In general, which one is conveys a stronger conviction/opinion? I did some quick google search but didn't find any interesting results.
I'm positive that
or
I strongly believe that
Word Choice – I’m Positive That vs. I Strongly Believe That: Proper Usage
word-choiceword-usage
Best Answer
"I'm positive" is typically used for factual questions and means there is no doubt whatsoever. "Are you sure that you have enough money to pay for a sandwich?" "Yes, I'm positive, I have two thousand dollars in my pocket!" or "No, I'm pretty sure, but I'm not positive, let me count."
By contrast, "I believe" is more typically used for opinions. "I believe" expresses an opinion and "I strongly believe" simply makes the opinion more strong (just like it says).
You can also use "believe" for a fact. If you use "believe" for a fact, rather than an opinion, then it's inherently weaker than being positive. You can say for instance, "I believe that I am older than you, but I'm not very confident in that belief." Again putting "strongly" here increases certainty. However, "positive" means that you are 100% certain.
The word "positive" can also be used to mean "optimistic," but typically means that one is optimistic in disposition, not about a particular opinion or fact.