How do I determine statistical significance value where the entire population gets the intervention and the results seem profoundly significant? Of course, finding the statistical significance for a value in a typical population containing both an intervention group and a control group is elementary.
However what if we consider the control group to be every single data point leading up to the experiment, essentially an infinite number of control data points?  Normally such a study is defined as having no placebo group, but for purposes of describing the significance of the findings, we should be able to define a placebo group as being all phenomena outside of (leading up to) the intervention. Yes?  How does that math look?
Here's a real world example.  50% of patients with sepsis-shock will die ... this is common knowledge.  It has always been so.  So:


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*Control Group: essentially infinite # of data points and ave. death rate = 50%


We discover a protocol that cures 90% of cases, and do this protocol for 200 patients (only 20 die).


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*Intervention Group: 200 data points (people), and the average death rate = 10%


This seems significant but the medical world says it's meaningless because there is no control group defined within the experiment.  How can we assign some sort of value representing the significance of the vastly improved outcome?  There has to be some kind of math to do this. Having a parameter that demonstrates the level of this statistical significance in these cases could have profound effects on medicine.
It seems especially indisputable in cases where there is a best-case ceiling (in the case of Sepsis) that is consistently being surpassed by a certain intervention.  The fact that this is ignored in medicine is unconscionable, yet nobody is willing to put their foot down and demand a more Hippocratic approach.
This is actually a real world problem, where there are just a handful of hospitals that use the new protocol, and 1000's of hospitals that refuse to because they are waiting for RDBPC experiments, which to date have been botched (do not match the life-saving protocol), meanwhile 300+ people needlessly die in the US every day from sepsis.  10,000 every day throughout the world.  Those who would do an RDBPC study correctly (using correct protocols) either don't have the resources or they consider it unethical (which it would be) when they know they can prevent 80% more sepsis deaths than conventional protocol causes.
 A: You could compare a very large sample (here essentially the whole population) considered as a treatment group with a traditional, 'well-known', or'standard' value. That would be a one sample test. Not a two-sample test of treatment vs placebo.
For the results to be worthwhile, it must really be true that the standard value is the generally accepted value for formerly untreated subjects from the same population.
However, you are not likely to get universal agreement about the continuing applicability of the standard value. Someone might argue that factors other than your treatment
have intervened to change that standard value. (Global warming, political strife, antibiotic resistance, etc.)
The question you need to ask yourself is why go to the
trouble and expense of treating the entire population, when you might get about the same result (reject or not) by treating part of the population and comparing that part with the untreated part. There is nothing quite as universally satisfying and convincing as a randomized trial of a control group vs. a placebo group.
