"Difference" and "Interval" commands

[Boulanger, Matthew Turner]

I was curious if someone could explain the proper use of the “Difference” and/or “Interval” queries in OxCal.  Basically, I am wanting to determine the amount of time separating the two series of events and/or the probability that the two series of events overlap.  The following code provides a model overlapping distributions for the two Phases, but perhaps it may be more appropriate to model them as discontinuous events?  In any case, I would like to determine the span of time separating the two Phases.  It is not clear to me from the OxCal help files how exactly I would do this in this particular model.

 

Thank you for any help that you can offer,

 

-Matt

 

 

Matthew Boulanger, M.A., R.P.A.
Archaeometry Laboratory
University of Missouri Research Reactor
1513 Research Park Drive
Columbia, MO 65211
 
573.882.5260 tel
573.882.6360 fax
boula...@missouri.edu
 
Archaeometry Laboratory
http://archaeometry.missouri.edu/

 

 

 

Phase("Megafauna")

{

  Sequence()

  {

   Boundary( "Beginning of Megafauna");

   Phase( )

   {

     R_Date("W-544",21200,1000);

     R_Date("WIS-1935",14240,150);

     R_Date("CAMS-13304",13840,80);

     R_Date("CAMS-12849",13320,70);

     R_Date("Y-2619",13320,200);

     R_Date("CAMS-13296",13180,80);

     R_Date("CAMS-13305",13150,90);

     R_Date("CAMS-13298",12920,70);

     R_Date("CAMS-12589",12750,70);

     R_Date("CAMS-12586",12720,70);

     R_Date("I-4137",12530,270);

     R_Date("CAMS-12592",12430,70);

     R_Date("BETA-49776",12210,120);

     R_Date("Dutchess Quarry Peccary",12198.4,48);

     R_Date("UGA-666",12190,215);

     R_Date("Scarborough Mammoth 2",12189.71,36.59841);

     R_Date("BETA-141061",12180,60);

     R_Date("QC-296",12130,210);

     R_Date("I-838",12100,400);

     R_Date("Marshalls Creek Mastodon",12090,127.2792);

     R_Date("W-2006",11900,750);

     R_Date("CAMS-12587",11670,70);

     R_Date("BETA-176928",11630,60);

     R_Date("AA-7397",11565,105);

     R_Date("BETA-135234",11480,60);

     R_Date("CAMS-54734",11460,60);

     R_Date("GX-9024G",11440,655);

     R_Date("AA-4935",11362,115);

     R_Date("Elizabethtown Muskoxe",11270.17,108.9747);

     R_Date("I-11286",11230,160);

     R_Date("Cohoes Mastodon",11070,60);

     R_Date("AA-1506",11070,130);

     R_Date("Y-460",11029.66667,410);

     R_Date("NZA-12584",11000,80);

     R_Date("GX-2675",10995,750);

     R_Date("TO-3194",10990,100);

     R_Date("I-4016",10950,150);

     R_Date("AA-1505",10930,315);

     R_Date("L-231",10890,200);

     R_Date("BETA-176929",10890,50);

     R_Date("Pound Ridge Mastodon",10850,270);

     R_Date("BETA-176930",10840,60);

     R_Date("CAMS-62560",10810,50);

     R_Date("Scarborough Mammoth",10569.42,210.6697);

     R_Date("BETA-24412",10515,120);

     R_Date("AA-4943",10465,110);

     R_Date("W-1038",10450,400);

     R_Date("DIC-709",10340,125);

     R_Date("Arcadia Mastodon",10340,170);

     R_Date("I-3785",10000,160);

     R_Date("AA-61942",10000,95);

     R_Date("I-6634",9860,225);

    Interval( "Duration of Megafauna");

   };

   Boundary( "End of Megafuana");

  };

  Sequence()

  {

   Boundary( "Start of Fluted Points");

   Phase( )

   {

     R_Date("Saugus Quarry",8095,415);

     R_Date("Rimouski",8150,130);

