# Measurement Tool Question

Six Sigma – iSixSigma Forums Old Forums General Measurement Tool Question

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• #45826

GB in Training
Participant

Please I could use some help.  I need to measure the statistical significance between two small sets of data (6 data points in each set).  Each data set (before and after process improvements) is measured in time to complete the process.
I thought use moods median since it is a small population of continuous data.  I get a low p value meaning it is a significant change.
Other suggestions for how to look at this data?
Thanks.

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#150889

Philip
Participant

First a little theory (sorry)
All statistical hypotheisis tests (other than Bayesian) give you the probability that you would get data as impressive as the data you got, given that the null hypothesis was true (p=Pr(data|hypothesis)). Contrary to popular opinion, this is not the probability that the null hypothesis is true given the data (Pr(hypothesis|data)). Also the null hypothesis is not just the hypothesis of no effect; it includes the validity of the assumptions of the test (Normally, Independently, and Identically Distributed, or NIID)
The normality bit is usually not as critical as some people think (except for testing differences in variances) but the “independently and identically distributed” criteria are. These are usually approximated by randomising the trials, so that any unknown causes are equally likely to occur for any of the “treatments”. From what you say, I gather that you just ran a before and after, without randomisation. This means that any conclusions you draw may be seriously affected by any other effects you don’t know about. (But it may still be considered a strong clue) This will apply to any analysis method you choose, but especially to small sample sizes.
As with all designed experiments, the best proof is non-trivial replication (i.e. run the experiment several times and see if you get a consistent result)
Hope this helps
Philip

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#150904

Ken Feldman
Participant

Sure, the computer programs will run the data all day long but sorry, 6 data points is a bit too little for my taste.  Did the two sets of data hint at being normal?  Such a small set will usually do that. But does that make any sense at all since time will not usually be normally distributed nor would I put much trust in 6 points to tell me much about whether the process changed or not.  I wouldn’t advising making any great declarations of change and spending a bunch of money implementing the new process.  BTW, the t test is for small samples, the Mood’s Median is for skewed or non normal data sets.  Bottom line, get wayyyyy more data before putting your neck on the line.

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#150921

Hal
Participant

It would be nice, just for ince, to see someone here who knows how to describe a problem.  SS training gets so lost in numbers it forgets what it is trying to achieve.

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#150929

TVI
Member

Very little data.  Be careful.  A t-test is better here than your median based test, as they are designed for extremely small samples with an unknown population variance measure, although 6 data points is awfully thin statistically speaking.  You can also look at simpler MSA techniques as well:  a simple calibration test (test, retest) in which you complete 15-30 runs using the same piece, same operator, same device, same sop for each set of conditions (before and after) followed by a simple t test (paired perhaps) to check for statistical difference between the change and again against the standard might be all you need…it will indicate variability in your equipments ability to be consistant, but not your operators…but easy and quick…think about what you are trying to accomplish.  less is more if possible. And check my advice before implementing….Darth, Stan, QualityColorado, etc. are all SME.  good luck

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#150935