# what is the minimum Sample required?

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• #44507

Abdulrahman
Participant

what is the minimum Sample required to draw conculsions?
and from where this 30 sample units came, is it enough for larger population?
thanks
Abdulrahman

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#142693

Darth
Participant

Since you took the time and effort to post a really well thought out question here are the correct answers to your questions.1. You need exactly 137 as your minimum sample to draw conclusions.
2. The 30 sample units came from a bar near the Toronto airport called The Landing Strip. Those posters who have been there can confirm this. It is always enough for a larger population especially like New York.Good luck on your quest for knowledge.

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#142697

Eric Maass
Participant

Abdulrahman,
The sample size of 30 that you may have heard is a rule of thumb for certain statistical tests, such as the Student’s t-test and ANOVA to determine whether the means or averages of samples taken from different circumstances are the same or different.Appropriate sample sizes for other statistical tests may be different; oftentimes, the appropriate sample size for a test involving proportions can be in the thousands or more.
Some statistical packages provide a way to determine the appropriate sample size for the statistical tests you intend to try. For example, Minitab has this capability under the menu system Stat/Power and Sample Size.
Also, to your question whether 30 samples is enough for a larger population – actually, the sample size generally does not depend on the size of the population. If you were performing a Student’s t-test for some dimension or property from some component, and were comparing the averages for components from two suppliers – the appropriate sample size might still be 30 whether the size of the population of components were 500 or 500,000,000.

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#142698

leo
Participant

as the hypothsis test, we have a formula to calculate the simple size.
N=(2*(Za/2+Zbeta)**2)/(delta**2/sigma**2)
N: simple size
a: significiant
1-beta: power significiant
delta: different in means to be detected
sigma: standard deviation of the measure simple.

Leo

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#142699

Abdulrahman,
If you know you have a normal distribution then a sample size greater than about n = 30 will not give you any more information.
When you have an unknown population, and you don’t want to assume normality, homogeneity, independence or anything else, you have to consider taking larger sample sizes. The question as to what sample size exactly will depend on the results of ‘exploratory data analysis.’
For example, one approach assumes an unknown distribution, variance, but independent ‘values.’ The central limit theoren is then invoked to calculate a sample size. (There are simulations on the internet that show how this works.)
In summary, all sample size calculations assume some knowledge about the population distribution and data. When you know nothing about the data, you should try to study the granularity and the sources of variation. This is why one of the best ways to collect data is by tagging the source by location, type, sex, etc.
Regards,
Andy

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#142700

Abdulrahman
Participant

thanks for all for the valubale inputs.
As a new comer to the filed of six sigma,  I noticed  some   sigma practitioners (BB and MBB) are not giving more attention to sampling ,
and they are giving more attention to improvements even if its relyied on wrong samples.
what is the reason for that?

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#142701

Abdulrahman,
There is a saying .. “many are called, but few are chosen.”
In the case of Six Sigma, “many are chosen, but few are called.” :-)
Good luck.
Andy

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#142703

Orang_Utan
Participant

If you are trained properly in six sigma, you shall know how to compute minimum sample size with your alpha risk, beta rish and shift desired.

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#142710

Abdulrahman
Participant

dear Eric
still I am not convinved with  your statement
” the appropriate sample size might still be 30 whether the size of the population of components were 500 or 500,000,000.”
let us imagine we are taking about Indai population ….in this case I think we are neglecting basic part in sampling which is representative
thanks for all

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#142711

Robert Butler
Participant

I don’t think you are being fair to Eric.  Your initial post was generic in the extreme.  You asked “what is the minimum Sample required to draw conculsions?
and from where this 30 sample units came, is it enough for larger population?”
Eric was kind enough to try to offer an answer and he chose to make some assumptions about your population and answer accordingly. Instead of thanking him you now choose to offer up some post hoc caveats – “let us imagine we are taking about Indai population”
and cast doubt on his response.
The the very generic short answer to your very generic post is that the minimum number of samples required to draw a conclusion is one per population.
The reality is that the sample size is going to be whatever is economically feasible.  The magic number of 30 is driven by a whole host of assumptions. Violate any one of those and 30 just goes away.
For example, if it cost’s \$5,000 per sample I can assure you that you won’t be given the option of 30 samples per population – you will be lucky to get 2 and if under these circumstances you are given 2 samples per population you will be expected to analyze the resultant data and provide meaningful guidance.
Now, if you want to add particulars like sampling the Indian population then you are in a different realm.  For that population you will have to do stratified area random sampling and you will probably need around 5,000 to get a sampling error of plus-minus 5 percent to a given question.  Of course, if you can only afford to talk to 100 people then that is what you will do and your error will be larger.
In summary, if you want a precise answer to a question concerning sample size you will need to provide precise information concerning the population, your resources, and the aims of the sampling effort.

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#142713

Hans
Participant

Robert,
What a great response!
Also, I came across your response to an article published in Quality Digest in 2003. I couldn’t agree more with you! Also, just for you fyi, whenever I have deployed a six sigma program in the past and had the opportunity to hire staff, I made sure that at least one industrial statistician was hired for the very reasons that you outlined in this response. So be assured that at least some of us do not only see the benefits for a close collaboration with statisticians and six sigma but translate that need into action. As always respectfully, Hans

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#142717

Anonymous
Participant

Dear Abdulrahman,
Are you based in Dhahran?

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#142720

Eric Maass
Participant

Robert,
Thanks for your well-written and well thought-out response!
Best regards,Eric

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