Results

Plot Library

Figure 12. Plot 1, estimated weight percent gelatin by year.


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

Cite as: . “Results. Plot Library.” Paper through Time: Nondestructive Analysis of 14th- through 19th-Century Papers. The University of Iowa. Last modified . .