Looking at the anchoring

Becker has created a mean value curve (a chronology) which, he claims, ends at year 859.
To anchor this curve into the then current late time chronology, starting at year 832, he needed and found a stem, the Eiche Aalen, that should bridge the time gap.
In a curve diagram, shown in the previous section, he demonstrated how the Eiche Aalen matches the historical standardcurve and how his new chronology matches the Eiche Aalen.
We will now look into the details of this matching.
(This section added Nov 12 2008)

Steps to go through for the analysis

We have:
1. The whole Master chronology of Becker covering the time BC370-AD1950.
2. The 120 years long late end segment of the Frümittelalteriche Eichen Maintal chronology taken from Becker's diagram covering the time AD740-859 according to Becker.
3. The Eiche Aalen sample covering AD744-980 taken from the diagram.
4. The early segment of the Huber standardcurve covering AD832-986 taken from the diagram.

To get the full length Huber standardcurve we will use the AD982-AD1950 segment of Becker's master chronology and add the standardcurve segment AD832-986 from the diagram (4. above).

We will then first analyse and show that Eiche Aalen really matches the full length Historical standardcurve as created above.

To study the anchoring process we need the full length of the Frümittelalteriche Eichen Maintal chronology starting at BC370 and ending at AD859. To create that we will use the segment BC370-AD740 of Becker's Master chronology (see discussion below) and add the late end segment AD740-859 of the Frümittelalteriche Eichen Maintal chronology from the diagram (2. above).

We will then add the Eiche Aalen to the Historical standardcurve to make a new reference and then see how the full length Frümittelalteriche Eichen Maintal chronology is anchored into the full length Historical standardcurve (with Eiche Aalen included). That anchoring itself seems to be severely in error!
A further analysis of the Frümittelalteriche Eichen Maintal chronology reveals that the late end segment of 154 years matches AD859 (the intended place) with a T-value of only 3.1 but with a T-value of 6.6 at AD1076! That clearly indicates that at least the late end of Becker's Frümittelalteriche Eichen Maintal chronology is incorrect. Adding the ring width pattern from AD922-1076 into the chronology at AD705-859 also made the final Becker chronology have two look-alike segments laying 217 years apart.

Testing that the Eiche Aalen sample really matches the Historical standard curve

To make this analysis we have to extend the diagram's Historical Standardcurve towards later times. For this we can use a segment (block) of Becker's published chronology between year 982 and 1950.

To create that segment from the full chronology:
Open the Master Chronology by double-clicking on the member BECMCR.
In the "Look at a single block.." frame on the Curve display tab, set Start at = 0 (corresponds to 1950) and End at = 967 (corresponds to year 982).
Click the Create sample from block button to create the block/segment.
Save the new segment as e.g. MCR982.wid and add it to your collection at offset 0 (year 1950) as shown above.

See that only the members BECAAL, BECSTD and MCR982 are checked as above.
Save them with the command Collections/Write Collection as Decadal file WITH comments as LateBeckerChronology.rwl

That file is available for your reference and research as LateBeckerChronology.rwl

Using the LateBeckerChronology.rwl file

Click the Create mean value sample button with the two members checked as shown above to get the Historical Standardcurve in its full length as a reference.
A double-click on the unchecked BECAAL (the Eiche Aalen) member will then open that sample in a new window with the standard curve as the reference.
A correlation analys shows:

```
Transformation: Baillie/Pilcher (5,-2,T,eLog)
--Rel Over   Corr TTest   GLK  (year)
-year  lap  coeff
970  147   0.36   4.7  0.67   (980) (as dated)
777  235   0.28   4.4  0.60  (1173)
981  136   0.26   3.2  0.52   (969)
918  199   0.20   2.9  0.56  (1032)
34  235   0.19   2.9  0.55  (1916)
631  235   0.18   2.8  0.54  (1319)
620  235   0.18   2.8  0.51  (1330)
951  166   0.21   2.8  0.55   (999)
577  235   0.17   2.7  0.57  (1373)
535  235   0.17   2.7  0.55  (1415)
997  120   0.23   2.6  0.56   (953)
```
Using instead the Hollstein transformation gives CorrCoeff=0.38 and TTest=5.0.

