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Sample Size Calculation

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  • #48430

    MaJo
    Participant

    I am in the Measure phase of a project and used a 1-sample T-test to calculate if the target I have defined is significant different then the current baseline. Now I would like to calculate how many samples of the improved process I will need to take, to prove the succes of my project.
    Should I use a 1-sample T-test or a 2-sample T-test?
    Please advise -thanks

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    #163206

    Six Sigma guy
    Member

    2 Sample T test- My opinion. Because you are looking for statistically significant difference before and after improvement. Again if you are trying to do it with a standard/hypothetical mean then go for 1 sample t test. What is that you want to prove? is there any improvement in mean from measure to improve phase or is there any difference in mean from a standard mean.I hope your data is normally distributed..
    I hope i am clear. When you frame your hypothesis correctly then choosing the test becomes easier.

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    #163208

    MaJo
    Participant

    Thanks SS-Guy. I am doing a cycle time reduction project at a manufacturing facility. We have defined a target cycle time for the project. The hypothesis was to see if the target cycle time is statisticallty less than the baseline cycle time mean. I used a 1-sample T-test (correct?).
    The next thing I would like to know is, how many samples (cycle changes) do I need to take to statistically prove that the improved cycle time is less than the baseline.
    I used a 2 sample t-test in Minitab using baseline StDev (assuming equal variance) and a power of 0.9.
    I presented the results to the project team and we got into a discussion when to use 1 sample t-test and when to use 2 sample t-test for sample size calculations. And I still not sure when to use the 1 sample t-test for sample size calculation.
    Please enlighten me.
    Regards.
    MaJo

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    #163209

    Six Sigma guy
    Member

    I think i misinterpreted your question. You need to choose 1 Sample t test ( i hope you are doing it in minitab). Since you are doing 1 sample t test to statistically prove/disprove that target is less than baseline etc you need to choose 1 sample t test to determine the number of samples required.
    Instead if you want to prove that after doing improvements your cycle time has improved/decreased from baseline then go for 2 sample t test.
    Ok to summarize
    if its before and after then go for 2 sample t test
    if its target and actual then go for 1 sample t test

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    #163212

    At Nib Mi
    Participant

    Here is the Answer:
    1 Sample Z-a sample mean and a target value when population standard deviation is known
    1 Sample t -a sample mean and a target value when population standard deviation is not known (Note: Normality assumptions relaxed when the number of sample observations is large (generally true when sample size >30))

    2 Sample t-means obtained from two independent samples
     Paired t-mean differences obtained from paired samples
     
    Note: Above tests are used when the dependent variable (response) iscontinuous and the independent variable (factor) is discrete
     

     

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    #163240

    Erik L
    Participant

    MaJo,
     
    If you are interested in the minimum sample size to catch a reduction in your average cycle time, you would use the Stat>Power and Sample Size>2 Sample T (if using Minitab) or DOE>Sample Size and Power>Two Sample Means (if using JMP).  In determining the minimum sample size, one of the important facets that you must determine is what the business considers practically significant when reducing TAT.  Is 30 minutes significant?  3 hours?  3 Days?  Simply showing ‘statistical significance’ means the result seen was unlikely to have occurred just by chance.  With enough data, you can make relatively small differences in average performance statistically significant, but is it something that the business would make an investment in to achieve the projected improvement? 
    The greater the uncertainty that is used in providing some of the key pieces of information (e.g. standard deviation, delta, etc.); the more you’ll want to pad the sample size that comes back.  Typically, I suggest an extra 20% over what the software reports for sample size.  This helps guard against estimates that don’t match with reality.
     
    Regards,
    Erik      

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    #163249

    annon
    Participant

    Unless I am missing something, the aforementioned suggestions havent addressed your original question.  The  hypothesis tests are not going to indicate how many times you should confirm the results of your changes.  This is a function of the natural cycle of the process and should be discussed with your MBB or process owner.
    As for when to use 1 v. 2 sample t tests, use the t-test anytime the population std dev is unknown and/or when dealing with small sample sizes (when n<30)…this will be most of the time….use a one-sample t test when comparing an independent population against a target or stated value (like you did earlier) and a two sample t test when dealing with two independent populations, such as taking another measure of your process and comparing it with the original sample you took to confirm the change. 
    Dont forget to check the underlying assumptions…normality, independence, and equal variation (this one for the 2 sample t)….for example, cycle time data often will not approximate normality. 
    Good luck.

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    #163250

    MaJo
    Participant

    Thanks you all for your valuable input – the difference between 1-sample & 2 sample t-test is very clear now.
    I would like to address Annon’s point. Some background info: the project is about reducing the cycle time between two production campaigns. On this plant we produce 2 different products and there are not that many campaings – so data is limited  – change over approx every six weeks.
    I can discuss with the process owner when he would agree that the changes implemented are sustained – but the culture at my company currently is that once a project is finished (that is a change has been implemented) the project is succesful.
    So to change the culture to become (more) data driven and to get peolpe used to the idea that statistics could be a very powerful tool in data analysis (when used properly) – I wanted to use the sample t-test to make my point that we just can not walk away once a change is implemented.
    Any thoughts, comments, helpfull tips?

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    #163255

    fake accrington alert
    Participant

    Excellent as  usual

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    #163270

    annon
    Participant

    The control phase of DMAIC will address these issues.  Not only will it work to sustain the gains you have made, but it provides a valid methodology for closing and signing over the project to the process owner.  See the blue bar for some good introductory info.
    Mistake proofing (ie polka yoke) and SPC (ie control charting) are two techniques you might want to research while formulating your control strategy. The former is generally considered preferrable, while the latter is often a useful secondary option….see the ASQ website for some good control chart templates if you decide to go this route. 
    Good luck.

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    #163294

    MaJo
    Participant

    I agree that the methodology and tools will take care of sustaining the improvements – if the companies culture allows it. In our company we are not at that point yet.
    So we need more (data, change leadership,….) to convince people that they need to follow the methodology and use the appropriate tools.

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    #163295

    BritW
    Participant

    Majo:
    Erik makes a good point. I also pad the sample size with 10% usually, but anywhere between there and 20% will suffice.  Keep in mind the cost of the sampling process as you add to yoru minimum sample size – will the return outweigh the cost…

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    #163304

    annon
    Participant

    If you cant get someone to follow a basic control plan, then I wouldnt be in there wasting my time and hurting my reputation. This is the kind of CAP issue you want to discuss in DEFINE and clearly state in  ¨roles and responsabilities¨ or ¨stakeholder analysis¨. 
    But if you do not have the avid support of the process owner AND the project sponsor (preferably at a Director level or above), dont go near it.  Thats my advice. 
    Good luck.

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