Can you logically prove the validity of a statistical worldview without resorting to statistics tests?

Can you show that belief in probability will make one's life better without using statistics that involve probability to show that those who believe in probability have a statistically significant better life based on a statistics test for a measured outcome that invokes the assumption of a probability distribution function for a measured outcome?

That is you could for example experimentally test a claim that those who believe in probability and apply statistics that invokes probability to their life decisions have a statistically significant chance of having a higher income in their bank account than those who reject a statistical worldview using probability within an alpha value of 0.05 for a paired or unpaired and dependent or independent one tail t test.  And then either reject or fail to reject the null hypothesis for that test.  And additionally do a statistical test to make sure each of the samples tested for the t test are both selected from normally distributed populations within an alpha value of 0.05 and either rejecting or failing to reject the null hypothesis that they are normally distributed on that test and in the case of failing to reject that null hypothesis concluding there was  at least a 95% chance you were correct to choose to do a t test but in the case of rejecting the null hypothesis conclude that a t test would have at least a 5% chance that it was not correct to select a t test in the first place and you should have selected another test because there was at least a 5% chance that the  sample for which you rejected this null hypothesis was not selected from a normally distributed population.

But would that be circular reasoning that never supports the validity of a statistical worldview in the first place without first assuming a very specific statistical worldview in order to test the claim that those who believe in such a statistical worldview are statistically significantly be more likely to have a better life outcome of the type you choose to measure and in the direction you chose to consider to be better?   This would beg the question if the statistical worldview you chose to measure this was correct in the first place and additionally only give the answer you desired to support the validity of statistics for the alpha value you chose but not for a lower alpha value greater than zero but less than the alpha value you selected and it would fail to support your claim at a probability of that alpha value  according to your statistical worldview you used to analyze this in the first place.

Once a event has already happened does it have a 100% chance that it would have occurred even though prior to the event happening it was assumed to have a percent chance that it would have happened less than 100% but  greater than zero percent?

Copyright Carl Janssen 2018 March 2


https://web.archive.org/web/*/https://en.m.wikipedia.org/wiki/Bayes'_theorem

https://web.archive.org/web/*/http://ecodevoevo.blogspot.com/2012/01/probability-does-not-exist-part-i-very.html


Bayes’ formula helps scientists assess the probability that something is true based on new data. For example, doctors can use the result of a mammogram exam, which is sometimes wrong, to assess whether they should revise their assessment that a patient has breast cancer. 

https://web.archive.org/web/20190302174347/https://qz.com/1315731/the-most-important-formula-in-data-science-was-first-used-to-prove-the-existence-of-god/