Checking with our HollsteinBestLateToYear410 collection as the reference gives

```
--Rel Over   Corr TTest   GLK  (year)
-year  lap  coeff
994  235   0.34   5.6  0.66   (980) (as dated)
1400  163   0.26   3.4  0.59   (574)
351  235   0.21   3.3  0.56  (1623)
```
With the Hollstein transformation the values are CorrCoeff=0.36, TTest=6.0

So Beckers dating of Eiche Aalen is reasonable!

Testing how the Maintal chronology matches the sum of Eiche Aalen and the Historical standard curve

Using the LateBeckerChronology.rwl file
Creating the reference
Check also the Eiche Aalen member (BECAAL) as shown above to make it included in the new reference!
When you then click the Create mean value sample button, you get a reference of about the same quality as that Becker had when he had added the Eiche Aalen sample to the Historical standard curve.
To set up for the matching of the Frühmittelalterliche Eichen Maintal (Early Middle Ages Oak River Main Valley) chronology we have to extend that chronology to older times not visible in the curve diagram which starts with its left margin at year 740.

For this we have not the extention of the actual Maintal chronology but only a mean value of several chronologies as published as Becker's Master Chronology.
As the Maintal chronology taken from the diagram has a correlation coefficient of 0.73 towards the Master Chronology, it seems reasonable to use a segment from the Master in place of the missing extension of the Maintal chronology.

To create an extended Maintal chronology, create a new empty collection and add the Maintal chronology of the diagram (BECMAI) to that collection.

Open the Master Chronology in a new sample window and create a block/segment covering the years BC 369 - AD 745 (index 1205-2317), save it in a .wid file as e.g. MTO745.wid and then add that to the new collection as shown above. Save the collection as e.g. MaintalExtended.rwl.

For your research and analysis that file is available as MaintalExtended.rwl

Creating the curve to be tested
When you click the Create Mean value sample button you get
an approximate extended Maintal chronology with all the data that Becker wanted to anchor into
the Eiche Aalen sample and the Huber Historical Standard curve!
When the sum of the MaintalExtended collection is compared to the sum of the LateBeckerChronology collection the correlation results are:
```
Baillie/Pilcher (5,-2,T,eLog)
--Rel Over   Corr TTest   GLK  (year)
-year  lap  coeff
1029  176   0.28   3.9  0.56   (921)
874  331   0.20   3.7  0.57  (1076)
1067  138   0.27   3.2  0.56   (883)
1091  114   0.28   3.1  0.65   (859) (as dated)
705  500   0.14   3.1  0.52  (1245)
766  439   0.14   2.9  0.51  (1184)
377  828   0.10   2.9  0.54  (1573)
1163   42   0.41   2.9  0.67   (787)
1098  107   0.27   2.8  0.55   (852)
:
Testing the MaintalExtended collection towards ONLY the Eiche Aalen sample:
193   42   0.41   2.9  0.64   (787)
97  138   0.37   4.7  0.58   (883)
-1064  163   0.33   4.5  0.59  (2044)
121  114   0.33   3.7  0.63   (859) (as dated)
184   51   0.31   2.3  0.60   (796)
-204  235   0.26   4.1  0.59  (1184)
59  176   0.25   3.4  0.55   (921)
:
A block correlation towards the sum of the LateBeckerChronology collection reveals:
:
Block length: 150   Table sorted by Corr coeff.
Block  -----Aimed------   -------Best    ------------Three best matches with {hitAt,Corr coeff.,SetsSampleTo}
start  --------at  year   around that    ---1stBestMatch-------    ---2ndBestMatch-------    ---3rdBestMatch-------
0   1091 0.28   859    1091 0.28       874 0.47  874 (1076)     1163 0.41 1163  (787)     1154 0.31 1154  (796)
10   1101 0.26   849    1101 0.26       884 0.50  874 (1076)     1108 0.33 1098  (852)      443 0.31  433 (1517)
20   1111 0.23   839    1111 0.23       894 0.48  874 (1076)     1159 0.36 1139  (811)      842 0.29  822 (1128)
30   1121 0.30   829    1121 0.30       904 0.45  874 (1076)      852 0.30  822 (1128)     1121 0.30 1091  (859)
40   1131 0.25   819    1131 0.25      1151 0.39 1111  (839)      914 0.34  874 (1076)     1069 0.31 1029  (921)
50   1141 0.26   809    1141 0.26      1161 0.40 1111  (839)     1148 0.31 1098  (852)     1079 0.30 1029  (921)
60   1151 0.22   799    1151 0.22      1158 0.34 1098  (852)     1157 0.33 1097  (853)     1089 0.32 1029  (921)
70   1161 0.24   789    1161 0.24      1099 0.38 1029  (921)      927 0.31  857 (1093)      733 0.29  663 (1287)
```
I.e. a 150 years long block at the late end of the Maintal chronology ending at year 859, matches much (!!) better at year 1076.

