Fig. 3 : Boxplots of the accuracy of bounded three-point
normalizations based on whether the matrixes of the standards and the
quality controls are the same (matched) or mixed. If the three standards
and the two quality controls are both composed of a combination of
matrixes, the normalization is classified as “both mixed.”
Significance is shown in the compact letter display, where any two
matrixes with the same letter are not significantly different as per
Dunn’s post-hoc testing. Nitrogen (uppercase) and carbon (lowercase)
letters are not compared with each other.
To better understand how extrapolating outside of the normalization
curve contributes to normalization errors, we assessed the impact of
extrapolation on three-point normalizations that were matrix-matched
(Fig. 4). Three-point normalizations that had at least one quality
control within the isotope range of the normalization (i.e.,
“bounded”, n = 102) had decreased normalization errors for N and C
(median error = 0.064‰ and 0.056‰, respectively) compared to
extrapolated normalizations (n = 30) for N (median error = 0.116‰,p < 0.0001) and C (median error = 0.132‰, p< 0.0001).The isotope ranges of the two-point and three-point
normalizations were then binned into three categories for statistical
assessment: less than 15‰, 15‰ to 30‰, and greater than 30‰. When only
bounded matrix-matched normalizations are considered, neither two-point
or three-point normalizations exhibit a significant relationship between
isotope range and normalization error (Fig. 5A, 5B), with median
normalization errors less than 0.1‰. However, when the data is
constrained to extrapolated matrix-mixed normalizations, normalizations
with a range less than 15‰ have significantly greater errors for both
two-point and three-point normalizations (Fig. 5C, 5D). Under these
conditions, three-point N normalizations with an isotope range less than
15‰ had significantly higher normalization errors (median error =
0.171‰, n = 170) compared to those with a range of 15‰ to 30‰ (median
error = 0.093‰, n = 46, p = 0.0109) and those with a range of 30‰
to 45‰ (median error = 0.075‰, n = 62, p < 0.0001).
Similarly, three-point C normalizations with an isotope range less than
15‰ had significantly higher normalization errors (median error =
0.219‰, n = 186) than those with a range of 15‰ to 30‰ (median error =
0.147‰, n = 92, p = 0.0045). Two-point normalizations that were
extrapolated and matrix-mixed also fared worse: N normalizations with a
range less than 15‰ exhibited significantly higher normalization errors
(median error = 0.262‰, n = 200) than 15‰ to 30‰ (median error =
0.0890‰, n = 56, p = 0.0023) and those with a range of 30‰ to 45‰
(median error = 0.0923‰, n = 18, p = 0.0155), and C
normalizations with an isotope range less than 15‰ had significantly
higher errors (median error = 0.360‰, n=248) than those with a range
between 15‰ and 30‰ (median error = 0.107‰, n = 26, p <
0.0001). No C normalizations that were extrapolated and matrix-mixed had
a range greater than 30‰.