# normality fails, but far from spec

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kkolste
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I have a data set where we are looking at reaction time. The specification for this reaction is that it occurs in less than 2 seconds. The reaction can be detected visually, so we use a camera watching both the reaction and a stopwatch. Unfortunately the stopwatch only has a resolution of 0.01 s, and the range for our data is 0.81-0.88, causing the data to appear discrete and failing normality (probability plot attached). I have ideas for improving the process, but we are trying to show 95%/95% reliability/confidence for this process, but cannot use standard practices because it fails normality tests. Any ideas on how to justify it’s acceptable given that the range is 0.07 s and the highest value in the data set is 1.12 s from the specification even though the data are not normal?

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#259590

Robert Butler
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The simplest thing to do would be to take your data and run a one sample t-test against a target of 2 and see if they are significantly different. The t-test is robust with respect to non-normality so that shouldn’t be a problem (if you need a reference – The Design and Analysis of Industrial Experiments – Davies – 2nd Edition pp.51-56).

If you are uncomfortable with this approach then take your data, plot it on normal probability paper and identify the 97.5 and 2.5% points – these correspond to your 4 standard deviation spread. If 2 is outside of that range then you have shown your system meets/exceeds the spec.

If you want to check further and see what happens for 3 standard deviations pick of the .135 and 99.865 points – these correspond to your 6 standard deviation spread – who knows, you might even have a case where 2 is outside of that range as well. If you need a reference for this method it is Measuring Process Capability – Bothe pp.431-434.

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