If we create a 154 years long block from the late end of the sum of our extended Maintal collection, that block matches towards the LateBeckerChronology like this:

```
Transformation: Baillie/Pilcher (5,-2,T,eLog)
compared to the reference LateBeckerChronology_2.d15  Dated to 1950
Minimum overlap used when finding best match: 40
Table sorted by TTest
--Rel Over   Corr TTest   GLK  (year)
-year  lap  coeff
874  154   0.47   6.6  0.66  (1076)
1029  154   0.30   3.9  0.58   (921)
846  154   0.28   3.5  0.53  (1104)
483  154   0.27   3.4  0.60  (1467)
433  154   0.26   3.3  0.52  (1517)
1067  138   0.27   3.2  0.56   (883)
1091  114   0.28   3.1  0.65   (859) (as dated)
338  154   0.24   3.1  0.62  (1612)
174  154   0.23   3.0  0.60  (1776)
451  154   0.23   2.9  0.52  (1499)
524  154   0.23   2.9  0.61  (1426)
822  154   0.23   2.9  0.58  (1128)
1163   42   0.41   2.9  0.67   (787)
1098  107   0.27   2.8  0.55   (852)
20  154   0.22   2.8  0.59  (1930)
```
My conclusion: There is something wrong with the late end of Becker's Frühmittelalterliche Eichen Maintal chronology and its dating to year 859!

Note:What may have happended is this:
The late end of Beckers Maintal chronology is not correct because it is based on a tree from year 1076 and not from 859.
Then Becker added the Eiche Aalen to that erroneous Maintal chronology according to this:

```
Transformation: Baillie/Pilcher (5,-2,T,eLog)
--Rel Over   Corr TTest  BaPi   Skel  Skel   GLK  (year)
-year  lap  coeff        corr   Chi2  corr
-97  138   0.37   4.7  0.38    7.2  0.33  0.58   (956)
1064  163   0.33   4.5  0.33   17.1  0.32  0.59  (-205)
204  235   0.26   4.1  0.26    9.4  0.22  0.59   (655)
-121  114   0.33   3.7  0.32    5.5  0.34  0.64   (980) (as dated)
1041  186   0.25   3.5  0.25    6.6  0.20  0.64  (-182)
-59  176   0.25   3.4  0.25   10.8  0.28  0.55   (918)
```
Becker selected the 980 match because of the 0.64 GLK-value!
With the Eiche Aalen added to his already erroneous Maintal chronology he got a chronology which ended with data that actually SHOULD be anchored at 980.
```
Transformation: Baillie/Pilcher (5,-2,T,eLog)
--Rel Over   Corr TTest  BaPi   Skel  Skel   GLK  (year)
-year  lap  coeff        corr   Chi2  corr
970  147   0.31   4.0  0.30    3.8  0.33  0.65   (980) (as dated)
-253 1095   0.11   3.7  0.11    2.3  0.10  0.53  (2203)
-897  451   0.15   3.1  0.15    6.8  0.13  0.54  (2847)
777  340   0.17   3.1  0.16    0.2  0.10  0.52  (1173)
-923  425   0.15   3.1  0.15    0.2  0.13  0.59  (2873)
```
So the result depends a lot on in which order we do these things.
High correlation coefficient values and high T-values are not characteristic for the way this GLK technology was carried out.
As it looks, Becker had very limited computer resources! It is the technology he used that led him to make errors.