     R_Date("Dutchess Quarry Cave No. 8†",8290,100);

     R_Date("Little Ossipee North (ME7-7)[1]",8470,110);

     R_Date("Rocky Brook†",8510,140);

     R_Date("Bull Brook 2†",8565,284);

     R_Date("Jefferson II (27CO29)",8570,60);

     R_Date("WMECO†",8685,370);

     R_Date("Turkey Swamp",8739,165);

     R_Date("Bull Brook[2]",8790,50);

     R_Date("Michaud",9130,200);

     R_Date("Hidden Creek (72-163)[1]†",9180,30);

     R_Date("Little Ossipee North (ME7-7)[2]",9350,90);

     R_Date("Bull Brook[1]",9450,40);

     R_Date("Steel (28CM42)",9530,60);

     R_Date("Weirs Beach (NH26-32)",9615,225);

     R_Date("West Creek (28OC45)",9850,160);

     R_Date("Whipple[1]**",9960,200);

     R_Date("Esker (ME86-12)",10090,70);

     R_Date("Caratunk (ME86-12)",10110,70);

     R_Date("Neponset/Wamsutta (19F70)",10210,60);

     R_Date("Templeton",10210,90);

     R_Date("Janet Cormier (ME27-25)",10240,90);

     R_Date("Poland (ME23-25)",10240,90);

     R_Date("Hidden Creek (72-163)[2]†",10260,70);

     R_Date("Brigham (ME90-2C)",10290,460);

     R_Date("Colebrook (27CO38)",10290,170);

     R_Date("Vail (ME81-1)[1]",10310,75);

     R_Date("Arc***",10375,110);

     R_Date("Bull Brook[3]",10395,40);

     R_Date("Hedden****",10540,40);

     R_Date("Debert",10580,40);

     R_Date("Shawnee-Minisink*",10935,15);

    Interval( "Duration of Fluted Points");

   };

   Boundary( "End of Fluted Points");

  };

};

 

 

 

 

[Christopher Ramsey]

The interval command finds the difference between the dates that constrain the command. In the first case here:

Interval( "Duration of Megafauna");

will find the difference between "Beginning of Megafauna" and "End of Megafuana". To work interval commands must be in the right place.

The difference command is usually put anywhere within the outer command (Phase or Plot) of the model and specifies what difference you want directly so the following should give the same answer:

Difference( "Duration of Megafauna","End of Megafuana","Beginning of Megafauna");

Typically you would place it just before the last closing };

Christopher

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[Boulanger, Matthew Turner]

Chris:

Thank for the response and the clarification. With that and some playing around with OxCal, I think I've got it covered.

I am also curious about the "R_Combine" function. I understand that this relates to dates of the same event, but how does this differ from the "Pooled Mean" function of other programs (e.g., Calib)? Both procedures are evaluated using a chi-square test, but they produce slightly different results. I've seen some publications where a pooled mean has been calculated in Calib, and then calibrated and used in OxCal. Is a particular method preferable when combining dates from the same specimen (e.g., multiple dates on a single mammal skeleton)?

Thanks,

-Matt

[Christopher Ramsey]

Matt

R_Combine uses the error weighted mean - which is different. Each have their uses and strengths.

Christopher

[MILLARD A.R.]

> From: Christopher Ramsey
> Sent: 06 December 2010 14:15

>
> R_Combine uses the error weighted mean - which is different. Each
> have their uses and strengths.
>

> On 1 Dec 2010, at 19:40, Boulanger, Matthew Turner wrote:
>
> > I am also curious about the "R_Combine" function. I understand
> that this relates to dates of the same event, but how does this
> differ from the "Pooled Mean" function of other programs (e.g.,
> Calib)? Both procedures are evaluated using a chi-square test, but
> they produce slightly different results

They shouldn't produce different results because they are simply using different terminology for the same thing, combining or pooling dates using the method described for Case 1 of Ward & Wilson (1978). Can you give an example where OxCal's r_combine differs from Calib's pooled mean?

