I said similar, the equation has two variables, radiocarbon testing holds one variable constant, while half-life testing holds the other variable constant.
I understand that, but the Ward and Wilson test doesn't apply in your case. You seem to be trying to establish your own foundation of expertise. It therefore helps to conduct a little void dire before we decide to let you do that.
Uh huh, the chi-squared "whatever."
In your haste to be the teacher, you directed people to an irrelevant explanation. The Ward and Wilson method uses the chi-squared distribution, but it is not the same as the various tests of categorical covariance that you directed us to. You're the one trying to tell us the Damon findings rise to a particular level of suspicion that should be alarming. Our confidence in your judgment is shaken when it seems you're bluffing your way through the statistics. More likely you've just been told by others that the Ward and Wilson metric is suspicious, and you've decided to believe that. That's fine, but you have to contend with the notion that those who have suddenly decided that the Ward and Wilson metric is fatal to the radiocarbon dating findings are disproportionately those who seem to have other reasons for wanting the shroud to be authentic.
No statistic is inherently determinative. In fact, to suggest so is contrary to the very nature of statistics as a tool for inference. For example, in terms of
p-values for science, we arbitrarily say that
p < 0.05 is the threshold for significance. That's a threshold only because we adopt it as a norm, not because there is something numerically magical about the value 0.05. In a purely statistical sense, there is little difference between
p = 0.0499 and
p = 0.0501. But one makes a theory according to scientific convention while the other is merely, "Hm, nice try." It's not unreasonable question the arbitrariness of the distinction in such a case.
As you were told by the actual statistician you chased off, the threshold of significance is best established according to context. In science writ large, there is considerable debate over whether a one-size-fits-all
p-value is helpful. One edge of that sword is the argument that the nature of some sciences make 0.05 an unreasonable goal. The other is that
p-hacking has rendered the norm essentially irrelevant as an assurance of correctness. In these cases we turn to the practitioners for advice. And when everyone is okay with the Damon findings—Ward and Wilson notwithstanding in the one instance—except for those who have ulterior reasons to be disappointed by the radiocarbon date, we can put the statistic in a more helpful context.
You're quite welcome to continue believing that one outlier dooms the whole process. It's your privilege to resolve the uncertainty measured in the statistic in that way. But there's no justification for insinuating that the
only scientifically justified interpretation is that the findings
must be rejected because of some mathematical bulwark named [waves hands elaborately] ..."chi-squared whatever."