Infer or imply is a classic troublesome pair, especially in the context of academic writing.
And they actually represent two sides of the same story, meaning that it’s important to be able to distinguish them and use them the right way round. But then again, that’s true of all my Troublesome Pairs, isn’t it!
To infer is to deduce from evidence and reasoning.
To imply is to indicate by suggestion.
So the main difference here which needs to be remembered is the viewpoint from which the word operates. The two words can even describe the same situation, but from different sides.
If a person implies something, they are suggesting that something but not stating it directly: “By mentioning the high-priced bath accessories, but not going through the details of the newspaper report, the speaker was implying that the MP was over-claiming her expenses”.
On the other hand, if you infer something from what has been said or written by that person, you infer something from what they say: “Having been told about the high-priced bath accessories listed on the MP’s claims, we inferred that she was over-claiming her expenses”.
So the evidence implies this conclusion, or we can infer this conclusion from the evidence. Different sides of the same story, and two more words that require careful handling.
You can find more troublesome pairs here and the index to them all so far is here.