the water-vapour sorption isotherms of

Journal of Food Engineering 3 (1984) S l-73

The Water-Vapour Sorption Isotherms of Microcrystalline Cellulose (MCC) and of Purified Potato

Starch. Results of a Collaborative Study

W. Wolf, W.E.L. Spiess, G. Jung

Federal Research Centre for Nutrition, Engesserstrasse 20, 7500 Karlsruhe 1, West Germany

H. Weisser

University of Karlsruhe, Institute of Food Process Technology, Kaiserstrasse 12. D-75 Karlsruhe 1, West Germany

H. Bizot

INRA, Laboratory of Food Biophysics, Chemin de la Geraudiere,

F-44 072 Nantes Cedex, France

and

R. B. Duckworth

University of Strathclyde, Department of Food Science and Nutrition, James P. Todd Building, 131 Albion Street. Glasgow Gl 1 SD, United Kingdom

ABSTRACT

In a comprehensive collaborative study within the frame-work of COST

(European Cooperation in the Field of Scientific and Technical Research) _ the COST 90 project - the mean adsorption isotherms of MCC and a

potato starch and the precision data, viz. the repeatability/reproducibility

of the total sorption measurement procedures, were determined.

Recommendations on the practical determination of sorption isotherms

of foods based on this work are made.

INTRODUCTION

Sorption isotherms of ‘well-defined’ food materials published by

various authors differ, often considerably, from each other.

Journal of Food Engineering 0160-8774/84/$03.00 - 0 Elsevier Applied Science Publishers Ltd, England, 1984. Printed in Great Britain

52 W. Wolf et al.

Differences in the sorption properties of such products - like wheat of a special variety, meat taken from a selected muscle, or milk with a given fat content - can be attributable to biological variation of the substrate, differences in equipment design and different handling procedures.

To study the effect of the last two groups of influences on the sorption isotherm of a particular material in greater detail, a collaborative research programme was initiated within the COST 90 Project on physical properties of foodstuffs. The objective was a standard equipment for sorption isotherm measurements on selected materials for reference purposes.

The programme, in which 3 2 laboratories participated, was carried out in three stages.

In the first stage, a substance with defined and stable sorption properties was selected which could be used for the analysis of methodological problems and which could serve as a reference material for calibration purposes. In the second stage, sorption equipment was designed and constructed which allowed well-controlled undisturbed heat and mass transfer between sorbate source and substrate. In the third stage, the precision data of the system : reference material-recommended equipment were determined together with the most probable sorption isotherm of the reference material.

The criteria for the selection of the reference material were:

(1) Stability in sorption behaviour over several adsorption and desorption cycles and to exposure to extreme ambient temperatures when shipped or stored.

(2) Absence of hysteresis between adsorption and desorption. (3) Relatively rapid rate of equilibration. (4) Its sorption isotherm to be sigmoid in shape as are those of many

food products. (5) Homogeneity of the material in its physical structure and distri-

bution of components. (6) The determination of its water content to be possible in an un-

equivocal way. (7) Easy availability and easy handling properties.

Among a variety of homogeneous purified substances, such as starches and silicic acid, microcrystalline cellulose (Avicel, PH 101 from FMC) was chosen as the reference material because it fulfilled most of the above criteria, except that it exhibited hysteresis between adsorption

Sorption isotherms of MCC and purified potato starch 53

and desorption isotherms (Wolf and Spiess, 1980; Wolf et al., 1980). MCC had also been used in a previous study by Vos and Labuza (1974) as a reference material when determining the a, of products in the high water-activity range (0.85-0.98).

When adsorption isotherm measurements are made, three critical stages are involved:

(1) Desorption in the course of sample preparation to attain zero water content.

(2) Equilibration at the different water-activity levels. (3) Transfer of the samples from sorbostat to weighing equipment.

In order to avoid problems connected with these critical stages, it is necessary to design the equipment and the mode of operation accordingly.

The equipment components which could influence the sorption kinetics must be designed in such a way that the resistances to heat and mass transfer within the equipment are always less than they are within the product. The product itself should be disposed in such a way that sorption is complete within a reasonable period of time. Any handling procedures affecting the sorption process must be carried out in such a way that the intended processes are achieved; this applies, for example, to the desorption processes as well as to the adsorption processes. During manual operations the uptake or loss of water must not be significant otherwise the time required for individual operations such as opening the equipment, transferring weighing bottles from the sorption container to the balance, etc. must be standardized.

