Results: Plot Library

 

We have used plots as the primary means of reporting our research results. Most of the plots are accompanied by statistical information designed to help clarify the strength of the relationship between the two variables displayed. To see a plot in the table below, click on the plot number. Then click “Previous” or “Next” to move between plots sequentially. To return to the Plot Library table, use your browser Back button or close the plot window. Unless stated otherwise, all the plots shown are based on data from the interior of the specimen only; i.e., locations 2–5 indicated with blue arrows in figure 11. Any plot shown in gray type in the table below is planned but under development.

Plots appear in order of interest to the coauthors; our thoughts on what they reveal appear in the DISCUSSION section.

Inclusion of Error/Precision/Uncertainty in Plots

A simplified overview of our plotting work includes the following guidelines: (1) the black dots represent the observed data reported by the instrument, (2) the light gray circles indicate the range of error in the analysis method, (3) the red line shows the estimated mean as a function of year, and (4) the blue outer curves indicate the reliability of these mean estimates. In other words, with 95% confidence the actual means are between the two blue curves. Thus, in summary, to get a more reliable sense of the trend for the weight percent gelatin concentration over the centuries in figure 12, plot 1 (above), one should consider not only the red line, but the swath described by the space between the two blue outer curves. Even more telling are the tabletop graphics at the top of the plot that illustrate, by their relative heights, the change in mean values from century to century.  If the tops appear at different heights, the changes can be considered statistically significant. The tabletop units coincide with the vertical axis units but their scale has been compressed for display purposes. It is important to point out that a statistically significant difference does not necessarily imply a significant practical difference. In other words, within certain mathematical parameters, we can have confidence an observed difference is not a chance occurrence; however, whether that difference has real-world implications is open to discussion.

A more detailed description of our plotting work follows below.

Sources of error, and uncertainty, and the degree of precision possible with different instruments are included in some but not all plots. For instance in plot 1 (above) the gelatin data (solid black symbols) are shown for the 1,578 specimens plotted over time. The vertical scale displays the predicted weight percent gelatin concentration. The tabletop display across the top of the graph depicts the mean levels across the centuries. The thickness of the tabletop gives the 95% confidence interval for the mean. Nonoverlapping tabletops imply that the difference between the means is statistically significant.

The red (center) curve represents a locally smoothed estimate of the mean, as a function of year. The blue (outer) curves give the pointwise 95% confidence intervals for the means over the years. We used LOESS (locally weighted scatter-plot smoothing) in R to compute the smoothed estimate of the mean. The confidence bands were derived using Monte Carlo simulation. The confidence bands account for the measurement error as described in the next paragraph.

The black points in the scatter plot represent the observed values. These observed values were measured with some error, so if we had carried out the same measurement procedures on the same samples, we would have come up with slightly different values. As discussed earlier, precision in our work was calculated differently for the XRF and the UV-Vis-NIR instrumentations. Using the respective precision parameters, corresponding to each observed datum (solid black symbol), we generated ten auxiliary data points (light gray circles) that represent data we would expect to see if the same measurement process was repeated ten times. The light gray circles represent potential values under replicate measurements. The spread of these potential values reflects the lack of precision in the measurements; i.e., the more spread out these potential values are, the less precision.

The statistic R is a generalization of the Pearson correlation coefficient. Whereas the correlation measures the strength of the linear relationship between X and Y, the statistic R measures the strength of the functional (linear or nonlinear) relationship between X and Y. If the observed (X, Y) values fall close to a smooth, nonconstant function of X, then R will take on a value close to 1. If X and Y are linearly related, then R will be numerically identical to the absolute value of the correlation coefficient. Numerically, R is the correlation between the smoothed estimates of the Y means and the observed Y values. As mentioned above, we used the function LOESS in R to compute the smoothed estimates of the Y means, and the P value was computed using a nonparametric bootstrap approach.

Plot Library Table

*Plot numbers with asterisks have error incorporated; all other plots are based on “observed” data. Units for elements (Ca, K, S, and Fe or Log Ca, Log K, Log S, and Log Fe) are displayed in parts per million (ppm).

