Sample size…Why 30?

DT,
You ask a very good question. There are various responses based on situation, tool you are using, type of data.
One reference says determining the sample size depends on (1) the level of confidence (2) margin of error tolerated, and (3) variability in population studied. 
The above reference is right in general. Formulae for sample size calculation vary depending on the test you are going to conduct.
The parametsrs/issues you need to address are:

Type of test e.g. 2 sample T, Z, ANOVA etc
Standard Deviation (variability) of the process
Delta that is significant in distinguishing 2 or more effects
Alpha (level of significance of the test)
Power of the test (1-beta). Beta is the probability of type-II error
Number of levels (ANOVA). In case you know how many levels/effects are you aiming to distinguish.
Sample size
The interesting part is that in Minitab (assuming you would use it) allows you to vary any 2 parameters from Delta, Power and Sample size for any given number of levels. Try Stat>Power and Sample Size>ANOVA or the tool you want to use.
That lets you know the error (or lack there of, since you are measuring power) associated with each sample size and delta for any given setting. So you could make a trade-off study and see where your sweet spot lies. In cases where testing involves capital & consumables, this is a great tool. In your case you have the data. So it is not resource intensive that way. Still this is better than using 30 blindly.
There is a reason 30 is widely used. It is a result of simulation studies involving the Central Limit Theorem. If you are interested in the “histroy”or reason for prevalence of 30 samples as aguidance, i could give you  a few pointers.
I have a project that is similar in tool usage. There are quite a few neat things one could do with power and sample size studies.
Good luck,
Sambuddha 
 
 
 

DT,
Check your email. I have sent some information.
Hope that helps.
Best,
Sambuddha

Hrishi,
No problem. Post your email address. Either me or DT could email you.
The reason, I cannot post it here is that it is a scanned picture attachment and it is easier perhaps to email.
Best and welcome to this community,
Sam

Sambuddha
Yes as Gabriel says you can post it on his site. I am curious too.
Thanks for sharing
DD

Sambudhha
Can I also share the info on sample size of 30. I will appriciate you emailing me the same at
piyush_a@hotmail.com
 

Making the assumption that even with the ability of most software to sort and count the numbers out of your population of 100,000 records you wish to sample, there are two questions you have to ask. How many do I take and what risk can I assume in making the wrong assumption from the statistic.
A number of answers here address why 30 samples are needed to approximate a normal distribution allowing for the estimation based on the probabilities of the normal curve. However, once the mean and std dev have been estimated, and the cumulative probability found up to and including the critical limit you set. The second question comes into play, specifically how sensitive are you to making an error in assigning that proportion to your population.
As an example, say 6% of your population was expected to fall below your cut off, how sensitive are you that the true proportion isn’t 7% or 8% or 10% etc. You would need to calculate the Beta risk of assuming the proportion at 6% given your original sample size and the statistics you calculated. If you utilize minitab (or other software perhaps) you can adjust the minimum sample size you need to take for the risk you choose. Under the power and sample size tab – 1 proportion test, you can enter both the calculated proportion (as a percentage) and the critical proportion, along with the level of risk (beta) and it will calculate the number of sample you need to take. Go back, resample to that level and run the calculation again to find the proportion defective (credit levels below your cut off), and rerun the beta again with the new numbers. The process is iterative until you are satisfied with number of samples vs the risk you are willing to assume. Therefore you might start out with a sample of 30, find that the beta risk is too high and have to take 400 samples, do so and recalculate and find that you actually need 435 etc etc. Others here might have a better way to adjust for risk and sample size without all the iterations but that’s the only way I’ve found to consistently do it.
My other question for you however is what do you plan on using the data for. Be careful if the intent is to show that you get higher numbers of defaults with credit scores below a certain number using those accounts in default as your population for the hypothesis. Your choice of frame for the population would be wrong in that kind of test.
hope that helps.

Dear Sambuddha,
I was only reading about this discussion topic from the newsletter link today, could you also send me in a separate email on the 30 sample size information as well? appreciate it.
Best regards,
Lawrence.

Dear Sambuddha,
Could you also send me in a separate email on the 30 sample size information as well? appreciate it. jamackall@statestreet.com
Best regards,
JA.

Sambuddha,
 
Could you please forward the Sample size information to me as well.  cedric.betts@scotts.com   Thank you.
Cedric

DT,
I have not read the entire string so if some of this is redundant I apologize. Sam gave a good answer whaen he said it was different for different situations.
Assuming that everything works off of 30 is incorrect.
Frequently you will see variable control charts listed as a sample size of 25-30. They typicaly are speaking of a sample size of 25-30 groups of 5. That makes it 125-150 actual samples. It is the subgrouping giving you a distribution of averages (Central Limit Theorem) that makes it work.
When you are doing hypothesis testing and using ANOVA the sensitivity of the test is extremely dependent on sample size. I was doing site support and found a guy who could not understand why his 2 sample t test was showing significance. He was sure it should not. His sample size was >400. The test was sensitive to < a .1 sigma shift.
There are sample size implications with virtually every tool. 30 is not a catch-all particularly if you are working with attribute data.
Good luck.