The equipment finally agreed upon consisted of a rather simple arrangement: I-litre glass jars with vapour-tight lids as the sorbostat in the bottom of which the sorbate source was arranged. The substrate was placed in small weighing bottles standing on trivets directly above the sorbate source and the jars were submerged in a thermostatically controlled waterbath almost to the lid. To protect the substrate against radiative heat exchange with the environment, waterbath and jar were covered with insulation (Wolf et al. in preparation).

IMPLEMENTATION OF THE COLLABORATIVE STUDY

Participating laboratories

Within the framework of the project, 32 laboratories from 11 countries took part. Six of the laboratories were industrial research institutions

54 W. Wolf et al.

in which sorption measurements were carried out as routine work together with other quality-control measures. Of the 26 laboratories associated with research institutions or universities, 13 groups had been active in research on water activity for more than 10 years and had considerable experience in the subject; the remaining teams had carried through sorption isotherm measurements only occasionally in the past in the course of other research work such as investigations on product stability, etc. Their experience in the field of sorption isotherm measurements could, at the beginning of the study, be regarded as rather limited. A list of the laboratories which contributed results is given in Appendix 1.

Materials and methods

The test substrate, Avicel PH 10 1 MCC, was received from the producer as analytical grade in a loo-kg amount. This quantity was divided into portions each of 100 g by means of a sample divider. These portions were packed in polyethylene-coated aluminium pouches, sealed hermetically and mailed to the participating laboratories together with recommendations for the design of the standard equipment, the preparation of the sorbate source and the handling procedures.

The starch samples (purified potato starch) were prepared by one of the participating groups and distributed in the same way as the MCC.

It was made obligatory that the sorption isotherms were measured on the standardized equipment. Saturated salt solutions had to be used as sorbate source. The water activities of the solutions selected were fairly evenly distributed over the activity range 0.1-0.9. The exact values are given in Table 1. At each water activity, five replicates were to be measured in one sorbostat. The main features of the method used are given in Table 2.

RESULTS

General

Of the 32 laboratories provided with material and instructions, 24 returned pertinent results. Together with the results a completed questionnaire was received in which the methods and the equipment used were explained in detail.

Sorption isotherms of MCCand purified potato starch 55

TABLE 1 Salt and Water Quantities to Prepare the Saturated Salt Solutions Required for One

Sorption Container

Salt Relative

humidity

(RHja

(%)

Standard

deviation

Quantity

Salt (gl Water (ml)

LiCl 11.15

CHsCOOK 22.60

MgClz 32.73

K2C03 43.80

WWM2 52.86

NaBr 57.70 SrC12 70.83 NaCl 75.32

KC1 84.32

BaC12 90.26

0.37 0.5 0.16 0.33 0.23

0.4 0.04 0.12

0.38

150 85 200 65 200 35

200 90 200 30

200 80 200 50 200 60 200 80 250 70

aRH-values and standard deviations (s) of the salts according to Greenspan (I 977).

TABLE 2 Principal Features of the Method used for the Measurement of Sorption Isotherms

of MCC and Starch

Sorbostat 1-litre glass jar Sorbate source Saturated salt solutions (aqueous)

Measuring method Gravimetric, discontinuous

Mode of sorption Integral

Sample mass 400 mg Sorption temperature 25 k O.l”C Precision of the balance 0~0001 g Sample holder Weighing bottle (25 x 25 mm) with ground-in stopper

From this information it became clear that two laboratories had

carried out their experiments in a way which was not in conformity

with the prescribed procedure and so their results were excluded from

subsequent evaluations.

56 W. Wolf et al.

Other deviations from the recommendations reported by the individual laboratories were as follows:

(1) Instead of a water bath a thermostatically controlled chamber (incubator) or an air-conditioned room was used for temperature control. Since the temperature fluctuations were, with one exception, less than +0.3”C, the data from these experiments were accepted because the influence of temperature on the sorption isotherms of MCC and of starch is very small (Wolf et al., 1980).

(2) Instead of the recommended glass equipment (jars and weighing bottles) equipment showing minor differences in the important dimensions was used. Since the pathways for the mass transfer from the sorbate source to the substrate are not affected by these differences, the data from these experiments were also accepted.