PLOT CLASS, NUMBER	VARIABLE 1 versus	VARIABLE 2	COMMENTS
CHRONOLOGICAL
FULL DATA SET
1*	Gelatin	Year
2*	Log Ca	Year	The natural log transformation was used to compresses the spread of high and low values by reducing the amount of skew leaving patterns in the data more clearly visible.
3*	Log K	Year	ditto
4*	Log S	Year	ditto
5*	Log Fe	Year	ditto
6	Log S	Log K	by century
7	Thickness one sheet	Year
8	Thickness ten sheets	Year
9*	Delta L*	Year	The delta L* vertical scale progresses from 0 (white) toward -30 (colors increasingly closer to black)
10	Chlorine (Cl) peak intensity	Year	Cl was not in the calibration so reported values in this plot indicate Cl peak height intensity rather than ppm
12	Calcium Carbonate	Year	Based on all observed Ca = calcium carbonate
12a	Log CaCO3	Year	Based on all observed Ca = calcium carbonate
12b	Ratio gelatin:CaCO3	Year	Based on all observed Ca = calcium carbonate
12c	Ratio gelatin:CaCO3, zoom 1	Year	Based on all observed Ca = calcium carbonate
12d	Ratio gelatin:CaCO3, zoom 2	Year	Based on all observed Ca = calcium carbonate
12e	Calcium (ppm)	Year
13	Alum	Year	Based on all observed S = potassium aluminum sulfate prior to 1800, aluminum sulfate post 1800
14	Potash alum K	Year	Based on all observed K = potassium aluminum sulfate prior to 1800 only
14a	Log potash alum	Year	ditto
14b	Potash alum S	Year	Based on all observed S = potassium aluminum sulfate prior to 1800
15	% alum on gelatin	Year	Based on all observed S = potassium aluminum sulfate prior to 1800, aluminum sulfate post 1800
15a	% alum on gelatin, zoom	Year	Based on all observed S = potassium aluminum sulfate prior to 1800, aluminum sulfate post 1800
16	% alum on CaCO3	Year	ditto
16a	% alum on CaCO3 , zoom	Year	ditto
LEAF TYPES
98	Log Ca	Year by leaf type	All leaf types
98a	Log Ca	Year by leaf type	Art prints, blank leaves, MS books, MS leaves
98b	Log Ca	Year by leaf type	Printed leaves, printed books
98c	Ca (ppm)	Year by leaf type	All leaf types
98d	Ca (ppm)	Count by leaf type	Bar graph
99	Log K	Year by leaf type	All leaf types
99a	K (ppm)	Count by leaf type	Bar graph
100	Log S	Year by leaf type	All leaf types
100a	S (ppm)	Count by leaf type	Bar graph
101	Log Fe	Year by leaf type	All leaf types
101a	Fe (ppm)	Count by leaf type	Bar graph
102	Gelatin	Year by leaf type	All leaf types
102a	Gelatin	Year by leaf type	Art prints, blank leaves, MS books, MS leaves
102b	Gelatin	Year by leaf type	Printed leaves, printed books
102c	Gelatin	Year by leaf type	Printed books
102d	Gelatin	Year by leaf type	Printed leaves
102e	Gelatin	Count by leaf type	Bar graph
NON-CHRONOLOGICAL
FULL DATA SET
17*	Gel	Delta L*	The delta L* vertical scale progresses from 0 (white) toward   -30 (colors increasingly closer to black)
18*	Log Ca	Delta L*	ditto
19*	Log K	Delta L*	ditto
20*	Log S	Delta L*	ditto
21*	Fe	Delta L*	ditto
22	Delta L*	% alum on gelatin	ditto
23	Delta L*	% alum on CaCO3	ditto
24*	Gel	Delta a*	The delta a* scale indicates more red as the positive numbers increase, more green as negative numbers decrease.
25*	Log Ca	Delta a*	ditto
26*	Log K	Delta a*	ditto
27*	Log S	Delta a*	ditto
28*	Fe	Delta a*	ditto
29	Delta a*	% alum on gelatin	ditto
30	Delta a*	% alum on CaCO3	ditto
40*	Gelatin interior	Gelatin edge
41*	Ca interior	Ca edge
42*	Fe interior	Fe edge
43*	S interior	S edge
44*	Log Ca	Gelatin
"ORNAMENT" PLOTS
FULL DATA SET
46	Gelatin	M&W (materials and workmanship)	Ornament plot showing the average estimated concentrations for M&W grade 1 (worst) to grade 5 (best).
47	Log Ca	M&W	ditto
48	Log K	M&W	ditto
49	Log S	M&W	ditto
50	Log Fe	M&W	ditto
51	Thickness 1 sheet	M&W	ditto
52	Delta L*	M&W	ditto
300 DARKEST vs 300 LIGHTEST SUBSET			300 darkest and lightest specimens from the full 1,578-specimen data set.
53	300 darkest & 300 lightest	Delta L*
54	300 D & 300 L	Year	Plot shows distribution of specimens by year.
55	300 D & 300 L	Gelatin
56	300 D & 300 L	Log Ca
57	300 D & 300 L	Log K
58	300 D & 300 L	Log S
59	300 D & 300 L	Log Fe
60	300 D & 300 L	Thickness 1 sheet	ditto
FROST = GRADE A SUBSET			295 specimens graded "A" for "aqueous intervention unlikely" by conservator  G. Frost.
69	50% darkest & 50% lightest	Delta L*
70	50% D & 50% L	Year	Plot shows distribution of specimens by year.
71	50% D & 50% L	Gelatin
72	50% D & 50% L	Log Ca
73	50% D & 50% L	Log K
74	50% D & 50% L	Log S
75	50% D & 50% L	Log Fe
76	50% D & 50% L	Thickness 1 sheet
"SAME BOOK DIFFERENT PAPERS SUBSET"
77	Delta L*	Gelatin	Trends evident in paired specimens in the same book: one darker, one lighter.
78	Delta L*	Log Ca	ditto
79	Delta L*	Log K	ditto
80	Delta L*	Log S	ditto
81	Delta L*	Fe	ditto
82	Delta L*	% alum on gelatin	ditto
83	Delta L*	% alum on CaCO3	ditto
84	Delta a*	Gelatin	ditto
85	Delta a*	Log Ca	ditto
86	Delta a*	Log K	ditto
87	Delta a*	Log S	ditto
88	Delta a*	Log Fe [or Fe]	ditto
89	Delta a*	% alum on gelatin	ditto
90	Delta a*	% alum on CaCO3	ditto