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What measure of central tendency is robust when outliers are present?
Meanlol
Which measure of central tendency is robust when outliers are present?
mean
Are heteroscedasticity robust standard errors consistent?
The answer depends on consistent with WHAT!
What are the advantages and disadvantages of arithmetic mean?
Advantages:Linear unbiased estimate of central tendencyThe arithmetic mean has a Gaussian (Normal) distribution which is well studiedMany robust methods to test for equality of (difference between) meansDisadvantages Cannot be used for qualitative dataMore difficult to calculate than some other measures of central tendencyMay be affected by outliersMay not be a value that can be realised: for example, the mean number of cars per household on my street is 1.7, but nobody has or can have 1.7 cars!
How do you find the outlier number?
Find the inter quartile range, which is IQR = Q3 - Q1, where Q3 is the third quartile and Q1 is the first quartile. Then find these two numbers: a) Q1 - 1.5*IQR b) Q3 + 1.5*IQR Any observation that is below a) or above b) can be considered an outlier. Chadwick, quartiles are considered robust, meaning that they are not highly effected by outliers. This is because it takes location into account, not the values. Let's look at your data set (sorted). 2 3 6 9 13 18 21 106 position of Q1 = (8+1)/4 = 2.25 Q1 = 0.75(3)+0.25(6) = 3.75 position of Q2 = (8+1)/2 = 4.5 Q2 = (9+13)/2 = 11 position of Q3 = 3(8+1)/4 = 6.75 Q3 = 0.25(18)+0.75(21) = 20.25 Notice that none of these actually use the value 106. Let's continue. So IQR = Q3-Q1 = 20.25-3.75 = 16.5 Q1-1.5*IQR = 3.75-1.5*16.5 = -21 Q3+1.5*IQR = 20.25+1.5*16.5 = 45 No numbers are below -21, but 106 is above 45, so it can be considered an outlier.