(3) Instead of the recommended equilibration times, longer and, in one case, slightly shorter, equilibration times were used during pre-drying and adsorption. Because MCC and starch had proved very stable in their sorption properties against moderate heat treatments (Wolf et al., 1980) no change in the product and the results was expected as a result of the longer exposure times in either stage of the determination.

As the shorter equilibration time used in the one case was within the tolerance interval encountered when the study was planned those results were also accepted.

(4) Other minor differences reported by the laboratories were also considered as not significant.

Statistical treatment and evaluation of precision data for the results obtained for MCC

The sorption data obtained were, after a first screening test, evaluated for mean value, standard deviation, repeatability and reproducibility according to standard test methods based on BS 5497 :Part 1: 1979 issued by the British Standards Institute (1979), DIN-IS0 5735 issued by the Deutsches Institut fur Normung (1978), and a report on the planning and statistical evaluation of ring tests issued by the Bundes- gesundheitsamt, Berlin (Goetsch et al., 1978).

In detail, the procedure comprised the following steps (see Fig. 1. A

Sorption isotherms of MCC and purified potato starch

A

ELlMlNATlON

OF DUlLiLR

GRUBBS-TEST FOR

OlJlLlERS FOR

EAtH LAB FOR

LACIl SALT

ELIPIINATE

THE OUTLIER

CAI CULATE f OR

EACH SALT FOR EAM LAB

MEAN

STANDARD DLVIATION J

B I

1

EXAMINATION I

OF SYSTEMATIC VAR. ANAL, DlXuN TEST

ERRORS I I

ELIMINATE THE

VALUES OF THIS

LAB WHICH CAUSE

SIGNIFICANT DIFFE

RENCES BETWEEN

D MEAN VALUES

REPEATABILITY

REPRODUCIBILITY

NO

ci5 _

REPEAT THE CALCULATE

COLLAB. STUDY REPEATABILITY

REPRODUCIBILITY

Fig. 1. Flow diagram of the principal steps in the statistical analysis.

58 W. Wolf et al.

brief description of the statistical tests together with an example of the results analysed is given in Appendix 3 ):

(A) Identification and elimination of outliers within each individual experimental data set (Grubbs test).

(B) Comparison of variances (Cochran test j.

(CT) Identification of systematic deviations (Dixon test). (D) Calculation of mean values, standard deviations, repeatability

and reproducibility on the remaining data.

The two terms which describe variability, viz. repeatability and reproducibility, in most practical cases of routine experiments sufficiently

characterize the precision. Repeatability refers to tests performed at short intervals in one

laboratory by one operator using the same equipment, while reproducibility refers to tests performed at different laboratories which implies different operators and different (if not dissimilar) equipment.

The following definitions are used:

( 1) Repeatability, r. The value below which the absolute difference between two single test results obtained within a short interval of time by the same method on an identical test material under the same conditions (same operator, same apparatus, same laboratory) may be expected to lie within a specified probability: in the absence of other indications the probability is 95%;

(3) Reproducibility, R. The value below which the absolute difference between two single test results obtained with the same method on an identical test material under different conditions (different operators, different apparatus, different laboratories and/or at different times) may be expected to lie within a specified probability; in the absence of other indications the probability is 95%‘.

An analysis of the measured sorption data for the various selected water activities showed that they are normally distributed, at least on a 0.1% significance level with the exception of the results for barium chloride (BaCl,) (a, = 0.9). However, since there is no reason why the measured values for BaCl, should not be normally distributed, the data at this water-activity level were still retained for further statistical treatment.


Regarding step A, in which the original data were considered, it was found that outliers could be identified only in a few cases; this con- firmed at the outset that the experiments had been carried out by all laboratories with sufficient care; in statistical terminology, the data sets after the first outlier tests contained, in the majority of all individual data groups (data for one salt from one laboratory being equal to a mathematical cell), a similar number of test results. Furthermore it was found that in no group was the variance of the data zero. Therefore both the Bartlett and Cochran tests could be applied in step B to the evaluation of the homogeneity of the variances. The results of either test are comparable since the tests yielded different results only in a few cases.

The compilation of the test results shows that variances causing inhomogeneities are accumulated in certain laboratories. These could be regarded as laboratories with limited experience, whereas in the laboratories with extensive experience practically all variances were homogeneous. In accordance with the recommendations of the statistical test procedures used it was decided that laboratories in which more than 50% of the cell variances were found to cause inhomogeneity were excluded from further evaluation. From the remaining laboratories those individual data groups which caused inhomogeneity of the variances were carefully examined on the basis of the information obtained from the individual laboratories on the experimental work and also rejected in all cases.

