You are saying, I think, that you want Y to be within 2% of X. So you want Y to be between 0.98X and 1.02X. That is, . That is the same as saying [tex]-.02X\le Y- X\le .02X[tex] and then (for X positive) . Y+ X has no part of this.
My question relates to the above and which is better to use when comparing two values.
I have a value X. If then (randomly) produce a value Y. Y can be accepted if Y = X is to within 2%.
In order to find this should I be using % change (i.e. ((final - initial)/initial) * 100) or % difference (i.e. ((final - initial)/((final + initial)/2))*100)?
In what situations would one be used as opposed to the other.
Any opinions would be gratefully received.
You are saying, I think, that you want Y to be within 2% of X. So you want Y to be between 0.98X and 1.02X. That is, . That is the same as saying [tex]-.02X\le Y- X\le .02X[tex] and then (for X positive) . Y+ X has no part of this.
Use percent change when you have a situation with a starting value and you want to decribe how the ending value differs. Presumably some factor has worked to cause change in the value, and you want to measure the effectivemess of it. A common example is the percent growth in the stock market over the course of a year - you have a beginning and ending value and can think of the percent change as what would happen to a dollar invested during that time. Other examples would include comparing growth rates of plants with and without fertilizer, or decrease in one's blood pressure after starting a medicine.
Use percentage difference if the two values are samples of the same population - with neither being considered "before" and "after" - and you want to determine the variability of the sample. For example if you compare golf handicaps of different players you might use this to describe the percent difference between two players' handicaps. Or rainfall in Maine versus Texas.
In your case, if the change from x to y is due to some process you are performing, then use percent change to see the affect of that process. But if they're simply two different samples, use percentage difference.