[Elecraft] Power Measurement - Where am I wrong?

[Francis Belliveau]

I do not have a power meter so I figured that I could compute power from a
peak to peak measurement using my scope.  This should be accurate enough for
ballpark knowledge.
However, the measured voltage increases as frequency increases with the 10
meter voltage being nearly double the 80 meter voltage.  This would mean
power increases with frequency unless the formula I was going to use is
missing a frequency dependent component.

I have a KAT2 installed and I used a good 50 ohm resistive load.

My math follows:

Vrms = Vp-p/(2*sqrt(2))
Vrms = Irms*R assuming purely resistive load
or Irms = Vrms / R

if Prms = Irms*Vrms
substituting yields
Prms = (Vp-p * Vp-p) / (8 * R)

I know that Pave = Prms / 2
but that does not help much because I would still get more than 10 Watts out
on 10 meters when set for 5 watts out.

Where did I go wrong?

Fran