That's great! Not believing studies, I mean. They're not religious artefacts handed down by gods above

What you _can_ do, is read the study, especially the introduction, where it states what the study is about, the methods, which describe how the actual study went in real life, and the conclusion, which summarizes what we've learned from this.

After doing this, you can then maybe try a synthesis between the study thesis and your antithesis? Y'know, something a bit more substantial than a random drive-by comment

I only skimmed it so far but am having trouble believing it too. All their regression lines very clearly show a positive association between the variables, and it seems that they only failed to reject the null hypothesis because they didn't have a large enough sample size.

Also, regarding the bodybuilders, note that this study only measured the normal "day-to-day changes", and if we were to extrapolate their findings, it would likely show a much larger association when given exogenous testosterone.

Adding exogenous testosterone to the system might be very different than relying on the system's own T production.

It's reasonable that there are more homeostatic effects (upstream and downstream of the T) when you're just working with your body's own testosterone even if it's on the high end of the ref range. You'd skip that when you inject it.

The study was evaluating human-produced testosterone, not exogenous testosterone supplementation. If you take testosterone, it has been shown to increase sexual desire and is an approved treatment for sexual desire disorders. This is not what the study analyzed.

Are those body builders controlling for other variables? Changes in diet, exercise, performances, routines, etc?

I'd believe any number of things could correlate with body builders as they spend a lot of time changing their bodies.

"I have a hard time believing this study."

Until the data has been scrutinized and the study replicated it's not worth paying a second of attention to.

Are you talking about ”normal” variations in testosterone like plus or minus 10-20% or like doubling?