# Weighing the chronology of physical manuscripts using chi squared

#### Peter RF Brown

##### New Member
Greetings. I hope to receive feedback on a possible application of the chi squared test to a situation in ancient history. I have made a study of the chronology of physical manuscripts of texts which fall into the class of the New Testament Apocrypha. See: New Testament apocrypha - Wikipedia

The mainstream paradigm theory for the chronology of the appearance of these manuscripts in antiquity is during the period (approximately) 125-425 CE.
I seek to establish an alternate theory in which proposes these manuscripts appeared during the period (approximately) 325-425 CE

Some time ago I attempted to conduct a chi squared test on the data by considering two chronological "buckets" 125-324 and 325-424
You will find this here: Weighing the chronology of the Gnostic "page counts" > 325 CE (mountainman.com.au)

I have been given advice that the application of a chi squared test is not appropriate here because the the survival rate of manuscripts from antiquity is not a random variable. Now - quite obviously the more centuries we go back the less historians find. The variable, it was claimed, was unknown, but not random. I was advised to make a study of the general survival rate of manuscripts over time. And then apply this to the analysis. But I have nagging doubts that it is entirely reasonable to use a chi squared test and examine the weighting between the two chronological "buckets".

I hope this question is relevant for discussion in this forum.
Otherwise any other advice would be appreciated.
Thanks.

#### katxt

##### Active Member
I was advised to make a study of the general survival rate of manuscripts over time. And then apply this to the analysis.
Hi Peter. I have read your post and your article and I have to say that I agree with the advice about survival rates. In fact, you could use the same data and null hypothesis to model the changing survival rate over time.
Of course, things are even more complicated than that. You would need a model that accounts for the fact that copies were continually being made and lost (and found again) at different rates as the centuries passed.
But I have nagging doubts that it is entirely reasonable to use a chi squared test and examine the weighting between the two chronological "buckets".
My opinion is that you are laying on the chi square test more weight than it can reasonably bear.

#### Peter RF Brown

##### New Member
Interesting text!
But what is the question? I can not find any.
Thanks! The question is about the validity (or otherwise) of the chi squared test (outlined in the link).

#### Peter RF Brown

##### New Member
Hi Peter. I have read your post and your article and I have to say that I agree with the advice about survival rates. In fact, you could use the same data and null hypothesis to model the changing survival rate over time.
Thanks for taking the time to check the claim and provide an opinion. I did spend some time thinking about how to model and then factor in differing expected survival rates over the entire span 125-425 of 300 CE. In the end I essentially allocated a 200 year bucket (125-325) and a 100 years bucket (325-425). This basically assumes a doubling of the survival rate per century between the two buckets.

Of course, things are even more complicated than that. You would need a model that accounts for the fact that copies were continually being made and lost (and found again) at different rates as the centuries passed.
Yes there are complications to any general theories for fluctuating expected survival rates of physical manuscripts from antiquity. For a start this appears to be confined to places where the weather is dry and the material doesn't rot away. Most of the surviving data (manuscripts both as complete codices and fragmentary pages) is from Egypt. Then there are natural disasters and the various man-made issues such as destruction and book burning. For example we know that many of these physical books were explicitly targeted for destruction, Any general theory for the preservation of these remains would have to allow for chaotic epochs.

My opinion is that you are laying on the chi square test more weight than it can reasonably bear.
Thanks. I can take that on board but I still have some reservations.

For example: the discoveries of these books and fragments of books are (again IMO) essentially random events. When the (randomly discovered) physical books and fragments are dated it may be argued that the date of these are consistently after 325 CE and that none of them are securely and confidently dated prior to that date. The mainstream hypothesis for their chronology expects material over the 300 years 125-425. The proposed alternate hypothesis for their chronology expects material only after 325 and no such manuscripts before 325. This is (arguably) precisely what we find.

The chi squared test should be able to have something to say on this random distribution. (if it is considered random).

#### katxt

##### Active Member
This is (arguably) precisely what we find.
Your overall conclusion may well be correct, but you would be lucky to find a statistician who finds your chi squared analysis at all convincing. kat

#### Peter RF Brown

##### New Member
Your overall conclusion may well be correct, but you would be lucky to find a statistician who finds your chi squared analysis at all convincing. kat
I appreciate your responses to this - thanks.

To your knowledge would there be any other form of statistical testing capable of being applied to this situation?

#### katxt

##### Active Member
No. The problems discussed would almost certainly apply to any analysis designed to prove your point.
You need a very strong and robust argument to hope to change an established view in any field.