TOUGH Textual Criticism math statistics question

Eturnal said:

TL;DR Summary: If text A is 87% similar to text Z

And text B is 87% similar to text Z

Text A & B are 92% similar

Each text is 10000 words (approx)
What are the odds that when Text A and Text B disagree one of them will agree with Text Z?

Okay let me rephrase this math question and frame it. It is math dealing with ancient Biblical texts and textual criticism.
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Codex 01 (350AD) agrees with the MT (mjority text) about 87% of the time.

Codex 03 (350AD) Agrees with MT about 87% of the time.

01 and 03 agree with each other about 92% of the time.

When 01 and 03 disagree, there is an 87% chance that one of them agrees with the MT.

Wouldn't you expect that number to be lower if these disagreements were random?

Please help math geniuses. Thank you!

Eturnal said:

TL;DR Summary: If text A is 87% similar to text Z

And text B is 87% similar to text Z

Text A & B are 92% similar

Each text is 10000 words (approx)
What are the odds that when Text A and Text B disagree one of them will agree with Text Z?

Wouldn't you expect that number to be lower if these disagreements were random?

Eturnal said:

So there are about 7,000 words in each text in the texted section.
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but we should be able to do the percentages so that shouldn't matter right? We have 8% of each text agreeing to disagree. Then we take a random splatter of 26% between the two texts (13% each text). But oh yeah we would have to account for all the letter/ word possibilities in those slots as well wouldn't we?

PeroK said:

This is even less clear than your original post. Mathematics and statistics require a well-defined problem - even if the definition includes uncertainties and probabilities. This is different from the humanities where you can argue endlessly over ill-defined concepts!

PeroK said:

This is even less clear than your original post. Mathematics and statistics require a well-defined problem - even if the definition includes uncertainties and probabilities. This is different from the humanities where you can argue endlessly over ill-defined concepts!

Eturnal said:

Take two texts of 100 characters and highlight 8% representing the disagreement between 01 and 03.

Now randomly select 13% of each text representing the disagreements between 01/03 & the MT.

What are the odds those 13 places overlap the 8%?

Now, should we account for each character having 24 different options (letters in the Greek alphabet)? Or should we just pretend it is an A/B in eaxh character slot for simplicity sake?

PeroK said:

You can only produce probabilities from a large sample of data or by understanding where the source material came from and hence you have some underlying assumptions.

It's a common misconception that probabilities can be conjured from one sample of data without underlying assumptions. I think this is what you trying to do here. That somehow, these percentages themselves will reveal something mathematically robust.

You can determine from the texts how correlated they are (and, indeed, that's what your percentages are trying to show). But, there is no magic wand that will tell you how likely that correlation was. The probability of a given correlation is not inherent in the data. It can only be calculated when you have a model for how the data was generated. The same correlations might be almost inevitable in one case and highly unlikely in another - even in cases where the raw data is the same.

Eturnal said:

Humor me. I'm sure someone can draw up a useful piece of math on this although yes everything will have some assumptions plugged in.

PeroK said:

Being an inveterate frequentist, I'll leave that to the Bayesians!

Eturnal said:

Someone posited that there is an 87% chance that the disagreements between 01 and 03 land on MT just because each agrees with MT 87%. I don't feel like their math is correct. Thank you for your help!!!

Eturnal said:

Humor me. I'm sure someone can draw up a useful piece of math on this although yes everything will have some assumptions plugged in.

Dale said:

I don’t think that will be possible without some additional information about the similarity measure. It doesn’t seem like a probability to me. So I don’t think the math of probability will apply.

PeroK said:

Being an inveterate frequentist, I'll leave that to the Bayesians!

Dale said:

I don’t think that these percentages for agreement are probabilities. Probabilities are between zero and one, so it is common to write them as percentages. But that doesn’t imply that everything that is written as a percentage is a probability.

In particular, a probability is always a measure on some space of events. For example, if you are rolling a single dice then the space of events could be “a 1 is rolled”, “a 2 is rolled”, …, “a 6 is rolled”.

Here, I cannot see that there is a space of events. So I don’t think that “text A is 87% similar to text Z” is a probability. If it is a probability then what exactly is the event space and what sample of events is described by the statement?

I don’t think that will be possible without some additional information about the similarity measure. It doesn’t seem like a probability to me. So I don’t think the math of probability will apply.