Best wishes

Andrew
--
 Dr. Andrew Millard                       A.R.M...@durham.ac.uk  
 Durham University
 Senior Lecturer in Archaeology              Tel: +44 191 334 1147
 Archaeology:      http://www.dur.ac.uk/archaeology/       
Personal webpage: http://www.dur.ac.uk/a.r.millard/

[Christopher Ramsey]

Andrew

Well I assume that Calib can used the non-error-weighted mean and pooled variance method - but I have not investigated. I don't think the term 'pooled mean' is used for the error-weighted mean and the associated method of uncertainty calculation. But I may be wrong. OxCal does indeed use the method outlined by Ward and Wilson.

Christopher

[MILLARD A.R.]

> From: Christopher Ramsey
> Sent: 06 December 2010 14:43

>
> Well I assume that Calib can used the non-error-weighted mean and
> pooled variance method - but I have not investigated. I don't
> think the term 'pooled mean' is used for the error-weighted mean
> and the associated method of uncertainty calculation. But I may be
> wrong. OxCal does indeed use the method outlined by Ward and
> Wilson.

The Calib manual gives the same formula for the test statistic as the OxCal manual and cites Ward and Wilson [1]. The quantity described in the OxCal manual as "a combined determination r_c" [2] is what Ward and Wilson call a pooled mean, A_p, and give in their equation 6. OxCal has always given the same answer as my spreadsheet implementation of Ward and Wilson, so I am confident it does indeed use that method. There should be no difference in Calib, and the one example I've tried gave exactly the same results in both programs.

[1] http://calib.qub.ac.uk/calib/manual/chapter2.html under 'Tools / Sample Significance'
[2] http://c14.arch.ox.ac.uk/oxcalhelp/hlp_analysis_inform.html#calib under 'Maths'

[Boulanger, Matthew Turner]

Andrew et al.:

Quickly, the following should illustrate what I'm dealing with:

R_Combine("Samples")
{
R_Date ("P-977", 10113, 275);
R_Date ("P-743", 10452, 128);
R_Date ("P-970", 10477, 90);
R_Date ("P-972", 10496, 120);
R_Date ("P-741", 10531, 126);
R_Date ("P-966", 10557, 121);
R_Date ("P-967", 10626, 244);
R_Date ("P-973", 10637, 114);
R_Date ("P-739", 10642, 134);
R_Date ("P-971", 10758, 226);
R_Date ("P-974", 10824, 119);
R_Date ("P-975", 11011, 225);
};

The above command in OxCal gives a mean of 12540 calBP, and 2 ranges at 95.4%: 12636-12515 calBP (69.9%), and 12500-12424 calBP (25.5%).

Using Calib's (v. 6.0.1) "Pooled Mean" function returns the following:

Radiocarbon Age 10581±39
One Sigma Ranges: [start:end] relative area
[cal BP 12437: cal BP 12462] 0.204478
[cal BP 12528: cal BP 12596] 0.795522
Two Sigma Ranges: [start:end] relative area
[cal BP 12423: cal BP 12503] 0.298296
[cal BP 12514: cal BP 12631] 0.701704

Both are using IntCal 09. The Calib dates are different. Admittedly the differences are slight and may be due to how each program handles rounding. These differences would essentially disappear if I rounded the confidence limits of the dates to the nearest 10. But, in this instance, the means reported are 40 years appart. Thus, rounding the means to the nearest 50 yrs. would make this difference 50 cal yr. (or 100, if I round to the nearest 100 years). I'm not sure how this would impact the results of my study, but I just noticed that the output was different.

Because I am dealing with several instances where I have multiple dates from the same event, I was unsure how best to treat them. A similar study I read used Calib to create a pooled mean, and then used OxCal to calibrate and create a summed-probability model of all their dates. I would prefer to use 1 program (OxCal) to do the entire analysis (including a summed-probability model and Bayesian analysis), so using the "Combine" function seemed the most logical (and simpler) choice.