The remaining data sets, however, qualified for the Dixon test, step C; according to the test procedure, this test was applied to identify mean values which differed significantly from the comparable data base. Only four individual data groups (cells) had to be excluded after this test procedure.

From the remaining data for each salt (on the average 80 measurements) the mean value, the standard deviation, the repeatability standard deviation and the reproducibility standard deviation were calculated (step D); from the latter information, the repeatability and the reproducibility values were derived (see Table 3).

The standard deviations of the equilibrium water contents vary from SmiIl = 0.19 to s,,, = O-3 1 g H,O/lOO g DM (dry matter). Since there is no clear correlation of standard deviation and other precision data with water activity, the mean standard deviation and the means of the pre-

60 W. Wolj.et al.

TABLE 3 Adsorption Isotherm Data for MCC at 25°C; Repeatability and Reproducibility Values of a Precision Study with 24 Laboratories (Mean Standard Deviation 0.25;

Mean Repeatability 0.17; Mean Reproducibility 0.72; all in g HzO/l 00 g DM)

0, Mean water content (X)

Standard Repeatability Reproducibility deviation (s) (r) (R)

0.1 1 2.02 0.25 0.13 0.72 0.23 3.19 0.21 0.11 0.63 0.33 4.06 0.75 0.11 0.73 0.44 5.04 0.19 0.14 0.54 0.53 5.82 0.27 0.23 0.79 0.58 6.48 0.21 0.07 0.61 0.7 1 8.21 0.20 0.22 0.57 0.75 8.83 0.31 0.21 0.89 0.84 10.95 0.29 0.19 0.85 0.90 12.96 0.30 0.26 0.88

cision data can be calculated; the mean standard deviation within the range covered by the experiments is s, = 0.25 g H,O/lOO g DM, the mean repeatability is r, = 0.17 g H20/ 100 g DM, and the mean reproducibility is R, = 0.72g H,O/lOOg DM.

From sorption measurements carried out at higher temperatures by the same method as recommended, similar precision data were obtained (Wolf et al., 1980). It can therefore be concluded that the values of mean repeatability r and mean reproducibility R derived from the results of the collaborative study are also valid for experiments with MCC in the standardized equipment in the temperature range 1.535°C.

The calculated mean values of the equilibrium water contents for the

10 water activities were used to construct the most probable sorption isotherm for MCC as the mean sorption isotherm.

For the computer plot of the sorption data the G.A.B. Model (Guggenheim-Anderson-De Boer according to Van den Berg (1981)) was used to interpolate sorption isotherms:

X Cka, -= xln (1 -ka,)(l -_a, +Cka,)


where

a, = Water activity, C = Guggenheim constant = C’ exp [(H, - H,)/RTl,

HI = Total heat of sorption of the first layer in primary sites, H, = Heat of condensation of pure water vapour, H, = Total heat of sorption of the multilayer which differs from

the heat of condensation of pure water, k = Factor correcting properties of the multilayer molecules

relative to the bulk liquid (k = k'(H, - HJRT), X = Water content on dry basis,

f

c z 0.4 0

/ I

.t 5 0.8 1.0 Water activity a,

Fig. 2. Adsorption isotherm for MCC at 25°C; result of a collaborative study with 24 laboratories. (G.A.B. constants: X, = 4.064; C = 8.776; k = 0.772.)

62 IV. Wolf et al.

X, = Water content on dry basis corresponding to saturation of all primary adsorption sites by one water molecule (formerly called ‘monolayer’ in BET theory).

As the most prominent result of the entire study, Fig. 2 shows the mean MCC isotherm with standard deviations at the measuring points. Since each of these points represents 75-85 individual values (depending on the salt in question) the confidence intervals of the mean values (at the 95% probability level) have a width of 0.11 g H,O/lOO g DM (for the calculated mean standard deviations).

Sorption and precision data for potato starch

The results of the sorption isotherm measurements on potato starch were evaluated in the same way as described above for MCC.

