9.2.5. Dixon-Grubbs-Neumann

A single column is selected as [Variable]. For 3 £ n £ 25 the Dixon statistic, Q is given. The data is considered in an ordered sequence and Q is calculated as:

     

UNISTAT reports the maximum Q and minimum Q. These two values can be considered as the two different ways of sorting the data. The maximum Q tests the largest value in the column and the minimum Q tests the smallest value in the column. For probability values of the Dixon statistic refer to tables.

For n > 25 the Grubbs statistic is given instead of the Dixon statistic. The test statistic Q is calculated as follows:

     

where is the maximum observation. The Grubbs test requires that the data is approximately normally distributed. The 1-tail probability is computed according to the following inequality:

     

The Neumann trend statistic T is calculated as follows:

     

This can be thought of as the mean square successive difference divided by the variance. The approximate tail probability for the Neumann trend statistic is calculated from the following Z transformation, which is assumed to follow a N(0,1) distribution.

     

See Sachs, L. (1984). For Dixon and Grubbs tests see pp. 277-79 and for Neumann test pp. 373-75.

Example

Open TIMESER and select Statistics 2 → Forecasting → 9.2.5. Dixon-Grubbs-Neumann and select Cola Sales (C2) as [Variable].

Dixon-Grubbs-Neumann

Data variable: Cola Sales

Number of Cases = 36

Grubbs outlier test is selected.

 

Maximum deviation from mean / Standard Deviation:
Q =	2.6584
1-Tail Probability =	0.1879
Neumann trend =	0.3995
Approximate Probability =	0.0000

 

Open TIMESER and select Statistics 2 → Forecasting → 9.2.5. Dixon-Grubbs-Neumann and select Failure time (C7) as [Variable].

Dixon-Grubbs-Neumann

Data variable: Failure time

Number of Cases = 8

Dixon outlier test is selected.

 

Q(min) =	0.1173 (X(1) - X(2)) / (X(1) - X(N-1))
Q(max) =	0.2582 (X(N) - X(N-1)) / (X(N) - X(2))
Neumann trend =	0.2101
Approximate Probability =	0.0019