How convenient. You know the truth and are able to do away with experiments.
The experiments have already been done—by physicists. They have shown that there is no "luck" particle or force that could physically affect purely chance outcomes of games in a particular way for a particular individual. If there were such a particle or force physicists would have already found it, because they have performed an exhaustive experimental search of the entire parameter space. This has ruled out every paranormal phenomenon. Thus it is a waste of time to research ESP, psychokinesis, etc, etc, etc, and luck.
If we want to be "open-minded," at least formally, we could say that there is a tiny probability that all those physics experiments were wrong; then, that tiny probability would be an upper bound on the probability of your luck hypothesis. But even still, the many biases that could be responsible for your significant observed effect would be more plausible by many orders of magnitude than a new phenomenon of persistent luck. Thus, even if your hypothesis were true, you cannot convincingly demonstrate it by frequentist statistics alone.
[W]e continue to collect data and determine whether the empirical data are as we expect according to the laws of physics and random chance.
The folly of your efforts was, perhaps, best explained by the great statistician Dennis Lindley, who wrote:
Because scientific measurements typically contain unknown and undetected biases, precision can increase without limit but accuracy cannot. Statisticians, with their emphasis on standard errors that ignore the bias, have confused the issue in some scientific experimentation because the error they quote is substantially less than the true error.
I would add that by ignoring the range of plausible biases in their data, they often come to the wrong conclusion when they find a significant p-value or a confidence interval that excludes the null value.
The "effect" you have found, about 2%, is within the range of likely biases in data collection or reference null values. But rather than concede their existence, you collect more data, which can achieve nothing more than an arbitrarily precise estimate of a biased result.
But I don't believe that people have a 'luck' attribute. I am merely willing to test that hypothesis, which only means I do not reject it a priori
Yes. You a believe that the existence of a phenomenon whose existence would contradict known physics is plausible, and you spend years using superficially scientific methods to test for it. That is precisely what parapsychology does. Congratulations, with such compatriots as Sheldrake and Radin, you're in fine company.
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I have appreciated your contributions to the discussion in that regard. I have no problem with identifying and eliminating flaws as we identify them and are able to do so.
But what Lindley was getting at is that you can never eliminate all bias from an experiment, and if you interpret your statistical results as if you have, you will often attribute to your hypothesis what should be attributed to bias. And at the risk of sounding like a broken record, the only plausible interpretation of a statistically significant effect in a test of any paranormal hypothesis, including your "luck" hypothesis, is bias.
In fact, my dh says if he weren't collecting the data himself, he would assume it was such an error.
In fact, it is precisely
because your husband is collecting the data that the biased data collection hypothesis is highly plausible. Your data is being collected by the subject of the study, who knows the research hypothesis, believes that it is true, and would like to be correct. And the data analyst is married to the subject. Not exactly a double-blind controlled clinical trial, is it?