The results are presented in Table 4 and Fig. 3. In contrast to the precision data for MCC in the case of starch r and

R are related to the water activity of the sample. The repeatability r and the reproducibility R of the water activity are represented by the

TABLE 4

Adsorption Isotherm Data for Potato Starch at 25°C; Repeatability and Reproduci- bility Values (in g H,O/lOO g DM) of a Precision Study with 23 Laboratories

a, Mean water Standard Repeatability Reproducibility content(X) deviation (s) (r) (RI

0.11 4.69 O-38 0.13 1.12

0.23 7.54 o-45 0.32 1.31

0.33 9.74 0.49 o-19 1.42 0.44 12.10 0.43 o-14 l-25 0.53 13.92 0.82 0.25 2.39

0.58 15.34 0.52 0.40 1.50

0.71 19.28 0.55 0.30 1.59 0.75 20.93 0.66 0.36 1.91

0.84 24.95 0.97 0.42 2.80 0.90 28.83 I.64 0.60 4.76


Water activity a,

Fig. 3. Adsorption isotherm of potato starch at 25°C; result of a collaborative study with 23 laboratories. (G.A.B. constants: X,,, = 10.312; C= 7.976; k = O-734.)

following linear regression equations which are valid for the range 0.1-0.9:

I- = 0.424~~~ + 0.08 (2)

R = 3.035a, + 0.36 (3)

In general at lower water activities measurements were carried out with greater precision than at higher activities. The reason for this is not completely clear; it could, however, be that at higher activities the time needed to incorporate water molecules into the starch varies and is in some cases extremely long so that equilibrium is not reached even after 7 days.

64 W. Wolf et al.

CONCLUSIONS AND RECOMMENDATIONS

It is evident that the determination of sorption isotherms can be rather difficult and cumbersome; if, however, sufficient care is taken they may be achieved with precision. The reference and precision data obtained may help to improve inadequate methods.

For practical applications, the method used in this study. namely to evaluate first the sorption behaviour of a relatively simple uniform product before more complicated systems are introduced, seems to be a useful approach to sorption measurements.

When sorption measurements are approached in such a way, errors caused by insufficient treatment of the substrate can be detected and distinguished from errors caused by equipment deficiencies more easily than when complicated substrates are used from the outset.

For practical sorption measurements the following procedure is recommended.

( 1 ) Measure the adsorption isotherm of MCC (Avicel) according to the standardized method (five replicates).

(3) Compare the results obtained with the mean value and precision data of the collaborative study.

(3) If good agreement is obtained, proceed with the material to be investigated. (a) Evaluate the necessary desorption (pre-drying) conditions for achieving zero water content. (b) Evaluate the necessary exposure time to reach equilibrium conditions.

(4) if the agreement is poor. search for and eliminate errors and repeat the measurements on MCC until good agreement is reached.

The question as to whether the agreement obtained is good or poor has to be decided with the aid of the precision data (reference value, repeatability. reproducibility ):

(1) If II determinations performed by one laboratory under repeatability conditions produce a mean value R that is to be compared to a reference value X,, then good agreement, at the 95% probability level, is obtained if the difference lx--X0 I is equal to or smaller than a so-called critical difference D,,, the value of which is defined by the term:

(4)

(2)

Sorption isotherms of MCCand purified potato starch

For the precision data obtained in the collaborative study:

r=Ol7gH,O/lOOgDM

R = 0.72 g HzO/ 100 g DM

65

n = five replicates in the laboratory under scrutiny

the critical difference has the value

D,, = 0.498

In a random case, for example; with X0= 5.6 1 g H,O/lOO g DM

(equilibrium water content of MCC for a water activity a, = 0.5, according to the sorption isotherm developed in the study) mean values of X which are within the range 5.1 l-6.1 1 are then in good agreement with the recommended sorption isotherm. Mean values falling outside the range are in poor agreement and should be considered as questionable. In most cases in which the difference I X-X,, I is larger than the critical difference Dcr, systematic errors in the experimental procedure are very likely. Where the mean value X of five measurements differs from the reference value X0 by not more than the critical difference, the standard deviation s obtained has to be compared to the repeatability standard deviation s, as established in the collaborative study for the experimental procedure in question, The repeatability standard deviation is defined as:

r

s =283 r (5)

where the factor 2.83 corresponds to the 95% probability level. (If another probability level is sought, this factor becomes 2.32

at the 90% and 3.65 at the 99% probability levels.) If s is equal to or smaller than s,, the experimental procedure

tested can be considered as good; if s is larger than s,, the variability in the results is too high; in this case a more careful repetition of the measurements is necessary.

REFERENCES

British Standards Institute. (1979). Precision of test methods. Part 1. Guide for the

determination of repeatability and reproducibility for a standard test method.

