Basic instructions can be found within each template.
The following gives more detailed instructions and explanations of the various elements.
How to use the Standard
The description that follows applies
specifically to the standard template (Precision_new.xltx). The other
precision (and accuracy) templates here are comparable, but cell positions can change from one
template to another. Information on the Bowker's test applies
only to the standard and 25-year precision templates.
Production (prod.) age is considered
to be the first age attached to a given fish, obtained while the
age reader is working with the entire set of samples (survey,
year, etc.). Ages obtained while re-ageing fish from
the precision subsample are labeled 'test ages.' (Note: In the
Accuracy template, reference (ref.) age is used to indicate the
known or consensus age for each fish.)
Note: All data shown in red on the template should be replaced.
Step 1: First, the two
sets of ages must be entered in columns A (prod. age) &
B (test age), starting at row 36. Overwrite the sample ages already
listed. Fish which are omitted in either ageing run may
be listed in the table at J36, but should not be included in this
section. Blank lines in the age data must also be avoided, as
these can artificially reduce the total CV.
Do not change the
first 34 rows of 'space-keeper' ages. They are included to ensure
that the Pivot Tables list all ages, which in turn allows other
calculations to refer to the correct locations.
Step 2: Once all ages are entered,
the calculations in columns C-J (starting at row 36) must be
copied downward to the last age pair. The computer may sometimes
do this automatically, depending on how the ages are entered.
These columns calculate the CV for each fish (indicated
by the subscript 'j'). Multiple columns were used in order to
simplify the equations. The column values are:
C, the average age, Xj;
D, the sum of the squared differences (SSD) between each age
E, CVj, the square root of the SSDj divided by Xj
F & G, random numbers to be applied to each age;
H, a checksum to test if the randomized age will be too high;
I & J, each age adjusted by the random number in F & G.
For fish for which both ages are zero, the 'IF'
statement in column E resets the CVj to zero to avoid an error
message. Note that if your data contain blank lines, the 'IF' statement would convert them to artificial
CVj values of zero; therefore, any blanks should be removed before copying the calculations.
(On the 30- and 50-year templates, any age-0 fish in columns
A or B will generate a '#ZERO!' message in column E, and the Pivot
Tables will not work properly.)
If asterisks (**) appear in column H, either use a template that accepts higher ages, or manually edit the randomized numbers so that they will be displayed on the agreement plot.
Step 3: Move to the upper right portion
of the template. Pivot Table 1 starts at cell AR1; Pivot Table
2 starts at AR23. Both Pivot Tables must be refreshed.
This can be done simply by right-clicking within each Pivot Table,
and selecting the 'Refresh Data' option. See below for more details on the Pivot Table layout. (On other templates, these tables begin
different positions but they are still to the far right.)
Step 4: At the top of Columns M-R, the labels should be updated:
M1, the sample type (survey, commercial,
etc.) and year the fish were captured;
M2, what is compared (e.g., repeated readings of the same fish/comparison
between two readers);
O5, the total number of samples aged from this sample set;
R1, the species name;
R2, the date the exercise was completed; and
R3, the name of the age reader.
At this point, all remaining calculations
& displays should be complete. Double-check that the total N,
CV, and the displayed data seem reasonable. If not, review Steps 1-3
to check if anything was overlooked.
Step 5: Save the file to a new,
distinctive filename before printing. A file name which incorporates
species, sample source, and age reader is recommended. For example,
"ER_WNFL_2017Q1.xlsx" could refer to the exercise above.
The printed data (M1-AP39) show the sample size,
total CV (expressed as a percentage), percent agreement, and Bowker's
test results (if appropriate; see below).
A breakdown of the average test age for each production age (with
measures of variation) is shown, as well as both an agreement plot and an
age-frequency table. The header
lists the document name and the date printed. More information on these statistical measures and displays can be found at http://www.nefsc.noaa.gov/fbp/QA-QC/measures.html.
Click image to view full-size version.
For much of the printout, zeroes are not shown.
Disregard any "#DIV/0!" and "#NUM!", as all
ages may not be adequately represented in your sample. Do not
attempt to remove these from the template, as the calculations
in those cells may be needed in another precision exercise.
(The output for the
50-year template is arranged differently, but contains the same
Bowker's Test of Symmetry
In the standard template, the cells below the
printout (O45-AN85) are used in calculating the Bowker's test
(Hoenig et al. 1995). This considers only the samples for
which the age was not agreed upon. Comparisons are made on the
diagonal, i.e. fish with ages of (1, 2) are compared with
fish having ages of (2, 1).
Cells W46-AN64 calculate the chi-squared value
for each diagonal pair of ages, based on the data in the age matrix
table. Cells W67-AN85 indicate which of these pairs include actual
fish; this total (cell P59) is the number of degrees of freedom
for the test. In cells P46-P55, the chi-squared values are summed
for each difference between the two ages (i.e. 1 year,
2 years, etc.), with an overall total in cell P58. Differences
of 10 or more years are combined in cell P55, and broken out in
cells P65-P71. Hopefully, there will be few disagreements of this
The results of the Bowker's test are reported
in the printout (T6-T9) only if the percent agreement is below 90%. A
significance level of P<0.05 is used to distinguish between
significance (**) and non-significance (n/s). If the test is not
reported, these cells contain 'N/A' for 'not applicable.'
Note: The standard and 25-year precision
templates are the only ones in this set which incorporate a Bowker's
test. This test is not applicable to an accuracy exercise against known-age
samples, nor are the necessary calculations conducive to inclusion
on the precision templates for long-lived species. If a symmetry test is
needed for older fish, use Symmetry50yr.xltx and it's embedded directions.
Pivot Table 1
The upper Pivot Table (AR1-AV20) calculates the
Total CV and statistics for the test ages at each production age.
The Pivot Table refers to data in columns A, B, and E. Line 21 is included
to make necessary adjustments to the Pivot Table results, by accounting
for blank spaces in A2-B35. Mean CV is later calculated as (Sum
of Total CVs)/N from cells AU21 and AV21. Part of this table is
mirrored in cells Q13-R30 on the printout, as well.
Use of production age as the basis for these calculations
is arbitrary and is not meant to indicate that either set of ages
is more accurate. Either set could be used here and as the x-axis
in the agreement plot.
Pivot Table 2
The lower Pivot Table (AR23-BK43) is the basis
for the age-frequency table in the printout, and the source of counts
of fish and percent agreement values by age. It refers to columns
A and B only. Again, line 44 is present to adjust the totals because
of blank spaces at the top of Columns A and B.
Age Bias Plot
The age-bias plot can be found at column AW if it is needed.
Please contact Sandy
Sutherland if you need any
assistance with these templates, or would like advice in developing
Campana, S. E., Annand, M. C., and McMillan, J.
I. (1995). Graphical and statistical methods for determining the
consistency of age determinations. Trans. Am. Fish. Soc. 124: 131-138.
Chang, W. Y. B. (1982). A statistical method for
evaluating the reproducibility of age determination. Can. J.
Fish. Aquat. Sci. 39: 1208-1210.
Evans, G. T., and Hoenig, J. M. (1998). Testing and viewing symmetry in contingency tables, with application to readers of fish ages. Biometrics 54: 620-629.
Hoenig, J. M., Morgan, M. J., and Brown, C. A.
(1995). Analysing differences between two age determination methods
by tests of symmetry. Can. J. Fish. Aquat. Sci. 52: 364-368.
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