# Normal Distribution Test for Cpk (Minitab)

#### THEERANART

##### Starting to get Involved
Hi all,
I have a question .If I have a 5 sub group to calculate Cpk . I start to test normality in Minitab , result is Non-normal , However I send this data to test ANAVA and I obtain residuals colump . I brings this to test normality found that residual data are normal distribution . I summarize that data set are normal , so I choose Cpk by normal , however i compare with Cpk , it is differntal . How I will judgement my data is normal or not .
This is serious for me becuase if I have wrong judge normal type . it will affect to Cpk value .

Thank a lot for youe recommend.

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#### Stijloor

Staff member
Super Moderator
A Quick Bump!

Can someone help??

Thank you very much!!

#### Miner

##### Forum Moderator
Staff member
Do not get overly concerned about the formal normality test. The statistical Normality tests become more and more sensitive as your sample size increases. After a point, it is virtually guaranteed to reject any distribution. At 160 data points you are in that zone.

So, in your situation I would first assess the state of control. Your data are in control. Second, I would "visually" assess normality, but not look at the AD test. Use the old fashioned "fat pencil" approach. If you lay a fat pencil over the line, does it hide the data points? Does the histogram appear normal? In both cases, your data appears fine.

#### Miner

##### Forum Moderator
Staff member
Just a few more thoughts:
• Cpk is calculated from the subgroup variation, so it will not be affected by the overall normality (or lack thereof). Ppk would be affected.
• If you were to calculate the confidence intervals for Cpk using both approaches, I suspect that you would find that they overlap by a large margin.

#### THEERANART

##### Starting to get Involved
Thank you sir.
That mean I am no need to test residual again because both of approach give me diffent resulta, right? I can summarize that my data is normal and use minitab option >>>>Stat ..Quality tool---Capablity---normal .

Staff member
That is correct.

#### bobdoering

##### Stop X-bar/R Madness!!
Trusted Information Resource
Might want to read over this to get a firmer understanding of the concept of normality testing: Goodness of Fit: Is it normal? Probably...or probaby not - it's all probability

The one question the software can not answer: Does it make sense that the data is normal? Is the process output truly random and independent? If not, it is likely not normal. You may have a masking effect (such as gage or measurement error) that makes the data look normal, but shouldn't be. Verifying normality may just say that the statistical tool works on bad data. Not much value....

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