BS 5497 : Part 1.

66 W. Wolf et al.

Deutsches lnstitut fiir Normung. (1978). Bestimmung von Wiederhoibarkeit und Vergleichbarkeit. Entwurf DIN IS0 5725.

Goetsch, P. H., Krijnert, W., Olschimke, O., Otto, U. and VierkGtter, S. (1978). Planung und statistische Auswertung von Ringversuchen. Teil des Berichtes des Max von Pettenkofer-Institutes des Bundesgesundheitsamtes l/78, Berlin, Dietrich Reimer Verlag, Berlin.

Greenspan, L. (1977). Humidity fixed points of binary saturated aqueous solutions. J. Research of the National Bureau of Standards. A. Physics and chemistry, 81A(l), 89.

Van den Berg, C. (1981). Vapour sorption equilibria and other water-starch inter- actions; a physico-chemical approach. PhD Thesis, Agricultural University Wageningen .

Vos, P. T. and Labuza, T. P. (1974). Technique for measurement of water activity in the high a, range. J. Agric. Fd. Chem., 22 (2), 326.

Wolf, W. and Spiess, W. E. L. (1980). Use of reference materials for the measurement of water-vapor sorption isotherms of foodstuffs. fioceedings of the Inter- national Symposium ‘Production and use of reference materials’. Bundesanstalt fiir Materialpriifung, Berlin, p. 263.

Wolf, W., Spiess, W. E. L., Weisser, H., Gril, S. and Bizot, H. (1980). Mikrokristalline Zellulose als Referenzmaterial zum Bestimmen des Wasserdampf-Sorptions-

verhaltens von Lebensmitteln. ZFL, 31 (3), 148. Wolf, W., Spiess, W. E. L., Weisser, H., Bizot, H., Duckworth, R. B. and Jung, G.

(to be published). Standardization of water sorption isotherms: description of

equipment and measuring procedure.

APPENDIX 1: PARTICIPANTS AND THEIR ORGANIZATIONS

Bauder, U. Bizot, H. Casey, J. C. Casolari, A.

Delmer, M. Duckworth, R. B.

Eichner, K.

Evans, E. W.

Gil, S.

Knorr, Nihrmittel GmbH, Thayngen.

INRA, Nantes. Meat Research Institute, Langford, Bristol. Statione Sperimentale per 1’Industria delle Conserve

Alimentari, Parma. CTU, Nogent sur Marne. Department of Food Science and Nutrition, Uni-

versity of Strathclyde, Glasgow. Institut ftir Lebensmitteltechnologie und Ver-

packung, Fraunhofer-Gesellschaft, Munich. National Institute for Research in Dairying, Shin-

field, Reading. Organische Chemische Institut, Universittit Bern,

Bern.


Hallstrom, B.

Higgs, D. Jason, A. C.

Kleeberg, H.

Kluge, G. Linko, P.

Lintas, C. McKenna, B.

Multon, J. L. Pixton, S. W. Poulsen, K. P.

Rtiegg, M.

Schutz, M.

Simatos, D. Tanner, S. F. Tobback, P.

Weisser, H.

Wolf, w.

Division of Food Engineering, University of Lund, Alnarp.

Brooke Bond Liebig, Croydon. Torry Research Station, Aberdeen. Institut fur Physikalische Chemie, Universitlt

Marburg, Marburg. Pfanni Werke GmbH, Munich. Department of Chemistry, University of Technology,

Helsinki. Institute Nazionale della Nutrizione, Rome. Department of Agricultural Engineering, University

College, Dublin. INRA, Nantes. Ministry of Agriculture, Fisheries and Food, Slough.

Food Technology Laboratory, Danmarks Tekniske Hojskole, Lyngby.

Eidgen. Forschungsanstalt fur Milchwirtschaft, Liebefeld.

Ecole National Superieur des Industrie Textiles, Mulhouse.

Laboratoire de Biologie Physico-Chimique, Dijon. Food Research Institute, Norwich. Laboratory of Food Preservation, Catholic Univer-

sity of Leuven, Leuven. Institut fur Lebensmittelverfahrenstechnik, Univer-

sitat Karlsruhe, Karlsruhe. Bundesforschungsanstalt fur Ernahrung, Karlsruhe.

