Background
I'm doing a research project in astronomy and measuring equivalent widths of absorption lines using Gaussian fits from a star's spectrum in order to determine the star's chemical abundances. Each absorption line corresponds to a specific electronic transition in an atom of a specific element. One type of atom, say iron, produce many absorption lines at different wavelengths that we observe. In addition, different atoms produce different absorption lines. The equivalent width of a Gaussian fit allows one to quantify the strength of an absorption line observed in a spectrum (i.e., how strong a luminous intensity the line appears to have).
My data
I have measured equivalent widths for 54 absorption lines with Method A and B, as shown in Tables 1 and 2 respectively. Each "Equivalent width" value in tables is an average of two or three measurements for each line.
This is how the measurements are done (the full method is described here) but are summarized here https://gitlab.com/evgenyneu/2018_summer_project_logbook/raw/master/a2019/a01/a23_measuring_lines/three_measurements.gif. I fit the Gaussian profile to the observed data. For the first measurement, I make a fit with a Gaussian curve with a wide base. For the second I fit a narrower Gaussian to the peak region. If the observed line is good, I make an optional third measurement by making a what looks like a moderate fit, close to the full width at half-maximum (actually half-minimum as absorption curves are upside down) which is between the narrow and wide measurements.
The "uncertainty" column is the half of the range of the measurements of equivalent widths. For example, if we have two measurements, 10 mA and 16 mA, then the uncertainty is 3 mA ( (16-10)/2 ).
Table 1: Equivalent widths of absorption lines and their uncertainties measured with Method A. The units are angstrom (A) and milliangstrom (mA).
+----------------------------------------+------------------+
| Wavelength (A) | Equivalent width (mA) | Uncertainty (mA) |
+----------------+-----------------------+------------------+
| 4730.03 | 37 | 8 |
| 4731.45 | 79 | 9 |
| 4788.76 | 52 | 5 |
| 4890.75 | 153 | 20 |
| 4891.49 | 171 | 19 |
| 5814.81 | 8 | 2 |
...
... Skipped 47 rows
...
| 6703.57 | 22 | 1 |
+----------------+-----------------------+------------------+
Table 2: Equivalent widths of absorption lines and their uncertainties measured with Method B.
+----------------------------------------+------------------+
| Wavelength (A) | Equivalent width (mA) | Uncertainty (mA) |
+----------------+-----------------------+------------------+
| 4730.03 | 26 | 4 |
| 4731.45 | 52 | 7 |
| 4788.76 | 39 | 3 |
| 4890.75 | 116 | 18 |
| 4891.49 | 139 | 18 |
| 5814.81 | 6 | 1 |
...
... Skipped 47 rows
...
| 6703.57 | 16 | 2 |
+----------------+-----------------------+------------------+
Question
Should I compare methods A and B using $t$-testing or should I do something else?
Alternative methods
If paired sample t-test is not suitable, what alternative statistical tests should I use (Wilcoxon signed-rank test, chi square test of independence etc.)?
Sample size
54 measurements.
Independence
Equivalent widths measurements of 54 different lines are not be independent. For example, higher abundance of iron may result in wider equivalent width values of all its absorption lines. In my data it means that, for example, if measurement of a 4730.03 A line is wider, it is likely that measurement of 4731.45 A will be wider as well, if the two lines are produced by the same element.