When taking the standard deviation and mean as the reference info, the value out of 2 or 3 times std could be an anomaly, which works well in most cases. While the quartile concept is introduced, the value smaller than Q1 - 1.5 * IQR or bigger than Q3 + 1.5 * IQR is thought to be an anomaly. The former assumes that the data is normally distributed, what about the latter one? What are their individual advantages compared to each other? Please provide some real examples if convenient.
The former is suitable for normal data (normally distributed data). By some justification, it works for most continuous data. The latter applies to more dispersed data, including discrete data.
In addition, it depends on the data and you. For example, select the method that removes some cases (but not too many/much of them).
Hello Mengjie,
If the distribution is normal in shape, then the "far out" threshold proposed by Tukey for the box and whisker plot (upper hinge + 1.5*Midband spread; lower hinge - 1.5*Midband spread) equates to approximately the 99.7th and 0.3th percentile points, respectively. Thus, fewer than 1% of the cases in a normal distribution would be classified as "far out" cases using that threshold.
Good luck with your work.
Dear Mengjie Zheng ,
In addition to these helpful answers, I would not recommend adding or subtracting a multiple of the IQR to Q1 or Q3 as this might create non-physical values for non-normal data in the same way that SD differences from the mean can.
It would make more sense to divide your data into a greater number of percentage intervals, such as every 10% of the data, then use the values nearer the lower and upper limits.
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