A Statistical Estimation Approach for Quantitative Concentrations of Compounds Lacking Authentic Standards/Surrogates Based on Linear Correlations between Directly Measured Detector Responses and Carbon Number of Different Functional Groups
Table 6
Assessment of the PD values between the actual and projected RF values for arbitrarily divided chemical groups.
Order
Type of VOC groups
Number of chemical
Projected equationa
P value
PD valuesb of all and six individual (nonmodified) groupsc
Slope
Intercept
All
I
II
III
IV
V
VI
(A) 6 original functional groups
1
All
18
34,175
−82,472
0.9396
17.9
43.6
3.52
16.5
7.75
41.8
2.62
2
Aldehyde (I)
4
24,836
−60,290
0.9725
9.83
9.83
3
Aromatic (II)
6
29,456
−43,139
0.9713
2.03
2.03
4
Carboxylic (III)
4
29,818
−58,701
0.9012
12.7
12.7
5
Ketone (IV)d
2
*
*
*
*
*
*
*
*
*
*
*
6
Alcohol (V)d
1
*
*
*
*
*
*
*
*
*
*
*
7
Ester (VI)d
1
*
*
*
*
*
*
*
*
*
*
*
(B) 25 arbitrary groups
1
II + V
7
25,484
−12,686
0.9823
2.83
—e
2.60
—
—
4.26
—
2
II + VI
6
32,806
−69,569
0.9668
3.17
—
2.61
—
—
—
6.54
3
II + IV
8
35,411
−89,325
0.9856
3.97
—
3.29
—
6.03
—
—
4
II + III + VI
11
32,994
−71,393
0.9857
5.63
—
2.74
9.87
—
—
5.96
5
II + III
10
32,949
−70,402
0.9872
5.73
—
2.59
10.4
—
—
—
6
II + III + IV
12
33,650
−76,475
0.9845
7.33
—
2.94
11.1
13.0
—
—
7
II + III + V
11
31,181
−56,899
0.9654
9.89
—
2.11
17.2
—
27.2
—
8
III + VI
5
29,615
−57,914
0.9445
10.3
—
—
12.9
—
—
0.27
9
III + IV
6
30,661
−64,601
0.8746
12.0
—
—
10.3
19.0
—
—
10
I + IV
6
31,804
−85,229
0.9241
13.1
13.6
—
—
12.0
—
—
11
III + V
5
27,486
−42,376
0.6568
13.1
—
—
19.3
—
27.5
—
12
I + II + IV
12
37,696
−108,341
0.9787
13.1
29.7
4.26
—
6.63
—
—
13
I + II + III + IV
16
35,474
−91,942
0.9664
14.3
27.1
3.77
23.2
2.65
—
—
14
I + II + VI
11
38,121
−111,370
0.9773
14.7
33.4
4.32
—
—
—
1.75
15
I + II + III + VI
15
35,445
−91,569
0.9646
15.2
28.1
3.73
22.8
—
—
1.38
16
I + II
10
38,135
−111,661
0.9774
16.2
33.9
4.37
—
—
—
—
17
I + II + III
14
35,458
−91,524
0.9646
16.2
28.4
3.71
22.7
—
—
—
18
I + II + V
11
35,227
−89,454
0.9322
17.9
32.6
3.58
—
—
44.8
—
19
I + VI
5
33,109
−92,201
0.9272
18.7
20.6
—
—
—
—
10.9
20
I + II + III + V
15
34,080
−81,036
0.9372
20.7
47.4
3.34
15.1
—
40.7
—
21
I + III + IV
10
29,862
−69,448
0.8341
21.7
34.5
—
17.5
4.57
—
—
22
I + III + VI
9
30,162
−70,431
0.8311
24.1
34.9
—
17.5
—
—
7.46
23
I + III
8
27,327
−59,496
0.7476
26.8
37.1
—
16.5
—
—
—
24
I + III + V
9
25,591
−47,341
0.5444
35.8
57.4
—
12.9
—
41.0
—
25
I + V
5
20,967
−33,206
0.3434
47.7
48.3
—
—
—
45.7
—
Statistics
Mean
0.8955
0.0188
14.9
33.0
3.26
15.8
8.95
34.1
4.61
(n = 29)d
SD
0.1490
0.0586
9.90
12.1
0.74
4.45
5.36
14.0
3.67
Min
2.03
9.83
2.03
9.87
2.65
4.26
0.27
N
29
17
17
17
8
8
8
The projected equations are derived from linear regression analysis between the number of carbon (x-axis) and actual RF values (y-axis).
bPercent difference (PD) = /RF(Actual) * 100.
cI: aldehyde, II: aromatic, III: carboxylic, IV: ketone, V: alcohol, and VI: ester.
dAs three groups (ketone (IV), alcohol (V), and ester (VI)) have only the limited number of components (less than 2), their predictive equations cannot be made and are not considered from counting of total group numbers (7(A) + 25(B) − 3(A) = 29).
eNot computed.