This simple answer is, you can't know. When you implement a change and observe a result, it can be due to the change, be a false change like due to the Hawthorne Effect, your bias meaning you see a change but there is none, or be a random result. The only way to know, to arrive at a deduced conclusion that stands up to scrutiny, is to conduct many observations in a controlled environment and with some statistical analysis to rule out randomness and experimenters' bias. And when I say many, I mean many. Not like two or three sprints. Remember, you can flip a fair coin ten times and get eight heads. That does not change the 50/50 likelihood to 80/20. Observations can be trusted after hundreds of them, not just a few.
The take-a-way of knowing about Hawthorne, bias, and stochastic observations is about knowing how to apply a healthy skeptism of what you are observing. In other words, stick to the null hypothesis until proven otherwise. If you make a change and you observe some favorable results, the finding you walk away with is, 'this seemed to cause that,' not 'this caused that.'
Another thing to remember about the Hawthorne Effect is it was found in an operations setting where work was ongoing. They found an increase in performance caused by a benign variable, that decreased over time. With projects and sprints, you have a start - stop function. Therefore, you will not observe a steady decrease back to baseline. In this type of scenario, what you will likely observe is performance variability of up and down trends that may or may not be due to anything you implemented. You will simply need many observations over quite a period of time to rule out random effects, Hawthorne, or bias.