Don’t confuse population sampling with process sampling these are two very different animals.You need population variation, power etc when considering population sampling.When process sampling the purpose of taking 30 samples is to establish with reasonable certainty these issues and develop control limits. these limits remain constant unless significant changes are made to the process.It is common in SS training that the true essence of what is meant by the mathematics behind these issues are lost.Processs sampling also assumes a process that is in statistical control. If it is not stop fix the process then proceed. 

Sambuddha,
I, too, would appreciate your sharing/sending the information on the sample size of 30. Thanks.
dburns@verityinst.com

Hi add all,
it will be fine if you can send me also information or an example of the magic samplesize of 30!
Thanks in advanced
send it please to
saolim@gmx.de
 
 
 

Want to test magic number 30. Take any group of people, good party trick. Bet any one present that two or more of the group will have the same birthday. Month and date. This has 98% confidence.

Sambuddha:
Hi. I am very new to this forum.
Can you send me the information that on why a sample size of 30 is required ? I too am curious.

 
Thks.

There are several web references on the Central Limit theorem and 30 that are interesting.  When the sample size approaches 30, we don’t have to worry about the distribution of the population since it can be safely assumed to be normal for inference purposes.  Here are some references:
http://www.mathwizz.com/statistics/help/help4.htm
http://www.statisticalengineering.com/central_limit_theorem.htm
Here is a little more technical article on normal distributions and central limit theorem.
http://www.itl.nist.gov/div898/handbook/index.htm

Mr. Sambuddha,
I am a statistician by profession and as far as I know, sample size is determined by margin of error allowed, the estimate for the population variance, the risk factors (level of confidence, power as a function of the OCC, etc.), and most importantly, the assumed distribution of the population (or the estimable function) in study.
In my own experience, the magic number 30 is being used to approximate the normal distribution using the Central Limit Theorem, as used in regression analysis, factor analysis, etc., but not in sample size determination. 
I am also curios with this article. Would you be kind enough to send me a copy, too? Also, would you happen to know/ recommend six sigma training centers in the Philippines?
Thanks,
Beryl
CRomero@doleasia.com
 

I WOULD ALSO LIKE TO RECEVE THE INFROMATION / POINTERS.  CAN YOU EMAIL THEM TO ME AT THE ADDRESS BELOW,
herrerap@sybrondental.com
Thanks!
PH

I would also like to recieve the information/ pointers about the sample size of 30. My email adress is feteris@hotmail.com
thanks!
Tom

Dear Sambudda,
I too am interested in the “Why 30?” discussion.  Please e-mail me at:
haim@thepalace.org
Thank you,
Haim

I don’t believe 30 came from simulations involving the CLT. Please post some backup to this assertion. Sounds like Dr. Mikel’s proof of the 1.5 shift.
By the way, what advice do you give on choosing sample size when you are interested in reducing sigma instead of moving the mean?

Dear sambuddha
Thank you for your reply to that Query.Now i am in the interest to know the variables like slop,linearity,bias,and Uncertinity relation with Instrument Repeatiablity and reproduciablity.
CAn you   send the same in my mail id sathish_801980@yhoo.com
Expecting your reply
 
REGARDS
 
R.L.SATTHISH KUMAR
 

Pls email me the info for “why sample = 30”

Sambudha:
I forgot to mention my e-mail in my previous message…please e-mail to the following address…lamarcardinal@yahoo.com
Thank you for sharing.
Surya

 
Mark,
The central limit theorem applies to the mean not to individuals – 30 samples from a log normal distribution will not suddenly become normal.  The distribution of 30 averages of data from a log normal distribution, however, will be.  To this end, the first citation you mentioned (and as quoted below) is in error.  The second and third citations, however, are correct.  (Note: some of the text from your citations don’t copy over to the forum page so I had to rewrite the equation in the first citation). I also took the liberty of highlighting in order to emphasize the focus on distributions of means and not individuals.
#1 The Central Limit Theorem says that if you have a random sample and the sample size is large enough (usually bigger than 30), then
Z = (sample avg – pop avg)/(s/sqrt(n))
where Z is the standard Normal distribution with m = 0 and s = 1. This comes in really handy when you haven’t a clue what the distribution is or it is a distribution you’re not used to working with like, for instance, the Gamma distribution.
 
