Grubbs Test for Outliers and Why there are no Z-values for N>25

[patric wessels]

Dear all,

I am not sure if this is the right forum for this subject, but here's the question:

We are trying to assist our operators in determining whether a measured point is an outlier or not. We want to use the Grubbs test for this purpose. The problem is that in case of a large sample we measure 120 points and the tables with the Z-values (for 99% probability) only goes up to 25 samples points.

I am not an expert in statistics but I am sure there is a reason for this.

Can anyone help me out and explain why there are no Z-values for N>25?

Thanks.

Best regards,

Patric Wessels
QA Engineer

 

[Miner]

Dear all,

I am not sure if this is the right forum for this subject, but here's the question:

We are trying to assist our operators in determining whether a measured point is an outlier or not. We want to use the Grubbs test for this purpose. The problem is that in case of a large sample we measure 120 points and the tables with the Z-values (for 99% probability) only goes up to 25 samples points.

I am not an expert in statistics but I am sure there is a reason for this.

Can anyone help me out and explain why there are no Z-values for N>25?

Thanks.

Best regards,

Patric Wessels
QA Engineer

Unless I am misunderstanding your question, a z-table does not depend on sample size. You enter the table using a given z-value and obtain a p-value as an output.

The sample size does come into play when calculating the z-value. See http://www.changbioscience.com/stat/ztest.html for an online z calculator.

Are you sure that you want the z-value? The NIST guide (http://www.itl.nist.gov/div898/handbook/eda/section3/eda35h.htm ) shows that the t-value is used for Grubb's test.

 

[Tim Folkerts]

I found this table on line that goes up to N = 140. They claim it is for 95% certainty. I tried pasting it here, but it doesn't copy well.
http://www.graphpad.com/articles/grubbs.htm

Also, the NIST Statistics site mentioned on another thread recently has a discussion of Grubbs Test and the formula for calculating the "Critical Z"
http://www.itl.nist.gov/div898/handbook/eda/section3/eda35h.htm


I was curious, so I tried a spreadsheet to calculate this, which is attached. You can adjust the alpha level to whatever you want. By playing with the alpha value, I was able to reproduce the table at the first link, so that is pretty good assurance that the calculations are correct. (I included a variety o values for N from 3-1000. For other values you could either estimate between nearby values or just type the number you want in the first column somewhere).

For those, like me, who were rusty on the Grubbs test, basically you calculate the critical value in the table. Then any point more than that many standard deviations from the center is a likely outlier. For example, at N=6 and alpha=0.01, then Z = 2.0; so any point in a set of N=6 that is more than 2.0 standard deviations from the mean is likely an outlier.


Tim F

 

[Tim Folkerts]

One other side note, some sites seem to call the parameter of interest "Z", others "G", and others "Y". That might be part of the confusion. The "Critical Z" here is not the same thing as the "Z" from the normal distribution tables.

Tim F

 

[Statistical Steven]

One other side note, some sites seem to call the parameter of interest "Z", others "G", and others "Y". That might be part of the confusion. The "Critical Z" here is not the same thing as the "Z" from the normal distribution tables.

Tim F

Look into the ESD method.

 

[patric wessels]

Dear All,

Thank you for your contribution to my question. Especially the excel sheet was very helpfull. I think I have a solution for my problem now.

Best regards,

Patric

 

[Campy]

Note also that ASTM E 178-08: Standard Practice for Dealing with Outlying Observations presents Grubb's test as one method of detecting outliers. Its table goes to n=147 for six different levels of alpha.