I didn't know how crude the measurements actually are, so I took the time to calculate it through and see how badly we would actually be approximating the ratios... (the math nerd in me kept me from going to bed. It's 01:00am here)
If you just want the results, ignore the colored part.
The Hanna LR Nitrate checker (HI781) reads 0.00 - 5.00ppm NO₃ with an accuracy of "±0.25ppm ±2% of reading".
The ULR Phosphate checker (HI774) reads 0.00 - 0.90ppm PO₄ with an accuracy of "±0.02ppm ±5% of reading".
Let's say the true values are in the middle of each checker's range: 2.50ppm NO₃ and 0.45ppm PO₄.
The expected readings are then within the following ranges:
NO₃: [2.21; 2.81]
because
2.21ppm + 2.21ppm ⋅ 2% + 0.25ppm ≈ 2.50ppm, and
2.81ppm - 2.81ppm ⋅ 2% - 0.25ppm ≈ 2.50ppm
PO₄: [0.41; 0.49]
because
0.41ppm + 0.41ppm ⋅ 5% + 0.02ppm ≈ 0.45ppm, and
0.49ppm - 0.49ppm ⋅ 5% - 0.02ppm ≈ 0.45ppm
Now convert the readings to N and P masses:
[2.21; 2.81]ppm NO₃ ≈ [0.499; 0.634]ppm N (NO₃ to N by dividing by 4.427)
[0.41; 0.49]ppm PO₄ ≈ [0.134; 0.161]ppm P (PO₄ to P by dividing by 3.066)
True masses:
2.50ppm NO₃ ≈ 0.565ppm N
0.45ppm PO₄ ≈ 0.147ppm P
So we would expect an N:P mass ratio between 0.499 / 0.161 ≈ 3.1:1 and 0.634 / 0.134 ≈ 4.7:1
while the true mass ratio is 3.85:1
Converting to molar/atomic ratios (multiply the mass ratio by 30.974 / 14.007 ≈ 2.211)
we get a molar N:P ratio between 6.8:1 and 10.5:1
while the true molar ratio is 8.5:1
(Shortcut: molar N:P = ppm NO₃ / ppm PO₄ × 1.532)
That's roughly -20% / +23% in the worst case, where both checkers are off in opposite directions. If the errors are random, the error will typically be smaller, though.
However, this isn't the Hanna Checkers' worst-case scenario. The fixed error terms (0.02ppm & 0.25ppm) will make it really messy when you have low nutrient levels. If we had 1.0ppm NO₃ and 0.05ppm PO₄ (true molar ratio ≈ 31:1), the readings could produce much larger errors: anything from ≈ 15:1 to ≈ 68:1 or so.
All that work, just to say: You're right, Dan. At mid-range levels we get a ballpark figure. At low nutrient levels, the checkers are basically very expensive random number generators.