# Sampling size

Six Sigma – iSixSigma Forums Old Forums General Sampling size

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• #42797

Participant

Hi
In our organisation, as part of an improvement plan for a six sigma project we are going to implement a wellness programme for the entire shop floor. The project was on reducing the attrition of employees. The population that will be covered in this exercise will be around 1500. What is the sample size that i have to select in this population to see that this programme has yielded some fruit?
rgds

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#135273

magesh
Participant

150

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#135274

Participant

Thanks for the input.
But I would like to know if there is any formula for calculating this or is  just 10% of the population is enough to judge the effectiveness of any programme.
rgds

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#135275

magesh
Participant

Hi,
This is more of a common sense and 10% in this case is sufficient. But this 10% is not worth to go in for a population of a huge size…correct?
For a very small population also, it is not again 10%…hope u understood.
There is a template available for this… but normally statisticians won’t agree to this template…
Are you from India? Where are u working?

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#135276

Dartman_undersiege
Participant

Magesh,
Was this some kind of joke? What is the basis of this 10% ? Have you based this one an OC curve or by your own experience or any data to support this? Wow, your guesstimation was great !!
Dartman_Undersiege

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#135278

Dartman_undersiege
Participant

Attrition of employee have a different variation according to target personell. Employee have different reason per department that you might wanted to re-consider prior getting your sampling data. I guess your 1500 employee are not in one depatment alone thus suggest that you get your data and sampling calculation per department basis and not as a whole if you wanted to get statistically valid data..
You can use Minitab software, 1 sample proportion to calculate your sample size for this purpose. You only need to define what is the minimum proportion difference you wanted detect and the attrition rate per department.
Dartman_undersiege

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#135280

Participant

Dartman_undersiege,
I completely agree with your views. The problem here is the entire population of 1500 belongs to one department – shop floor. Any suggestions on how to proceed?
rgds

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#135281

R S MAHARAJAN
Participant

if you want to determine the sample size necessary to establish, with a confidence of , the mean value to within  when you know . you can use the formula given below.

The formula for the sample size necessary to produce results accurate to a specified confidence and margin of error is:

where:
is known as the critical value, the positive value that is at the vertical boundary for the area of in the right tail of the standard normal distribution.
is the population standard deviation.
is the sample size.

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#135282

Dartman_undersiege
Participant

I believe you don’t have initial data such as standard deviation (sigma) and others to calculate your sample size as well as OC curve.But you have a history of the attrition rate for people in this department say 0.4 % (6/ 1500) and you want to detect 1% (15/1500), your sample size is 978 @ 80% power , 1190 @ 85 % power and 1487 @power of 90%. (Minitab Software)
Dartman_Undersiege

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#135284

Participant

D U,
Exactly as you said I don’t have the initial data and that is the reason why posted this enquiry. I think I will proceed in the way you have suggested. Thanks a lot.

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#135286

Anonymous
Guest

The following webpage might be of interest since it covers situations where the standard deviation is unknown. Anyway, it is a good reference to have ..
http://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm

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#135290

Ken Feldman
Participant

Lots of stupid responses to the original post.  Dartman came closest.  Poster never said how he was measuring attrition so offhandedly recommending that he use the continuous data formula was premature.  As a rule, attrition will be attribute since they quit or they don’t, a binary condition.  Therefore, Dartman’s suggestion of considering the use of a proportion formulas is more appropriate.  Lastly, with a small population of 1,500 poster needs to at least consider the use of the finite correction factor.  Unfortunately, the generic sample size formulas never consider that.  The use of Minitab’s sample size formulas for hypothesis testing considers power but not population size.  Again the poster didn’t indicate whether the need was to look for differences between groups or some “spec” or whether he is just trying to get some population parameter estimate.  The 10% rule was the dumbest piece of advice given especially in light of the liklihood that we are looking at discrete data.  In that case, it often turns out to be about 50% of the population for a 95% confidence and 5% precision.

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#135293

march
Participant

The only clear thing here, seems be that without minitab one cannot calculate it. How did it before Minitab comes to us ?

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#135297

BTDT
Participant

March:Before software made the calculation of sample size more facile, tables and graphs were used.Operating Curves (OC) curves have been derived and published for all kinds of statistical tests. For example, see the following entry and derivation.http://www.itl.nist.gov/div898/handbook/pmc/section2/pmc232.htmCheers, BTDT

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#135298

BTDT
Participant

Oops, OC Curve – Operating Characteristic CurveBTDT

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#135302

Robert Butler
Participant

As Darth noted  the original posting leaves too much to the imagination and thus really is not amenable to a concise answer.  If we assume the issue here is one of percent loss of the workforce and we are going to try some new way of treating employees in the hopes of reducing this percent loss then the first thing that needs to be determined is what constitutes a meaningful reduction in this annual(?) loss.  If the percent loss is relatively low to begin with then, unless you are looking for a huge reduction in this loss, the power, even with all 1500 people used as a sample, will be very low.

For example if we assume a sample size of 1500 people and we want to have a power of 80%, and we want to make test for changes in either direction (after all – the new method could be worse) then for attrition rates of 10, 15, and 30% and percent reductions of those rates of 20, 30, and 40% we would have the following power

Attrition            % Reduction From Current Rate
20%        30%        40%
10%                  .27            .55          .84
15%                  .40            .74          .95
30%                  .74            .98          .99

I realize that Radha said the focus was on 1500 workers in a single department but unless all 1500 workers perfectly uniform with respect to age, gender, marital status, health, economic well being, earned income, seniority, etc. there will be, at the very least, major demographic differences and it may be that when you examine prior data you will find certain stratifications (don’t just limit yourself to demographics here) with retention rates much lower/higher than the rest.

I would submit that the first order of business would be to determine if the proposed change had any meaningful effect on these extremes of the employee population.  Use that segment of the population as your sample (or draw your sample from that group), make the changes as planned and just look to see if the proposed change has any impact.  A study of this type will necessarily be under powered but it will at least tell you whether or not it is even worth looking at the effect of policy changes on the larger population.  If it is, then you can start worrying about power and sample size.

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#135326

Dartman_underseige
Participant

March,
That’s the reason it is made. There is another software in the market with the same function, unfortunately for me and some of the guys, we used Minitab for this purpose. Pity for you if you don’t have one since you will be using OC chart instead. Happy hunting !!
Dartman Undersiege

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