Now it all comes back to me. I remember why I hated my statistics courses!!!!!!!!!! This is getting worse than the "How many PWP's does it take to change a light bulb". Only kidding and LOL! [log in to unmask] (home) [log in to unmask] (work) > ---------- > From: Gil Lieberman[SMTP:[log in to unmask]] > Sent: Sunday, September 13, 1998 1:57 PM > To: Multiple recipients of list PARKINSN > Subject: Median is not average > > Dear listmembers, > I have some comments re Dennis Greene's discussion below > based on what I learned about statistics terminology fifty years ago. > > There are four concepts which need to be considered: > 1.The definition of a measurement modeled mathematically as a random > variable.X > 2.The probability distribution of X. > 3.Measures of central tendency of the probability distribution of X. > 4.The populations from which the measurements were made. > The terms measurement and observation are used interchangably. > > The median of X is defined as the 50 percent point of the probability > distribution. > It is estimated from a finite set of data by finding a number for > which half > the data is larger and half the data is smaller. > > The term average is a general term referring to a measure of central > tendency of > the probability distribution of X.Usually,the term average refers > specifically to > the arithmetic mean of a set of measurments of X,but it could refer to > the > median, > to half the difference between the largest and smallest measurement,to > the > square > root of the product of the largest and smallest measurement(a > geometric > average), > the difference between the 75 percent point and 25 percent point,the > most > probable > value of the probability distribution and so on. > Depending upon the shape of the underlying probability > distribution,these > averages > can be vitually the same or quite different.Thus for a Gaussian > distribution,the mean,median, > and most-probable values are the same because it is a well-behaved > symmetric > distribution,whereas > for a nonsymmetric distribution,they will generally be significantly > different.There are > nonwell-behaved symmetric distributions such as the Cauchy > distribution for > which the arithmetic > mean is virtually useless,whereas the median or most-probable values > contain > more useful > information about the data. > > Finally,the usual basic assumption of the data is that the > observations were > made from the same > population.The model is one of a set of observations under similar > conditions.If however, > the observations are based on sampling from more than one > population,then it > is possible > that the probability distribution will not have a single peak and > therefore > may not have a > unique most-probable value.How the observations are defined determines > the > statistical > properties of the random variable X. > > Now to Dennis's discussion below. > Par.1:Based on the above,a median is an average,but an average is not > necessarily > a median.However,by definition,the median does split the > observed > population in two. > Par.2:Since for nonsymmetric distributions,the arithmetic mean and > most > likely values > are not the same,sentence one is incorrect since by > average,Dennis is > referring > to the arithmetic mean.The last sentence touches on the concept > of > population. > One population could be the population of PWPs.Another could be > the > population of > ages at which these PWPs experienced onset.But Dennis confuses > this > disinction. > Par.3:This confusion is continued here.Furthermore,the definition of > median > used here > is incorrect.The calculation of a median is based on the > complete data > set,not > just on the minimum and maximum values.For example,given 101 > data > points,the > median is calculated by ordering the numbers.The median is the > number > such that > 50 numbers are larger and 50 numbers smaller. > ------------------------------------------------------- > Date: Sat, 12 Sep 1998 08:09:58 +0800 > From: Dennis Greene <[log in to unmask]> > Subject: Median is not average > > Several recent postings have mentioned that 57 is considered the > median age > for the onset of PD. As far as I can see most have assumed that > "median" > and "average" mean the same thing and have concluded from this that > half of > the PD population are under the age of 57. However median and average > are > not the same thing, nor can you use either of them to conclude that > half the > PD population are under 57. > > An average age for something to happen tells you at what age the > event is > most likely to happen. In our case it would be calculated by adding up > the > age at onset of every PWP, and then dividing the total by the number > of PWP > (several million bits of information processed). Even if 57 were the > average age, it would mean that 57 was the age at which most people > experienced onset and consequently most PWP are older than 57. > > Median refers to the age itself, not to the numbers afflicted. It is > derived by finding the middle point between the age of the youngest > and > oldest age of onset (two bits of information processed). To have any > meaning > at all, a median value would need to be quoted in its context. By > itself > the statement "the median age of onset is 57" tells us very little. > It > would be true in both the following cases: > > 1. Youngest age of onset = 50 > Oldest age of onset = 64 > Median age of onset = 57 > > 2. Youngest age of onset = 20 > Oldest age of onset = 94 > Median age of onset = 57 > > > Dennis > > +++++++++++++++++++++++++++ > Dennis Greene 48/11 > > "It is better to be a crystal and be broken, > Than to remain perfect like a tile upon the housetop." > > [log in to unmask] > http://members.networx.net.au/~dennisg/ > +++++++++++++++++++++++++++ >