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Background to the Chromatography Data

Data analysed in: Kroonenberg, P. M. (2008). Applied multiway data analysis. Hoboken NJ: Wiley.

Spanjer's chromatography data were published in Spanjer (1984). The authors studied chromatographic retention characteristics of several chemical compounds. The basic purpose of this type of study is to determine which chemical compounds are present in a chemical mixture. To do this, the mixture is dissolved in a liquid, the eluent or mobile phase. This solution is entered into a vertical glass tube or column packed with solid material, the stationary phase. Different compounds or solutes travel at different speeds through the column, depending both on the phases and the affinity of the solute to these phases. The time it takes to travel through the column is called the retention time, and this differs with phases and solutes. It takes some time for a solute to emerge from the column but there generally is a single-peaked function indicating the amounts of a solute exiting the column over time. The instrument used to measure the relative concentration over time is called a chromatograph. Missing data can occur because some compounds take too long to travel through the column, so that their peaks do not emerge until after the experiment is concluded. Spanjer (1984) used the data set to estimate the missing data themselves. In particular, one may explore the effect of starting solutions, different algorithms, varying numbers of components, and effects of centering as was done in Kroonenberg (2008).


Data description

The data contains 21 missing data indicated by -9.99.

Rows (1st mode): Solutes

No.SolutesType of monosubstituted compound
1.mF Phenols
2.pF Phenols
3.mCl Phenols
4.pCl Phenols
5.mBr Phenols
6.pBr Phenols
7.mCH3 Phenols
8.pCH3 Phenols
9.mOCH3 Phenols
10.pOCH3 Phenols
11.mNO2 Phenols
12.pNO2 Phenols
13.mCN Phenols
14.pCN Phenols
19.mF Anilines
20.pF Anilines
21.mCl Anilines
22.pCl Anilines
23.mBr Anilines
24.pBr Anilines
25.mCH3 Anilines
26.pCH3 Anilines
27.mOCH3 Anilines
28.pOCH3 Anilines
29.mNO2 Anilines
30.pNO2 Anilines
31.mCN Anilines
32.pCN Anilines
35.3CL Pyridines
36.3BR Pyridines
37.4CH3 Pyridines
38.3CN Pyridines
39.4CN Pyridines

Columns (2nd mode): Adsorbents (Stationary phase)

No.Abbreviation Description

Slices (3rd mode): Eluents (Mobile phase)

No.Abbreviation Description
1.N-Hexa 35 v/v% methylene chloride in n-hexane
2.Methyl pure methylene chloride

Data arrangement

A three-way data array X = (x(i,j,k)) has the following form

                   |-----|    |i=2
                   |     |    |..
                   |     |    |..
                   |     |____|i=I=39
                   |_____|            k=K=2
                  j=1,.,J=3        k=1

The actual data file has the following form:

            |     |i=2
            |     |..     k=1
            |     |..
            |     |i=2
            |     |..     k=K=2
            |     |..

Thus the first mode (i) is nested in the third mode (k) and there are 39 (Solutes) times 2 (Eluents (Mobile phase)) rows and 3 (Adsorbents (Stationary phase)) columns.

Data handling


Spanjer did not preprocess these data. For details see Kroonenberg (2008). Applied multiway data analysis. Hoboken NJ: Wiley (Chapters 6 and 7).


These data have taken from Spanjer's thesis and are made available for bonafide researchers. Please be sure to quote his thesis, the paper mentioned above and this website when using these data in a publication.

[Download the zipped Chromatography Data]

| Centre for Child and Family Studies | Institute of Leiden Institute of Education and Child Studies | The Three-Mode Company | Three-Mode Data Sets | TOP |
P.M. Kroonenberg
Institute of Leiden Institute of Education and Child Studies, Leiden University
Wassenaarseweg 52, 2333 AK Leiden, The Netherlands
Tel. *-31-71-5273446/5273434 (secr.); fax *-31-71-5273945
E-mail: kroonenb at fsw.leidenuniv.nl

Created: 8-7-2009
Last Updated: 11-7-2009