Using the Hollstein data as a reference

If we check our 154 years long block against our HollsteinBestLateToYear410.rwl collection we get:
```
Transformation: Baillie/Pilcher (5,-2,T,eLog)
--Rel Over   Corr TTest   GLK  (year)
-year  lap  coeff
898  154   0.41   5.5  0.60  (1076)
870  154   0.32   4.2  0.58  (1104)
475  154   0.29   3.8  0.57  (1499)
1086  154   0.28   3.5  0.58   (888)
1053  154   0.26   3.3  0.56   (921)
18  154   0.26   3.3  0.55  (1956)
946  154   0.26   3.3  0.56  (1028)
1050  154   0.26   3.3  0.54   (924)
1106  154   0.24   3.0  0.56   (868)
1115  154   0.24   3.0  0.56   (859) (as dated)
1011  154   0.23   2.9  0.52   (963)
213  154   0.23   2.9  0.59  (1761)
548  154   0.23   2.9  0.61  (1426)
```
Though, if we look at only the latest 80 years the correlation of that segment/block towards year 859 of HollsteinBest is only at corr-Coeff= 0.03! The rest is at 0.53.

If we cut off these late 80 years from Beckers curve, the rest - back to year 410 - will match almost perfectly towards our HollsteinBestLateToYear410.rwl collection at the time where Becker wanted it to match!

A blockwise quality test showing incorrect matches, shows that the Becker Master Chronology has an ambiguity where a block from year 820 can be matched towards a point 217 years later in time with a TTest-value of 6.0 (see the upper part of the diagrams above).
The corresponding curve for our HollsteinBestLateToYear410 collection does not show a corresponding problem at these years.

I.e. there is no sign that Mother Nature has created some sort of same ring patterns for these two periods.
Instead, it looks as Becker has copied the ring width pattern of years 932-1037 into the "year-region" of 715-820 when he anchored his chronology into the Historical standard curve of Huber.

I.e. it looks as Becker had the ring width pattern from the period 932-1037 in the late tail of his chronology ending at AD859. So either the anchoring of Beckers chronology BC369-AD859 seems wrong
or the late pattern of his Early Middle Ages chronology seems wrong.

With the data of the tables above, I cannot justify Becker's choice of anchoring point!

To me (!) it looks as Becker wanted to anchor his chronology at year 859 because evidence in European history (the calender chronology) said it should be like that.

This all raises the question about other crossdatings done with other chronologies. With the acceptance of such low correlation values as above, errors have to be common!

The Roman time samples - A comment

As I have included also the Roman time samples with this article, I should comment on them.

BECRSU - Sulz: Sulz does not match properly towards the other samples.
BECRMU - Murrhardt: The late 27 rings have a negative correlation (-0.30) towards the rest of the samples (excluding Sulz).

Except for Sulz, these samples crossdate towards each other with a correlation coefficient between 0.5 and 0.6 giving T-values in the range 7.6-10.

Except for BECRSU and BECRMU (even without the late 27 rings) they all match reasonably well towards the Hollstein Roman collection.

The Sulz problem:

```
Running a correlation test of BECRSU (Sulz) towards the rest of the samples gives:
Transformation: Baillie/Pilcher (5,-2,T,eLog)
--Rel Over   Corr TTest   GLK  (year)
-year  lap  coeff
11   99   0.30   3.1  0.63   (170)
46   99   0.28   2.9  0.57   (135)
104   98   0.28   2.8  0.56    (77) (as dated)
5   99   0.22   2.2  0.53   (176)
39   99   0.22   2.2  0.58   (142)
-58   41   0.32   2.1  0.55   (239)
25   99   0.20   2.0  0.52   (156)
29   99   0.19   1.9  0.57   (152)
-16   83   0.20   1.8  0.52   (197)
124   78   0.19   1.7  0.47    (57)
17   99   0.16   1.6  0.51   (164)
76   99   0.16   1.6  0.54   (105)
30   99   0.16   1.6  0.53   (151)
158   44   0.24   1.6  0.53    (23)
```
I do not understand why the Sulz sample was at all included with the curve diagram - it looks like a mistake.

Continue with the next section, Summary and Conclusions!
 August 22 2008. Lars-Åke Larsson (Updated 12 Nov 2008)