#2 The distribution of an average tends to be Normal, even when the distribution from which the average is computed is decidedly non-Normal.
Thus, the Central Limit theorem is the foundation for many statistical procedures, including Quality Control Charts, because the distribution of the phenomenon under study does not have to be Normal because it’s average will be
 
#3 The central limit theorem basically states that as the sample size (N) becomes large, the following occur:

The sampling distribution of the mean becomes approximately normal regardless of the distribution of the original variable.
The sampling distribution of the mean is centered at the population mean, , of the original variable. In addition, the standard deviation of the sampling distribution of the mean approaches .

Hi Sambuddha,
Kindly mail me the same at  john.chandra@wipro.com
Thanks,
John C

Those are great URL’s for any beginner to study.
One might use some “rules of thumb” based on practical experience, as well as the more rigorous statistical methods.
For example, if the DATA is to be from a MECHANICAL process for making discrete parts, then one should first try sampling the FAMILIES of possible variation, using sample size 2 for each family, per Shainon’s recommendations.  2 sites on each of 2 parts, repeated every hour for 2 shifts perhaps, then graphed.  Once it is clear which family of variation is the main problem, then SPC sampling (subgroups measured over time) can be used IF the problem is temporal.  But if the problem is variation WITHIN the parts, then perhaps closer stratification of data is needed, or measuring more sites per part, or conparing that variation for all similar machines, or looking at tool wear trends of this “within-part” spread over time.  Means and ranges both can drift with tool wear.  Sampling for mean data involves the famous sample size of 30 (or 15) for OOC determinations. Sampling for changes in variance require much larger samples.  So a wandering mean is not the same as a wandering variance.  Think 1000 parts. 
RULE OF THUMB for SPC chart startup is given as 15 to 30 but if the process is non-stationary (drifts, has wandering mean and unstable variance, for example) then other methods are needed.   Box and Luceno’s book (Amazon.com) talks at great lenght about modern issues with process monitoring nad adjustment methods. Assessing non-subgrouped data is another issue.
RULE OF THUMB:  Individual Charts are less sensitive, less powerful, (they give more false alarms for each rule added, for example) than X-bar charts. 
RULE OF THUMB:  Subgroup size of 2 to 4 is common and usually adequate.  But for diagnostic reasons, many engineers use subgroups of 10 to 100 sites per part or parts per subgroup.  ASQ had a paper recently on effect of large subgroup sizes.  In general, it invalides the method used by most people to calculate control limits, as many of the subgroup sites or parts are CORRELATED and so the control limits would be wrong.  What is good for diagnostics is often not good for control, given various control models.  With automated gages, more data is cheap.  But how you use it depends on whether the data is really INDEPENDENT and RANDOMLY SAMPLED and IDENTICALLY DISTRIBUTED.  Most important is that INDEPENDENCE.  And if the data is AUTO_CORRELATED, its also messy (wandering mean, showing predictability instead of randomness). 
Then there is the data that comes from CHEMICAL processes, such as continuous refining.  Read Svante Wold or Dr. John McGregor’s books on PCA/PLS multivariate methods for sensor-based data, which is HUGE stream of data.   Rule of Thumb:  Get help.
Central Limit Theorem:   Only for subgrouped data!!! 
Shewhart Charts:  Only for stationary processes where samples are independent!!!  (I am not a statistician, and those guys are still arguing about these issues.  See Journal of Quality Technology, Woodall’s papers, for example. 
Don’t forget;  NIST online handbook.  http://www.itl.nist.gov/div898/handbook/

Reference sample size 30, reasonable amount to measure / analyse.
approximate 10% margin of error between a sample of 30 to 500.
Of course it would be better to do 500 for accuracy but you must take into account the cost between 30 and 500 pending what you are measuring. Remember the std dev (10%) margin and you should be fine.

Hi Mr. Sambudhha,
Could you also share the information about sample size 30 with me? I’m very much interested. Kindly email it to glo_blue10@yahoo.com
Thanks,
–Glo

Dear Sambuddha
could you  please send the reference to me, thanks very much
mzzhang@vip.sina.com
Leon

from vee
my email  wsu_vee@yahoo.com
thank again

Sambuddha/DT,
Please send me the information on sample size. I know this msg is 3 years too late, but would appreciate your or anyone’s help in getting this info to me.
Thanks
manavbhalla1@yahoo.co.in

Dave, might I suggest that you check the dates on any post that you respond to.  This is a really old one.  OK, Nick, how did I do????

