To the effect that…
Definition 1 of 1
Pro Tip 1/3Indirect Speech
Used to summarize someone's words without quoting them directly, often to convey the main point. 
The professor made a comment to the effect that the exam would be tough.
Pro Tip 2/3Written Summaries
Commonly appears in written summaries where the writer wants to capture the overall meaning but not the precise wording. 
The article mentioned a study to the effect that sleep quality has improved.
Pro Tip 3/3Avoid Misquoting
Prevents misquoting by indicating the message is paraphrased rather than a verbatim quote. 
The witness gave a statement to the effect that she saw the suspect leaving the scene.