I'll have a go.
Placebo effect - I assume you'd paid good money and so wanted the treatment to work?
Individual perception - was the increase in the mobility of your shoulder actually measured?
The natural healing process - your shoulder might have healed without any intervention. Without a control, you don't know.
The standard reposte against scientific arguments is that just because current scientific understanding doesn't align with the given explanation for the treatment's effectiveness (in this case 'subluxation') that doesn't make it not true. A fair comment, but for that to be valid the treatment has to be shown to work, even if we don't understand why it works.
The experimental methods and underpinning statistics for hypothesis testing (the hypothesis in this case being that chiropractic is an effective treatment for x) are very, very well-established. Unfortunately chiropractic scores very poorly when subjected to this kind of proper scrutiny.
At best, chiropractic is just an expensive massage. At its worst it's dangerous.
