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Statistical Analysis Of Key And Semi-Key Lincoln Cents

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drdave's Avatar
United States
721 Posts
 Posted 05/21/2011  12:01 am Show Profile   Bookmark this topic Add drdave to your friends list Get a Link to this Message Number of Subscribers
My little project for the day. This may have been done before, but I'd like to present my findings. I looked at mintage figures for the Lincoln cents 1909-2010. I divided them into the two traditional groups: wheats (1909-1958), and modern (1959-2010). I am not including varieties such as 1955 DD, 1960 small date, etc., since these have no specific mintage figures.

I took the log (base 10) of the mintage figures and determined their statistical z-score. (The log value gave, in my opinion, more realistic z-score distributions than using the raw mintage figures.) The z-score is a measure that tells how many standard deviations it is above or below the mean. Key dates would have very negative scores. What I was trying to do is to see what z-scores are for the traditional key dates and then compare these values to the more modern cents.

Here are the results for the LWC:
1909 S VDB -3.07 key
1931 S -2.71 key
1914 D -2.51 key
1909 S -2.25 key
1924 D -2.05 semi-key
1911 S -1.76 semi-key
1914 S -1.74 semi-key
1912 S -1.70 semi-key
1931 D -1.70 semi-key
1926 S -1.69 semi-key
1915 S -1.65 semi-key
1910 S -1.51 semi-key
1913 S -1.50 semi-key

I used the definitions of key and semi-key from http://www.lincolncentresource.com/index.html

Using the cutoff value for a key date to be -2.2 or smaller and a semi-key between -2.2 and -1.5, I then determined the following for the modern cents and used this definition to label them as key or semi-key:

(1959-2010):
1968 S -3.12 key
1973 S -2.87 key
1972 S -2.65 key
1974 S -2.55 key
1971 S -2.24 key
1969 S -2.20 key
1960 -2.10 semi-key
1962 -2.06 semi-key
1959 -2.06 semi-key
1970 S -1.90 semi-key
1961 -1.79 semi-key
1963 -1.79 semi-key


It is interesting to note that WITHIN these groups, the 1968 S is comparable to the 1909 S VDB! You can make similar comparisons between the groups, such as the 1974 S is very comparable to the 1914 D.

I know this is a long read and there are many interpretations, but I thought this was interesting. I also felt is was important to have the two groups of data span about the same number of years. I also know there are other variables to consider to determine what is a key date.

Finally, there has been talk about how low mintage the 2009 cents have been. Here are the results of these:

2009 P -1.32
This compares best with:
1923 S -1.29


2009 D -1.17
This compares best with:
1932 D -1.17

Comments? Thanks for reading...
Edited by drdave
05/21/2011 12:42 am
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bibd's Avatar
Canada
838 Posts
 Posted 05/21/2011  12:21 am  Show Profile   Bookmark this reply Add bibd to your friends list Get a Link to this Reply
This is awesome work you've done! It's really neat to see the comparisons between wheats and memorials like this. I suspect the Zincolns will be tougher to obtain in higher grades than the Coppers; however, if a lot of copper disappears in 20 years, we might just have some of these memorial "keys" show themselves as such!
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Scooby Due's Avatar
United States
4000 Posts
 Posted 05/21/2011  12:22 am  Show Profile   Bookmark this reply Add Scooby Due to your friends list Get a Link to this Reply
Interesting view.

I was following you until I got to:

Quote:
Finally, there has been talk about how low mintage the 1909 cents have been. Here are the results of these:

