normal distribution for data entered as percentages
 

normal distribution for data entered as percentages
dear all,
i am doing normal distribution analyses on parameters expressed in percentages. sometimes the parameters have specified ranges, sometimes not.
this works fine when the data and their specifications are in the mid percentage ranges. i can determine the number of samples expected in spec, out of spec, in some other given range, cp, cpk etc.
when however data/ specs are at the percentage extremes ie. close to 0 or 100 the analysis gives me expected stats for samples falling below 0 or greater than 100.
for example if the data has a mean of 95% and an sd of 2 it predicts that a percentage of results can be expected to have values >100% which of course they can't.
ok so i can add that percentage back into the those expected to fall =<100% but is that the correct way to handle this situation. i would prefer to stick with normal distibution analysis if possible because it works well for most parameters and i would like results across all parameters to be comparable.
any help would be much appreciated.
regards hugh.
if you stop usng percentages, and instead normalise everything as a function of the mean value, then all your problems will go away.
the %ages are not simple %ages, they are per cent of the mean value. as such 135% is a valid number.
cheers
greg locock
greg,
thank you for responding so quickly.
unfortunately i do not understand what you are telling me - so can you expand on it a little if not completely.
regards hugh,
suppose your mean value is 3, and your standard deviation is 2.
then your upper and lower 3 sigma limits are 9 and -3.
howver, since you have chosen to use %ages, your mean is 100%, +3 sigma is at 300%, and -3 sigma is at -100%.
these look daft, it is because you are normalising that which should not be normalised.
cheers
greg locock
greg,
i have not chosen to use percentages, the data i am working with is percents passing given sieve apertures. such data is always measured and specified in terms of percent passing in the aggregate/ construction industry. e.g. a material may be specified to have 95 -100 % passing a 20mm sieve, 30 - 50 passing a 28mm sieve and 0-10 % passing a 10mm sieve.
any particular reason why you are applying a normal distribution analysis to a non-normal distribution?
cheers
greg locock
greg,
it's just normally done that way.
so what distribution would you consider more appropriate?
would that apply just to the parameters (sieves) having values close to 0% and 100% or all of them?
regards hugh,
the common approach is to transform your distribution into a normal one. this is a bodge.
strictly speaking you can't apply normal distributions to any data that has hard limits. often we do, but it ain't clever.
this is not an appropriate forum for this discussion, you really need to sit down with a big stats book and figure out your own solution for non-normal distributions.
cheers
greg locock
greg,
ok, so the solution is not a simple one.
thanks for your help and a star for you.
kind regards hugh,
hughl - why not look up indiana's indot aggregate manual. they have a pretty good section on statistics and control of aggregate gradations. (p.s. to all: sorry this isn't "statistical"!)
bigh,
thanks for your feedback. the indot manual is interesting.
i see with some reassurance that indot (6. statistical qc for aggregate processing)stick with the normal distribution and simply add the percentages expected beyond zero and 100 back into the compliant group (as proposed in verse 4 of my original post). just why they present table 6-1 is a bit of a mystery because it can be simply derived from table 6-2 (a standard norm dist table) by adding 0.5 to all the values.
regards hugh,

glad it is of some help - it is how this is done in standard highway practice. i am in the process of implementing this same procedures for crushing operations at my project here in indonesia.