Pilot reported taxiing on to the runway and taking off in front of an aircraft on final approach that was forced to execute a go-around to avoid a collision.

Narrative

I was departing runway XX and did not see the Cherokee (N number unknown) on final approach. I do not have an electrical system or radio to monitor. As always; prior to entering the runway (at my home base ZZZ) I looked for traffic on downwind; base or final and either had aircraft structure obscuring the Cherokee (J-3 solo rear seat only) or the Cherokee was obscured by trees at the arrival end or unknown other reason. After lift off I noticed a shadow to my right and in parallel. It was at that moment I knew a landing aircraft had executed a proper go around. Once visible to my 2 o'clock position I recognized it as a Cherokee ; while it was climbing on the upwind. After securing my J-3 I went over to the school; to apologize; left my cell number for the instructor to call me for a debrief; and complimented; to the representative the instructor/student did an excellent job of risk mitigation. Lesson learned: look more than once prior to entering the runway at a busy uncontrolled airport.