# Calculate Z-Score for Non-Normal Data - I have two set of data

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#### utkarshdoshi

How do I calculate Z-score for non-normal data. I have two set of data. One is normal & other is non-normal. I have transformed the non-normal data to normal data in minitab but still not getting successful in calculating Z-score.

For normal data - I am good.

Thanks,

D

#### Darius

Re: Calculate Z-Score for non-normal data

Can you post some non-gaussian data, and what do you expect (why was your analysis wrong)?

#### bobdoering

Trusted Information Resource
Re: Calculate Z-Score for non-normal data

Can you post some non-gaussian data, and what do you expect (why was your analysis wrong)?
It would also be nice to know the source (process) of the data.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: Calculate Z-Score for non-normal data

why do you need to calculate a z score?

z scores by themselves are realtivley unhelpful - it's what you do wihthtem that matters and there are other ways of obtaining the intended answer besides using a z score.

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#### utkarshdoshi

Re: Calculate Z-Score for non-normal data

I would like to know the % probability of parts being out side of low specification. Yes - I found out another way to get the % and that is from the capability analysis. Looking at the PPM>LSL and then converting it to %. Seems to make sense. Do you agree?

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: Calculate Z-Score for non-normal data

I would like to know the % probability of parts being out side of low specification. Yes - I found out another way to get the % and that is from the capability analysis. Looking at the PPM>LSL and then converting it to %. Seems to make sense. Do you agree?
absolutely not. this ONLY works with Normally disctributed processes. there are many great discussion of this issue with capability studies in this forum, my suggestion would be to perfrom a search and do some research on the issue and then come back with questons.

In the meantime if you post your data, explain the sampling plan for it and the process that created it, we can help with alternate methods of determining the % out of spec.

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#### utkarshdoshi

Re: Calculate Z-Score for non-normal data

Yes I know about the normal distribution only but what if you tranformed the data to normal distribution prior performing capability analysis. Still not valid?

#### Miner

##### Forum Moderator
Staff member
Re: Calculate Z-Score for non-normal data

Bev D is correct. Just because you can calculate a z-score, which Minitab's non-normal benchmark capability analysis will do, does not mean that you should.

The z-distribution is a standardized, normal distribution with a mean of 0 and a standard deviation of 1. By its very definition, it is not appropriate for non-normal distributions.

A better way is to fit the non-normal distribution and directly calculate the percentages from that distribution. Minitab will do this, and any decent statistical package should do the same. Minitab's non-normal capability will also provide the percentages out of tolerance.

#### reynald

##### Quite Involved in Discussions
Re: Calculate Z-Score for non-normal data

Yes I know about the normal distribution only but what if you tranformed the data to normal distribution prior performing capability analysis. Still not valid?
FYI only:
Forum about data transformation to meet Normality

Regards,
Reynald

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: Calculate Z-Score for non-normal data

Yes I know about the normal distribution only but what if you tranformed the data to normal distribution prior performing capability analysis. Still not valid?
in addition to Miner's input, I would add that the intent of capability studies is to truly understand the capability of your process. This means passively studying the variation over time: what happens as raw material lots change, operators change and set ups change? this helps us with the next step of improvign our processes and actively studying the inputs and output response. None of this can be accomplished by calculating a z score...

In our busy worlds, it can be tempting to go to a mathematical formula and calculate an answer - but that is really a non value add short cut that in the end only keeps us from understanding our processes....

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