Within Dixon's Range Statistic, what does D represent?

Within Dixon's Range Statistic, what does D represent?

• A. Absolute difference between the most extreme value and the next nearest value
• B. Difference between the highest and lowest values
• C. Standard deviation of the values
• D. The mean of the most extreme value and the next nearest value

Answer: (A)

In Dixon's Range Statistic, D is the size of the gap between the most extreme observation and the next most extreme observation. This gap shows how far the potential outlier sits from the rest of the data, which is then evaluated relative to the overall spread (the range) to decide if it should be considered an outlier. For example, if the data are 2.1, 2.5, 2.7, and 9.3, the most extreme value is 9.3 and the next is 2.7, so D = 9.3 − 2.7 = 6.6, while the full range is 9.3 − 2.1 = 7.2, giving a large D/R ratio and suggesting the extreme value may be an outlier. The other options describe the full range, the spread (standard deviation), or the mean of the extremes, none of which capture that specific gap between the extreme observation and its nearest neighbor.

In Dixon's Range Statistic, D is the size of the gap between the most extreme observation and the next most extreme observation. This gap shows how far the potential outlier sits from the rest of the data, which is then evaluated relative to the overall spread (the range) to decide if it should be considered an outlier. For example, if the data are 2.1, 2.5, 2.7, and 9.3, the most extreme value is 9.3 and the next is 2.7, so D = 9.3 − 2.7 = 6.6, while the full range is 9.3 − 2.1 = 7.2, giving a large D/R ratio and suggesting the extreme value may be an outlier. The other options describe the full range, the spread (standard deviation), or the mean of the extremes, none of which capture that specific gap between the extreme observation and its nearest neighbor.