-Matt

Matthew Boulanger, M.A., R.P.A.
Archaeometry Laboratory
University of Missouri Research Reactor
1513 Research Park Drive
Columbia, MO 65211
 
573.882.5260 tel
573.882.6360 fax
boula...@missouri.edu
 
Archaeometry Laboratory
http://archaeometry.missouri.edu/

Best wishes

--

[Christopher Ramsey]

Ok - for this set OxCal gives 10585+/-39 rather than 10581. I think this is because the calculation in OxCal is performed in radiocarbon ratio space rather than in BP (which is a non-linear transformation of the same). The information is given on this page of the OxCal manual:

https://c14.arch.ox.ac.uk/oxcalhelp/hlp_analysis_inform.html#calib

where it says:

"Note that all calculations are performed in terms of radiocarbon concentration (rather than BP date). This includes calibration. If you wish to override this you can do this by setting the option 'Use F14C space' to off. This only affects the calibration itself all other calculations, such as reservoir mixing etc will be performed in terms of radiocarbon concentration F14C."

This makes virtually no difference for young dates - but becomes increasingly important as you get older. I have checked the calculation both ways using Excel and it gives the two slightly different answers.

Ultimately I think the combination in F14C or %modern is the right way to do this - and as the dates get close to background it is essential.

Anyway I hope this explains the difference you see here to your satisfaction.

Christopher

[MILLARD A.R.]

Dear Matt,

You are comparing the calibrated mean from OxCal with the uncalibrated mean from Calib. When I do these calculations I only get small differences:

Program Pooled mean Uncertainty Test statistic
Calib 6.01 10580.98 38.98903 14.86383
OxCal 4.1 10585 39 15.0
OpenOffice 10580.98 38.98903 14.86383

Calibrated results in cal BP:
Calib 6.01 OxCal 4.1 Build 61
68.2% 12437-12462 12439-12460
12528-12596 12529-12599
95.4% 12423-12503 12423-12501
12514-12631 12515-12636
For OxCal I used Resolution=1; Cubic=FALSE; UseF14C=FALSE to bring it as close as possible to what I believe Calib does.

If I calibrate one program's combined value in both programs, then the ends of the ranges differ by no more than 1 year, and the majority are the same. So the small differences in calibrated ranges above are due to OxCal's calculation of the pooled mean differing from Ward and Wilson's method as implemented in both Calib and my own spreadsheet.

Best wishes

Andrew
--
 Dr. Andrew Millard                       A.R.M...@durham.ac.uk  
 Durham University
 Senior Lecturer in Archaeology              Tel: +44 191 334 1147
 Archaeology:      http://www.dur.ac.uk/archaeology/       
Personal webpage: http://www.dur.ac.uk/a.r.millard/

[Christopher Ramsey]

Andrew

Yes - and the difference is that in OxCal the dates are converted to F14C - then the Ward and Wilson statistical method is applied - and then they are converted back. It does this regardless of whether UseF14C=FALSE or TRUE. The latter option only defines whether the calibration itself is performed in F14C space or BP space. In Excel, I also get 10580.98 with the BP combination but 10585.23 when converted to F14C space before combination. This latter agrees with the value calculated in OxCal (rounded to the nearest year).

Christopher

[MILLARD A.R.]

> From: Christopher Ramsey
> Sent: 06 December 2010 18:39

>
> Yes - and the difference is that in OxCal the dates are converted
> to F14C - then the Ward and Wilson statistical method is applied -
> and then they are converted back. It does this regardless of
> whether UseF14C=FALSE or TRUE. The latter option only defines
> whether the calibration itself is performed in F14C space or BP
> space.

I see now why there is a difference. OxCal's method is strictly the correct one as the approximation of normality of the errors in radiocarbon years BP is not used. Ward & Wilson suggest that the approximation only breaks down beyond 30,000 BP, but the shift of a few years between Calib and OxCal for this example illustrates that if high-precision posteriors are being obtained, then for accurate results it is necessary to work in F14C even at 10,000 BP.