Dear Sambudha
I am finding the answer about sampling size. Please kindly send me the information on why sample size = 30. Because I have to use this information for my report and if you have more information please reply me. Thank you very much.Best regards,
Kulananhttp://mailto: mprang@gmail.com

Sue,
This is a FOUR YEAR OLD thread.

Heebeegeebee,
…and unfortunately we have not see Sambuddah post on here for a couple years.
Regards

Sambuddha:
Hi. I am very new to this forum.
Can you send me the information that you sent to DT on why a sample size of 30 is required ? I too am curious.
mahesh.kumar.sridhar@accenture.com
Thanks.

Dear Sambuddha,
Could you also send me on the 30 sample size information as well? appreciate it. tanliren@hotmail.com
Best regards, Li Ren

DT,
I first came across the n = 30 rule of thumb duing a lecture by Dorian Shainin (1983). Dorian was brought to Scotland by someone called Ted Williams, who was instrumental in bring Dorian to Motorola in Phoenix some years before.
According to Dorian, if you plot the error of the estimate of sigma as a function of n, the curve becomes asymptopic at around n = 30, where it can be estimate with a 95% confidence for n = 30. As Stan has previously pointed out Dorian always used a 95% confidence.
As Mike Carnell has also noted, typcial X-bar and R charts use 30 subgroups of n = 3 or n= 5, which is a sample size of 90 or 150 – a far cry from n = 30.
Another issue lost on many is the use of multiple subgroups,which provide a pessimistic estimate of sigma, since both the data and the subgroup mean vary in small subgroups; so the entropy of a mulitple subgroups is larger than a single subgroup.
No one in their right mind would estimate process capability based on a single subgroup of n = 30.
Regards,
Andy
 

Hi Sambuddha,
Please email me the information on the theory and history behind sample size being 30
niteshrungta@gmail.com
Thanks,
Nitesh

Please forward me information about the history on a sample size of 30 as a rule of thumb.  Your help will be very appreciated.
 
 

Dear Sambudda,
Could you please mail this information to me (pointers for choosing sample size as 30). I recently had an interview when this question was asked and I drew a blank.
Thank you in advance.
Cheers
Pramod

Did you read any of this thread?
See: https://www.isixsigma.com/forum/showmessage.asp?messageID=112385

My background is in mathematical statistics but several years past, and I tried to read through this thread which appears to be it is quite complicated, but the actual question does not seem to be answered.  I am also new to 6 sigma, but did a google on 30/sample size and this appeared to have a good discussion so I will rephrase the original question and give my opinion:  that question is:
1.  Is 30 some magic number that can be used for an adequate sample size for “most” purposes”?
I recognize that in use, there are almost always assumptions about the underlying distributions and parameters, but the calculation of power and sample size are well worked out.  I can understand assumptions that the distribution of the mean for sample size of 30 should “look fairly normal for most distributions”, but the power/sample size strongly depends on the underlying variance as well as other variables that the field has not seemed to define. I suppose that we can assume that with a sample size of 30, we have a sample distribution that is normal with the population mean as the mean and the population variance divided by 30 as the sample variance.  We assume that the allowable power is .8 (why not .9 or .95?), and that the allowable difference between the true mean and estimated mean is x% of the population standard deviation.  (again arbitrary), then with all these assumptions and the right x%, perhaps a sample size of 30 might arise as a reasonable sample size.  However, we usually are more concerned with the absolute error between the sample mean and population mean which would completely negate the possibility that there is any unique N that could satisfy an adequate sample size since population variances have no bounds that I know of.  If however, there is some consensus that we are making all these assumptions it should be spelled out. 
Reading several of the comments, I contend that the number 30 is just some number that has nestled into the literature without any true mathematical/statistical verification.   Its small enough to be practical to do, but is an arbitrary number without true mathematical signficance.  What bothers me is that if we are talking about 6 sigma, it would appear that to accept 30 as a magic number for sample size rather than using the standard known statistical procedures to estimate the proper sample size is anathema to the underlying concept of precision which I am assuming that 6 sigma represents.

Arn’t you clever…oh yes you are…now reread your post and update with some additional builds to support your argument.
Grasshopper

So does the number 30 have significance in the use of an sample for an arbitrary population or is it just a number that “seems” to work because no one has actually tested it.

Can you also “E” mail this attachment.
 
Thanks in advance.

Hey Sambuddha,again, I’m a newbie here, could you please send me the info about why 30 sample size… pleasee… thank you so much.Please send it to me to devie_cynthia@yahoo.com, as i will need it for my final paper.Thanks again!

Hi sambuddha,
forgot to write my email id, quadrisyed@hotmail.com
appreciate your help!
Thanks
Syed

Because the Standard Error Of the Mean improves as sample size increase to 30.