# nomal probability test

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• #49937

mcintosh
Participant

Can we do  a normality test on discrete data ? I am sorry but i am new to six sigma .

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#171448

Outlier, MDSB
Participant

Tom,
Generally no, but sometimes yes. Normal distributions (to the degree that there is actually such a thing) generally occur with continuous data. However under certain circumstances, the normal distribution can substitue for a binomial distribution which is a discrete data distribution. You can do a search on line and find lots of information about when that is appropriate, but basically that condition occurs when proportion data is in the middle part of the binomial distribution.
More common circumstances where you might be able to test for normality on discrete data would be situations where there is sufficiently large enough range in the data with sufficiently granular data intervals. One example of this is when looking at large numbers of transactions where the output is money. Technically speaking, the count of money is discrete data, but there is often enough range and granularity that it can be treated as continuous data and be tested for normality. Many people consider monetary counts to be continuous data for that reason, though technically it is discrete.
Hope that helps.
O.

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#171452

benjammin0341
Participant

It depends – I concur with the previous assessment by O.
My first question would be what are you trying to do? If you did test for normailty, what would be your next step? I.e. are you planning to do a hypothesis test to detect a difference amongst samples, etc.
By first identifying what you are trying to prove or disprove first will guide your next steps.
Example. Say you have defective count data and you want to see if there is a difference among different suppliers, locations, or whatever. If this is the case, then normailty may not even be relevant as a simple chi square may give you the answer you are looking for.

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#171455

Outlier, MDSB
Participant

Right on, ben. The first question is, “What practical question are you trying to answer?” The next question is, “What kind of data do you have or do you need to help you answer the practical question?”
Beyond that, benjammin0341 has given you very good advice.

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#171461

mcintosh
Participant

I have first time right data which is purely discrete that is it does not have a range and is in there as – yes / no . I guess i canot do normality test on the data . My other query would be do we always do normality test on a continious Y and why not the X’s .

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#171464

Severino
Participant

Why don’t you just tell us what you are trying to do with the data?  Why are you looking to test for normality?  Why are you trying to investigate the nature of your X’s?

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#171477

Outlier, MDSB
Participant

Tom,
Data is data. It does not matter whether it is an input or an output with regard to whether you should test it for normality. What drives the question of normality is, “What practical question are you trying to answer, and what kind of statistical test do you need to run to answer it?”
The need to test for normality is only related to the kind of statistical tool you wish to use to answer some question. If your data can be treated as a “normal distribution” then there is a set of statistical tests you can use.

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#171485

Shereen Mosallam
Member

i totally agree with all replies provided. but regarding your Y which is first pass through (yield), it should be a percent which will have range and granularity. Theoritically it should follow binomial but even discrete distributions approach normality at np=>5
so there is no harm for you to check normality. if your data is too discrete with small range you will see it as normality plot will show data stacked in vertical lines at corresponding values and you will get a very low p value
good luck
http://www.symbios-consulting.com

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