Allegedly vs. apparently - Differences in connotation?
Neither are really appropriate here.
Use "reportedly," or "According to the Smith Report, the number of trades..."
I'd take out "In fact," as well.
Alleged/allegedly has a connotation of an accusation or other statement without proof (see below) and often implies doubt as to the veracity of the statement. Since you do not doubt that trades have declined by 55% after the law's* introduction, allegedly wouldn't be the right word to use in your current sentence.
Apparent/apparently has a connotation of an obvious conclusion based on evidence and logic. Maybe you've heard that "correlation doesn't imply causation"? While it might be a fact that someone is a soldier, it might not be apparent if they're off base and not in uniform. Based on the present wording of your sentence, apparent/apparently wouldn't be correct either. {{Ha! Apparently, apparently isn't the right word! I crack myself up...}} Again, it's simply a fact--as worded, there's no conclusion present.
If you rephrase your sentence, either allegedly or apparently could work. A few possible alternative phrasings:
- If you have evidence supporting a connection: "It is apparent that the introduction of the law* has caused a 55% decline in the number of trades (citation)." [present supporting evidence before or after this sentence]
- If you did doubt the fact: "A study completed in [year] alleges that the number of trades has declined 55% since the introduction of the law* (citation)."
- If you doubt the connection but not the fact: "A study completed in [year] alleges that the law* has caused a 55% decline in trades since its introduction (citation). However, I have not been able to verify the study's claim. / However, this claim has not been independently verified. / However, no outside evidence was found to support this claim." [depends on whether or not your style guide allows you to write in 1st person]
apparently
it seems apparent —used to describe something that appears to be true based on what is known
- an apparently happy marriage
- The window had apparently been forced open.
- Apparently, we're supposed to wait here.
allegedly
1 : accused but not proven or convicted
- an alleged burglar
2 : asserted to be true or to exist
- an alleged miracle
- an alleged conspiracy
3 : questionably true or of a specified kind
- He bought an alleged antique vase.
Both words indicate some .. questioning of the statement, but then the nuances diverge.
'Allegedly' has a legalistic connotation, as though the subject has been accused but the fact has not been proven. It indicates a lack of trust in the situation or the reference (the citation).
'Apparently' has a more attitudinal nuance. It indicates a vague informal sense of the speaker literally means 'it seems this is the case' but implies that it is new, a little surprising, contrary to the speakers expectations. It's not saying 'seems', as in expecting a different result (like 'ostensibly' would). It's not really calling the object that much into question. It's more of an understatement, that is saying 'this is sort of the case' when really, it is totally the case.
For example:
Biff is allegedly the father of Harriet's baby.
means someone has said that Biff is the father, but people aren't sure and no proof has been given (Biff denies it or no DNA test has ben done).
Biff is apparently the father of Harriet's baby.
means that Harriet wasn't sure or wasn't saying but Biff admitted it or the someone reported the DNA results.
In both cases, it was a it of a surprise or unknown beforehand. Also, they are both insinuations, not direct statements but implications.
In your example, only 'allegedly' implies some lack of trustworthiness in the citation source, 'Apparently' doesn't really cast doubt but more likely implies a bit of off-handed attitude by the writer.
I suggest neither is appropriate. For 'allegedly', you should add an appropriate sentence about doubts. For 'apparently', you just want to leave out any breezy, catty judgement of the situation.