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Graphical Analyses: Boxplots
The boxplot is a schematic graphical device for comparing the empirical
distributions represented by batches of numbers [14]
. For these data, (Table 2,
3) the analytical method (QXRD, OM-1, RR1-n) separates
the batches. This plot can be considered a visual one-way anova or t-test.
The location of the distributions, their spread, and extremes are embedded in
the graphical display. This allows meaningful comparison of distributional
information through rapid assessment of the alignment or mis-alignment of
median values and boxes, and differences in spread.
Important features of the boxplot are:
- the width of the box is proportional to sample size,
- the median value, used for its resistance to outliers, is identified by
the X,
- the interquartile range ("middle half") of the data are
represented by the body of the box, and
- the extremes (minimum and maximum) are represented by the ends of the
straight lines projecting out of the box.
One important consideration for these data are that the QXRD box
represents 36 numbers, the RM certificate data (OM) represents four numbers,
and the round robin data (RR) represents two numbers each. The boxes for the
RR groups, with only two observations, have the upper line of the box equal
to one observation and data point, the other line equal to the other, and the X in the middle denoting the mean/median of the two observations.
Table 2. Mass fraction (percent) by
QXRD, RM 8486 optical
data (OM), and round robin data (RR) following ASTM C 1356
[2]. QXRD analysis of nine vials (1-9) with
two splits per vial (a, b), with each split analyzed in duplicate
(1, 2).
|
Alite |
Belite |
Ferrite |
Aluminate |
Periclase |
|
1a1
1a2
1b1
1b2
2a1
2a2
2b1
2b2
3a1
3a2
3b1
3b2
4a1
4a2
4b1
4b2
5a1
5a2
5b1
5b2
6a1
6a2
6b1
6b2
7a1
7a2
7b1
7b2
8a1
8a2
8b1
8b2
9a1
9a2
9b1
9b2
OM1 a
OM1 b
OM1 c
OM1 d
RR1 a
RR1 b
RR2 a
RR2 b
RR3 a
RR3 b |
56.4
56.8
55.1
56.1
56.8
56.5
58.5
58.5
56.8
57.0
58.6
57.4
56.3
56.2
56.7
56.9
55.8
55.7
57.2
57.1
56.9
56.8
57.3
57.0
55.9
56.5
56.5
56.9
56.7
57.0
56.9
56.3
55.8
56.9
56.1
57.2
59.0
56.3
60.3
58.1
56.8
56.2
60.0
60.2
61.8
60.6 |
21.5
21.8
21.1
20.3
20.9
21.7
20.8
21.0
21.5
21.2
20.4
20.6
21.1
21.5
20.9
20.9
20.6
20.8
21.1
21.0
21.5
21.4
20.7
20.5
21.4
20.7
21.5
21.1
21.2
21.1
20.6
21.1
21.4
20.8
21.0
20.8
23.0
25.3
20.6
23.7
23.6
24.1
23.6
24.6
23.9
25.0 |
13.8
14.0
16.1
15.7
14.6
14.4
13.9
13.5
14.2
14.5
13.7
14.5
15.0
14.9
14.8
14.7
15.7
15.8
14.1
14.1
14.1
14.1
14.2
15.0
14.9
14.8
14.3
14.2
14.4
14.3
15.0
14.8
15.1
14.6
15.3
14.8
13.0
13.1
14.2
14.1
13.5
14.3
9.6
8.1 |
3.9
3.3
3.6
3.7
3.5
3.4
3.1
3.2
3.3
3.4
3.3
3.5
3.4
3.3
3.5
3.5
3.5
3.5
3.4
3.4
3.4
3.4
3.6
3.5
3.5
3.5
3.4
3.6
3.5
3.5
3.4
3.5
3.5
3.5
3.5
3.4
1.1
1.1
1.0
1.0
3.2
2.5
1.3
2.3 |
4.3
4.0
4.2
4.3
4.2
4.0
3.7
3.8
4.2
3.9
3.9
4.1
4.2
4.1
4.1
4.1
4.4
4.2
4.2
4.3
4.0
4.3
4.2
3.9
4.3
4.6
4.3
4.1
4.2
4.0
4.1
4.2
4.3
4.2
4.1
3.8
3.0
3.7
3.7
3.7
1.9
2.0
4.7
3.8
2.5
2.8 |
Table 3. QXRD Summary: 95 % Confidence
Limits for the
Mean (Mass Percent).
|
|
Upper |
Limits
Mean |
Lower |
|
Alite |
56.50 |
56.75 |
57.00 |
| Belite |
20.91 |
21.04 |
21.17 |
| Aluminate |
3.41 |
3.46 |
3.50 |
| Ferrite |
14.40 |
14.61 |
14.81
|
| Periclase |
4.07 |
4.13 |
4.20 |
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