker’s plot is a graphical method typically depicted by quartiles and inter quartiles that helps in defining the upper limit and lower limit beyond which any data lying will be considered as outliers. This chapter also describes the central limit theorem, which is frequently invoked in an attempt to deal with nonnormal probability curves. There are multiple ways to detect and remove the outliers but the methods, we have used for this exercise, are widely used and easy to understand. We can also detect the outliers and consider removing them. Example 7: Detecting Outliers. regression to conduct Run the regression Examine the coefficients Examine the residuals The mean should equal 0. A central assumption in statistical-based methods for outlier detection, is a generating model that allows a small number of observations to be randomly sampled from distributions G1,, Gk, differing from the target distribution F, which is often taken to be a normal distribution N ¡ „;¾2 ¢ (see (Ferguson,. Q1 – 3(IQR) = 3. These approaches are based on the assumption of normal distribution of data. The names of the counties were entered as case names. Models that ignore exceptional (and interesting) cases often perform poorly. The we determined a min and max value and used that to identify which values are Outliers. , and can be used as a screening tool for the initial identification of outliers. Notwithstanding the decision to remove, correct or leave an outlier (for a discussion on this topic see McClelland, 2000), it is necessary to be able to detect its presence. Normal Test Plots (also called Normal Probability Plots or Normal Quartile Plots) are used to investigate whether process data exhibit the standard normal "bell curve" or Gaussian distribution. And lastly, make a probability plot, normal and any other distribution surmised from the previous plots. There were 127 minus three SD is based on the characteristics of a normal distribution relevant hits.