2009 P -1.32
This compares best with:
1923 S -1.29


2009 D -1.17
This compares best with:
1932 D -1.17

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bibd's Avatar
Canada
838 Posts
 Posted 05/21/2011  12:24 am  Show Profile   Bookmark this reply Add bibd to your friends list Get a Link to this Reply
By the way, how about breaking 2009 down into LP-1,2,3,4, since mintages are available for those? Also, there are estimates on the variety mintages from circulation pulls. For these, follow the links on Clint's page (from Stanford U.) on U.S. Coin prices.
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drdave's Avatar
United States
721 Posts
 Posted 05/21/2011  12:30 am  Show Profile   Bookmark this reply Add drdave to your friends list Get a Link to this Reply
Scooby Due: The 2009 cents are relatively low mintage. I emphasize the word relatively. The 2009-P is comparable to the 1923-S, in terms of relative mintage within each of their groups. What I was trying to show is that the 2009-P is low mintage (1.1 billion) but it should be viewed in the same light as the 1923-S (8.7 million). The 1923-S is not considered a semi-key, but it does have a low mintage. We should view the 2009-P in the same way.
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drdave's Avatar
United States
721 Posts
 Posted 05/21/2011  12:37 am  Show Profile   Bookmark this reply Add drdave to your friends list Get a Link to this Reply
bibd: breaking down the 2009 mintages would make their z-scores around -3, but I'm not sure that's a fair comparison.
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Scooby Due's Avatar
United States
4000 Posts
 Posted 05/21/2011  12:38 am  Show Profile   Bookmark this reply Add Scooby Due to your friends list Get a Link to this Reply

Quote:
Finally, there has been talk about how low mintage the 1909 cents have been.


So, you meant 2009 there, not 1909?
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drdave's Avatar
United States
721 Posts
 Posted 05/21/2011  12:41 am  Show Profile   Bookmark this reply Add drdave to your friends list Get a Link to this Reply
OOPS - late night typing: "low mintage the 1909 cents have been", should have been 2009 cents!

I will edit my original post.
Valued Member
Waredu's Avatar
United States
397 Posts
 Posted 05/21/2011  12:45 am  Show Profile   Bookmark this reply Add Waredu to your friends list Get a Link to this Reply
I'm curious about breaking down the 2009s as well. I pull LP1s all day long, but I almost never see an LP4. It's gotten to where I pull the LP4s if they're even the slightest bit shiny with no pits anywhere. Zinc rot is so fast I really think that in another 10 years or so you won't be able to find them in circulation at all.
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drdave's Avatar
United States
721 Posts
 Posted 05/21/2011  01:00 am  Show Profile   Bookmark this reply Add drdave to your friends list Get a Link to this Reply
Here's the 2009 breakdown:
2009 P4 -3.05
2009 D4 -2.63
2009 P1 -2.26
2009 P3 -2.16
2009 D3 -2.10
2009 D1 -2.05
2009 D2 -2.02
2009 P2 -1.98
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EgCollector's Avatar
Egypt
3470 Posts
 Posted 05/21/2011  04:52 am  Show Profile   Bookmark this reply Add EgCollector to your friends list Get a Link to this Reply
Very good work, well done
Rest in Peace
biggfredd's Avatar
United States
9104 Posts
 Posted 05/21/2011  05:13 am  Show Profile   Bookmark this reply Add biggfredd to your friends list Get a Link to this Reply
OP-

I've always heard 65-66-67 and 69 cents being harder to find, yet they didn't make your list.
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bpoc1's Avatar
United States
4078 Posts
 Posted 05/21/2011  06:21 am  Show Profile   Bookmark this reply Add bpoc1 to your friends list Get a Link to this Reply
Once again great information! Thanks.
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nickelsearcher's Avatar
United States
15381 Posts
 Posted 05/21/2011  08:45 am  Show Profile   Bookmark this reply Add nickelsearcher to your friends list Get a Link to this Reply
Great analysis! You know I am a fan of coin statistics.

I'll read it again and think it through ... but enjoy the concept and methodology.

Well done.

David
Take a look at my other hobby ... http://www.jk-dk.art
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dMAN's Avatar
United States
103 Posts
 Posted 05/21/2011  09:43 am  Show Profile   Bookmark this reply Add dMAN to your friends list Get a Link to this Reply
bibd, you made a comment regarding the disappearance of copper cents. Do you believe this will have the same effect on the value of these coins as it did on the silver coins?
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drdave's Avatar
United States
721 Posts
 Posted 05/21/2011  10:33 am  Show Profile   Bookmark this reply Add drdave to your friends list Get a Link to this Reply
biggfredd: Here are the results for the 1965-1969 cents. I included the calculated z-score (not ranked). All but the 1969-D have negative values. There may be other reasons why certain coins may be hard to find in population; this is only one way to look at them.

1965 -0.94
1966 -0.47
1967 -0.06
1968 -0.78
1968 D -0.13
1968 S -3.12
1969 -1.28
1969 D 0.28
1969 S -2.20

So I would say they are less than average mintages, but the ones you mentioned would not be considered semi-keys.
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