Since you have 11 values, the median is the 6th value. The median is the value exactly in the middle of your dataset when all values are ordered from low to high. Step 2: Identify the median, the first quartile (Q1), and the third quartile (Q3) 25įirst, you’ll simply sort your data in ascending order. You have a couple of extreme values in your dataset, so you’ll use the IQR method to check whether they are outliers. We’ll walk you through the popular IQR method for identifying outliers using a step-by-step example. Your outliers are any values greater than your upper fence or less than your lower fence.Įxample: Using the interquartile range to find outliers Use your fences to highlight any outliers, all values that fall outside your fences.Calculate your lower fence = Q1 – (1.5 * IQR).Calculate your upper fence = Q3 + (1.5 * IQR).Identify the first quartile (Q1), the median, and the third quartile (Q3).This method is helpful if you have a few values on the extreme ends of your dataset, but you aren’t sure whether any of them might count as outliers. You can use the IQR to create “fences” around your data and then define outliers as any values that fall outside those fences. The interquartile range (IQR) tells you the range of the middle half of your dataset. As a rule of thumb, values with a z score greater than 3 or less than –3 are often determined to be outliers. If a value has a high enough or low enough z score, it can be considered an outlier. You can convert extreme data points into z scores that tell you how many standard deviations away they are from the mean. Statistical outlier detection involves applying statistical tests or procedures to identify extreme values. Many computer programs highlight an outlier on a chart with an asterisk, and these will lie outside the bounds of the graph. This type of chart highlights minimum and maximum values (the range), the median, and the interquartile range for your data. You can use software to visualize your data with a box plot, or a box-and-whisker plot, so you can see the data distribution at a glance. You sort the values from low to high and scan for extreme values. Example: Sorting methodYour dataset for a pilot experiment consists of 8 values. This is a simple way to check whether you need to investigate certain data points before using more sophisticated methods. You can sort quantitative variables from low to high and scan for extremely low or extremely high values. You can choose from several methods to detect outliers depending on your time and resources. While you can use calculations and statistical methods to detect outliers, classifying them as true or false is usually a subjective process. In practice, it can be difficult to tell different types of outliers apart. Your standard deviation also increases when you include the outlier, so your statistical power is lower as well. The average is much lower when you include the outlier compared to when you exclude it. Example: Distortion of results due to outliersYou calculate the average running time for all participants using your data. This type of outlier is problematic because it’s inaccurate and can distort your research results. This data point is a big outlier in your dataset because it’s much lower than all of the other times. You record this timing as their running time. Outliers that don’t represent true values can come from many possible sources:Įxample: Other outliersYou repeat your running time measurements for a new sample.įor one of the participants, you accidentally start the timer midway through their sprint. It’s important to select appropriate statistical tests or measures when you have a skewed distribution or many outliers. True outliers are also present in variables with skewed distributions where many data points are spread far from the mean in one direction. But these extreme values also represent natural variations because a variable like running time is influenced by many other factors. Most values are centered around the middle, as expected. Your data are normally distributed with a couple of outliers on either end. Example: True outlierYou measure 100-meter running times for a representative sample of 560 college students. True outliers should always be retained in your dataset because these just represent natural variations in your sample. What you should do with an outlier depends on its most likely cause. Other outliers may result from incorrect data entry, equipment malfunctions, or other measurement errors.Īn outlier isn’t always a form of dirty or incorrect data, so you have to be careful with them in data cleansing. Some outliers represent true values from natural variation in the population. Outliers are values at the extreme ends of a dataset. Frequently asked questions about outliers.Example: Using the interquartile range to find outliers.
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