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See also: Outlier Test - Dean and Dixon 

Walsh's Outlier Test

J.E. Walsh developed a non-parametric test to detect multiple outliers in a data set. Although this test requires a large sample size (n>220 for a significance level α of 0.05), it may be used whenever the data are not normally distributed. Following are the instructions to perform a Walsh test for large sample sizes:

Let X1, X2, ... , Xn represent the data ordered from smallest to largest. If n<60, do not apply this test. If 60<n<=220, then α = 0.10. If n >220 then α = 0.05.

Step 1: Identify the number of possible outliers, r >= 1.
Step 2: Computec = ceil(),    k = r + c,    b2 = 1/α, and

where ceil() indicates rounding the value to the largest possible integer (i.e., 3.21 becomes 4).
Step 3: The r smallest points are outliers (with a α% level of significance) if Xr - (1+a)Xr+1 + aXk < 0
Step 4: The r largest points are outliers (with a α% level of significance) if Xn+1-r - (1+a)Xn-r + aXn+1-k > 0
Step 5: If both of the inequalities are true, then both small and large outliers are indicated.

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