There is a lot of confusion that surrounds the lab reports concerning Purity, Potency and once in a while you'll get a source that throws the word assay out there. Trying to clear up some confusion here I did a little bit of searching around and came up with some information and noted where I got it from. Lets take a look at a few definitions first:

What is the difference between potency and purity in drug products?

A quick definition would be:
-Potency is a measure of drug activity expressed in terms of the amount required to produce an effect of given intensity.
-Purity is a measure of the amount of API present in a sample compared to those of related substances, impurities, residual solvents, etc.
http://kb.mtc-usa.com/article/AA-01279/0/What-is-the-difference-between-...

What is the difference between "assay" and "purity" regarding pharmaceutical analysis?

Accoring to the "WikiAnswers" website, an "assay" method provides an experimentally determined value for the content or potency of an analyte in a sample. In contrast, a "purity" methods provides an accurate quantitative statement of all impurities in a pharmaceutical sample.
http://kb.mtc-usa.com/article/AA-01095/0/

and finally I found a decent news article that helps to outline the difference. Most notable is the last paragraph.

How many times have you read scary stories in the press about addictive drugs of unprecedented purity? How often in movies has the villain been the one to cook up an incredibly pure drug? “Pure” in these cases is used as a shorthand for powerful and dangerous, but that isn’t what it means.

Purity is a measure of how much of some substance is “what it says on the tin”. Potency in contrast refers to the dose necessary for a substance to exert its effect on the body. Ivory Snow Soap, famously, is 99.4% pure. But its potency when ingested is far less than that of 1% pure heroin.

This ends up mattering more than one might think in drug policy debates. Policymakers and parents get scared when they hear that an addictive drug is pure. But a pure drug can be safer than an impure drug if the potency of the latter exceeds the potency of the former. Even within the confines of the same potent drug, purity can increase safety if the impurities are nasty things such as levamisole or strychnine.

One concrete area where this misunderstanding is influential and sometimes exploited for effect concerns methamphetamine. A prescription requirement for the pseudoephedrine-containing cold medicines that are used to make meth would virtually wipe out domestic meth labs. Opponents of this policy sometimes try to scare people by saying that the result would be an influx of “much purer” methamphetamine made without pseudoephedrine (PSE) in Mexican superlabs (PSE imports are banned in Mexico). Yes, that form of methamphetamine is purer, but it’s much less potent and hence less dangerous than methamphetamine made from PSE, even before you count up the burn injuries, explosions and fires that small-scale domestic meth labs cause.
http://www.washingtonmonthly.com/ten-miles-square/2013/09/purity_vs_pote...

Purity is expressed in a percentage and is a measurement of the analyte divided by everything else in the sample. It indicates quality; whereas Potency (or more often called concentration) is an expression of quantity. Lets look at an example like we're explaining it to a 3rd grader

A bottle of water is 100% pure water. If you mix it with dirt you will get mud and the mixture is no longer 100% water, yet 100% pure water still exists but is mixed in with dirt and we cannot separate them as easily as we added them together. At this point we bring in the mass spec and it can easily distinguish between water and dirt and will look at just the water and indicate that it is, truly, 100% pure water and is called the analyte. Then it will look at our mud as a whole and tell us what the overall purity of the mud.

Notice that nowhere in that example there was the need for a measurement? No ounces or pounds or kilos or grams.....just percentages

Potency/Concentration is the quantity of the product. This is where the grams and kilos and ounces and pounds come in. It functions completely independent of the purity and tells you how much of a product occurs in the test. In order to know how much good stuff is present they both have to be taken into consideration.

Both potency and purity determine the efficacy(how well it works) of the AAS.

Now there can be two ways that you can get screwed here when buying AAS, Low purity or low concentration. One is out of the brewers hands and one they control exclusively. If they put in a gram of powder (quantity) but it is only 50% pure (quality) then only half a gram of the good stuff is going to be in that vial and that is typically out of their control. On the flip side of that coin if they only put in half a gram (quantity) and it is 100% pure (quality) the same is true and it is only half a gram is going to be in that vial but that is exclusively in their control.

So knowing that ^^^^^^^^^^ we can look at some other potential scenarios and numbers.

If the purity of a sample is 80%(quality) and the concentration is 100mg/ml(quantity) then the amount of good stuff is 80mg/ml

If the purity of the sample is 50%(quality) and the concentration is 100mg/ml(quantity) then the amount of good stuff is 50mg/ml

If the purity of the sample is 20%(quality) and the concentration is 100mg/ml(quantity) then the amount of good stuff is 20mg/ml

If the purity of the sample is 80%(quality) and the concentration is 50mg/ml(quantity) then the amount of good stuff is 40mg/ml

If the purity of the sample is 50%(quality) and the concentration is 20mg/ml(quantity) then the amount of good stuff is 10mg/ml

Having the above knowledge and knowing the purity of the raw material a brewer can adjust the quantity of the raw material to compensate for the quality. So, if for instance they know that their raw material is 75% pure and they want to make 100mg/ml of ACTIVE INGREDIENT then they will need to put extra raw material in their concoction to the tune of 1.3 grams per vial instead of 1 gram but remember there is still 1.3g of material in there so .3 of it is ineffective. Putting too much powder may cause it to fall out of suspension since oil can only hold so much weight regardless of the type of weight.

People often ask me what the raw material is cut with and the answer there is typically nothing that it is cut with, occasionally we will find where they have mixed in other powders of the same color that are cheaper. This is often the case with high value raws. Too often what is seen is sloppy manufacturing and too much byproduct that makes up the crystalline structure of the compound. Crystalline structure is like a brick wall of sorts, it takes the bricks surrounding it to give it strength even if they are of different colors. A melting test can be used to some degree to determine what a substance is but if those bricks are put together with things that do not belong and they are not all identical then the crystalline structure folds easier thus the substance melts at a lower temperature. Its similar to building a steel roof on aluminum walls.

perhaps I digressed but it is another example of how purity affects the makeup of a compound and ultimately shapes its attributes.

If anyone has anything else they'd like to add I will put it in here. Thank you for reading through this and let me know if I need to clarify anything.