# normal distributiion?

Six Sigma – iSixSigma Forums Old Forums General normal distributiion?

Viewing 7 posts - 1 through 7 (of 7 total)
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• #31597

Sah
Member

Hi all
I have a problem assuming normality for my data. I measure the fluorescence out put from an instrument and then divide it by the background fluorescence.  Does dividing a variable by a constant violate the assumption of a normal distribution? i’ve gone through the previous threads in this forum but could not find an answer. Any suggestion is greatly appreciated. Thank you

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#83417

Robert Butler
Participant

Subtracting or adding or dividing or multiplying your data by a constant or any combination of the latter will not change your distribution ( we are, of course, assuming that you won’t try to multiply or divide by zero).
To illustrate this idea think of the way you transform a general normal distribution into a standardized normal distribution. You take each value and subtract off the mean and then divide this result by the standard deviation.  The result is a normal distribution with mean zero and unit variance.  The distribution has been centered and scaled but its shape and properties remain unchanged.

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#83445

Chatikobo
Participant

Hello
Just to build on the post from Robert…….Need to verify that the constant (or the base response for that matter) does not contain a logarithmic term or have exponential effects
Lance

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#83447

Dr. Steve W.
Participant

is normally distributed. However, the variace and typially mean will be different.

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#83468

Never Mind
Participant

A constant with exponential effect? Mmmm… no, I don’t get it.

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#83472

melvin
Participant

I agree, it will not harm the data to complete functions by a constant.

Bob

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#83475

JJL
Participant

Hello,Flourescence is not my particular specialty, and even so, it has been a few years since applying the physics around it. However, as I recall, the type of distribution you might find would be closer to Lorentzian than Normal.Another idea is that the background flourescence that you would want to remove from your signal might not be constant. Hopefully, the manual would have the specifics of your optics.To your specific question, dividing the variable in the exponent in the Normal distribution by a constant, should not affect its Normality, but it will change your variance and perhaps the mean (depending on where you are dividing in the exponential argument). If dividing the overall exponent by a constant, you will affect the magnitude of the distribution, but neither the mean or the variance.Good luck!-John

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