Vinsorized mean is a vinsorized statistical measure of the central tendency as a kind of convolution of arithmetic mean and truncated mean .
Calculation of the vinsorized mean is reduced to the fact that k% of the largest and k% of the smallest values (usually from 5% to 25%) are replaced by the smallest and largest values from the remaining data array, after which the arithmetic mean is calculated.
Content
Benefits
A vinsorized mean is less sensitive to outliers (outlayers) than a simple arithmetic mean while remaining an acceptable estimate in a number of statistical models. It belongs to the category of stable (robust) measures of the central tendency .
Disadvantages
The applicability of the vinsorized mean (as well as the truncated mean ) is very doubtful in cases with a small number of observations. In addition, the replacement of some values by others is not always substantively substantiated.
Example
Let there be a data set (sorted in ascending order): 2, 3, 4, 5, 7, 9, 10, 12, 14, 30
The calculation of 20% of the vinsorized average in our example involves the calculation of the arithmetic average of the first two and last two values in the data series (2, 3 and 14, 30): 4 , 4 , 4 , 5, 7, 9, 10, 12 , 12 , 12 .
After replacing and calculating the average result = 7.9.
Links
- Wilcox, RR; Keselman, HJ (2003). "Modern robust data analysis methods: Measures of central tendency". Psychological Methods 8 (3): 254–274. doi: 10.1037 / 1082-989X.8.3.254 .