What percentage does a Series need to be checked before a conclusion is valid?

braddick

DBL55 Got me to thinking on another Thread regarding the percentage of the 1981 Mint Sets that had been searched looking for the high grades. He estimated 5% (or less) and concluded this wasn't enough to make a determination of the coins grade rarity.
It got me to thinking. What percentage would be?
Lets say there are 3 million (pick-you modern) of something and over the course of a few years Collectors and Dealers have clammered to search for the high grades and 5% (or, about 150,000 coins) have been searched with NO MS67's located and just a scattering of MS66's. Now, I know it's safe to assume a few 66's may have slipped by during that search, but my question is, how many more coins need to be searched before it is safe to assume either NO MS67's will ever be located, or the number will be in the single digits?
10% (300,000 coins)? 20%?

dbldie55

Tell me the grades of all 150,000 and I will give you a very accurate number regarding the possibility one exists in 67 (it will not be 0).

braddick

Ok, I'll play. Now- know that only the BEST of the coins searched are going in, obviously, for examination and grading by PCGS. But, say out of that 150,000 coins searched 140,000 are average commercial UNCS, between MS60 and MS63+. Out of the remaining 10,000 or so screened, 9,000 are choice, MS64 and maybe ten percent of that (or, 900+ coins) are GEM MS65 but without a real shot at an upgrade. Now, you take the remaining 100 coins and most of those are premium MS65's that may upgrade on another day and the rest, say 30 or so did reach the MS66 pinacle. Those MS66's? Possibly two or three have a long shot at MS67 and out of those MS66's ten or so might cross into NGC MS67 holders. But, as it stands, NO MS67 PCGS coins are searched/ screened/ located, or made.

gmarguli

5% searched is well more than enough to draw an accurate statistical conclusion about the remaining 95%.

DRG

I just addressed the same issue on the other thread. Not that I have an answer. From my search of the 1980S I would say that MS66 coins were about 100X more common then MS67's. In other words I would expect that if there are actually 2,000 MS66's total there should be 20 MS67's. Then taking into consideration that the coins are likely tobe damaged over time it does become less and less likely that any will ever make it into a PCGS MS67 holder.

keithdagen

Use the CVC $5 as an example. There have been 705 graded by PCGS, so that's about 10% of the mintage.

2 in 67, 9 in 68, 660 in 69, and 34 in 70. Think the number of 70's could grow some more?

Keith

cladking

It would be a relatively simple matter to do a statistical analysis, but off the top of my
head I'd guess about 50,000 if the sets are a nice representative sample. As a practical
matter it is difficult to obtain a good sample because of the tendancy for gems to "bunch-
up" due to mint practices. There is also a good rule of thumb with clads that there is a
one magnitude drop between each of the higher grades. That is that there will be about
10 MS-66's for each MS-67. So there should be 1 MS-67 in about 10,000 sets if this holds
true. It would appear this coin doesn't exist. Mint practices can definitely throw a monkey
wrench in any conclusions. There are many factors which prevent coins from being MS-70.
Sometimes all these factors are being addressed my the operator and a few gems will
make it off his dies. If these get out of the mint and saved then it's possible that someday
someone will open up some fresh '81 mint sets (or '80 bags) and find some MS-68 81-S's.
There are other reports of modern coins which are found head and shoulders better than
the previous best.

supercoin

I'm not a statistician, but 5% is far more than is needed if it's a random sampling and perfectly consistent grading.

Neither of which caveat is true, unfortunately.

My biggest "fear" if paying big money for a 1981-S MS67 would be that grading standards would change, or coins that were "helped" out of the mint were discovered, something like that. It would be easy to make an MS69 if you worked at the mint.

Having said that, I'm a buyer for an 81-S PCGS 67 at $9500 last I checked.

dbldie55

Hey, I cludged through the numbers Braddick gave manually (ugh, but I haven't placed any more stats software on one of my machines), and with these numbers, not only is a 67 close to impossible, but so are the 66's. I did use a normal assumption, which should be considered invalid, but a more correct distribution would make the numbers even worse.

So I would say his numbers are near impossible too

merz2

Maybe I missed it but no one appears to have taken into account that only the first 50 or so off of the life of a die would qualify IMHO.

cladking

I've seen very nice high grade coins which exhibit a little die wear. The 1,000th strike
would show enough wear to keep it from being an MS-69 or maybe a MS-68, but not
an MS-67. Many dies now strike well over a quarter million coins, almost no coins can
make the grade if standards are too tough. Yes, I know that mint set SBA dies were
retired after only 15,000 to 25,000 strikes. Am I wrong here?

Dabigkahuna

Merz2
I think your right. Given a good planchet, the first ones off the new die and the first ones in the hopper that for that day may be the only source. Kinda of like a "glory hole" of gems that are in one bunch spread out near and far.

Larry
Dabigkahuna

Steve27

With numbers that large, five percent should be more than enough to develop a statistically significant sample. But due to the difficulty in obtaining a "random sample" (i.e. a single dealer might see a 100-1000 samples, but they may have been minted close to the same time), I would like to see several one-percent statistics from different parts of the country purchased at different times. The standard deviations and means could then be used to determine if these samples were from the same population. If not, then these could be combined into a single sample and another several one-percent samples could be collected/combined and the standard deviation and mean determined. These two several-percent samples could then be compared to determine if they were from the same population, and if not the process repeated again. Eventually, when they are shown to reflect the same population, you have a large enough sample.

cladking

Steve; this is well thought-out and impressive, but there are some real world-world
problems with it. The biggest probably is these sets are no longer original. People have
been going through them looking for gems and the like. The incidence of nice '81-S SBA's
in sets doesn't seem to have dropped that much around here but what about the area
where someone found a monster. Perhaps he's still buying all the sets there(No, I don't
know where it is unfortunately)(If it even exists). These sets are tough to find in unopened
boxes, so we'll probably just have to wait and see how it all shakes out.

If anybody does get a bunch of these for analysis or any other reason, I'd love a crack at
them. There is a type "D" (small motto) reverse quarter that shows up in this set.

supercoin

I would like to see several one-percent statistics from different parts of the country purchased at different times.

Ah, but there's the beauty of the PCGS pop reports -- despite the fact that grading is not perfectly consistent, what it does provide is a very widely scattered sampling.

Used properly (which in my opinion is for broad trends, not to say that something is a "pop 3" and thus rare) it's invaluable in providing a relatively consistent and impartial pooling of information.

Without that pop report, we could only rely on our individual experience and word-of-mouth. And if we believed word-of-mouth, there are plenty of MS67s.