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Using percentage change with different sample sizes, which is more significant?

Cross Validated Asked by Katie Fenton on September 30, 2020

I have some data that is looking at Virtual vs. Face to Face appointments (at a hospital) – please see data in pic below. This is split by first appointments and follow up appointments. I am comparing one month of data to another month (peak month vs. latest month). As expected, the number of face to face appointments is increasing whilst the number of virtual appointments is decreasing (as lockdown measures are relaxed). For virtual appointments, how do I work out if it is first or follow up appointments where the virtual appointments are most impacted? For example it is suspected that as lockdown measures ease, clinicians are returning to ‘business as usual’ for first appointments, seeing more patients face to face, whereas it’s suspected that follow up appointments will not be impacted as much and will remain more virtual. The second picture is the data for another hospital, how do I work out which of these 2 hospitals has seen a greater reduction in virtual appointments? I am confused because I don’t know how the percentage increase for face to face appointments impacts the percentage decrease of virtual appointments. Any help would be greatly appreciated.

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