What is the effect of paying credit card in full or with interest on your credit score?
Credit card issuers do not report whether you paid the balance in full to the credit reporting agencies. What is reported each month is your balance and whether you made the required payment, but not the size of the payment. From what I can tell, this is reported to the credit reporting agencies at about the same time as your monthly bill is issued, i.e., it's your statement balance.
If your monthly balance is reported as $4500 one month and then $4000 the next, there is no way to tell from your credit report whether you paid the $4500 in full and ran up another $4000 the next month, or made a single $500-ish payment and are carrying the balance.
Since this information is not on your credit report, it cannot (and does not) affect your credit score.
If the balance is higher than it otherwise would be because you are carrying multiple months of spending on the card rather than paying it off each month, this can affect your credit score because it increases utilization. The less utilization, the higher the score. It used to be that utilization didn't have too significant of an impact on your score until it reached 50%, but apparently it has some effect at 20%.
The fact that you carry balance by itself will not affect as it is not reported.
What's reported is your current balance, whether you pay "as agreed" (i.e.: at least the minimum), and whether you pay "more than minimum" (some creditors report that as well).
However, spending more than what you can pay over prolonged periods of time will definitely lead to higher debt to credit ratio, and this is what is affecting the credit score.