APPENDIX 2

In the following, the selected method of statistical evaluation will be explained by means of an example of the results obtained (see Table A. 1). In Table A. 1 each line indicates first the laboratory code number, followed by the five measured values (water content/dry matter) obtained by the individual laboratories, calculated means and the standard deviations calculated from these five measurements.

Considering now step A in Fig. 1 in which the original data were considered, first an outlier test according to Grubbs was made for the values submitted by each individual laboratory.

68 W. Wolf et al.

TABLE A. 1 Adsorption Data for MCC, Salt 5 (Mg(NO&), a, = 0.529. (All Values in g H20/

100 g DM.)

Labora- XI tory

x2

1 7

;

6 7

11 13 13 14 15 16 17 19 20 7, _I 25

26 28 30 31 32

6.32 6.18 6.67 6.65 5.14 5.18 6.04 60.5

5.88 5.98 5.96 6.00 6.04 6.00 5.61 5.63 5.83 5.81 5.97 5.96 6.03 5.94 5.70 5.55

5.94 5.91 6.3 I 6.42 5.93 5.85

5.65 5.59

4.81a 5.81

5.79 6.15

5.38 5.55 5.65 5.71 6.23 6.28

x3 x4

6.36 6.19 6.66 6.67 5.17 5.16

6-08 6.08

5.97 5.95 6.01 6.84

5.89 6.46 5.88 5.57 5.81 5.79 6.05 5.83 6.14 628 5.91 5.80 5.90 5.83 6.44 5.94 5.66 5.94

5.69 5.65 5.84 5.69 5.88 5.78

5.47 5.58 5.64 5.66 6.24 5.96

6.87 6,79a 5.13

6.08

5.90 5.99 5.94 5.75 5.82

6.08 6.04 561 5.85

5.99 5.77 5.70 5.73 5.97

d _

5,73 5-91

6.224 0.117 6.662 b 0.010 5.1 56b 0.02 1 6.066 0.019 5.936 0.044 6.000 0.029 6.066 0.228’ 5.672 0.098 5.812 0.015 6.018 0.052 6.086 0.130 5.714 0.145 5.886 0.045 6.220 o.239c 5.830 0.117 5.656 0.043 5.767 0.069 5.888 0.157 5.475 0.07 1 5.678 0.040 6.124 o.174c

x5 Mean Standard deviation

fs)

a Outlier within individual laboratory. eliminated (Grubbs test, 9970). b Mean value outlier, eliminated (Dixon test, 95%).

’ Standard deviation causing inhomogeneity of the variances, eliminated (Cochran test. 95%). d - No measured value.

If the nulnber of participating laboratories is m then the laboratories are characterized by the index i:

i = I. 7.. . . m (A.11


Within each individual laboratory, the measured values are characterized by the index k; the number of measured values in laboratory i is n(i):

k = 1, 2,. . . , n(i) (A.2)

Then, the measured value number k in laboratory i is denoted by Xik, the total number of all measurements in all laboratories is:

N = f n(i)

i= 1

The arithmetic mean in laboratory i, denoted xi, is:

xi = 1 y’ -&

n (9 k=l

and the standard deviation in laboratory i, denoted as si, is

TABLE A.2 Critical Values of the Grubbs Test According to Goetsch et al. (1978)

n fil Significance level

5% 1%

3 1.153 1.155

4 1.463 1.492

5 1.672 1.749

6 1.822 1.944

7 1.938 2.097

8 2.032 2.22 1

9 2.110 2.323

10 2.176 2.410

11 2.234 2.485

12 2.285 2.550

(A.3)

(A.4)

(A.5)

70 W. Wolfetal.

According to the Grubbs test, a measured value is identified as an outlier if its absolute deviation from the mean value 1 Xi, -Xi I divided by the standard deviation si is larger than a corresponding value given in Table A.?.

Any measured value with a superscript a in Table A.1 has been identified, by means of the outlier test, as an outlier and is not included in further calculations. The remaining values of the individual laboratories were then used to calculate the corresponding mean values and standard deviations.

In step B of Fig. 1 the homogeneity of the variances was then checked by means of the Cochran test. According to the Cochran test the variances sf for all laboratories (eqn (AS)), and hence the largest variance Sk,, , have to be determined.

If the value of the expression:

SZW C=--..-- (A.@

Jsi

is larger than the corresponding value (with due regard to m and n) from Table A.3, it may be concluded that the variance of this laboratory is larger than the variances of the remaining laboratories and causes inhomogeneity. A superscript c in Table A.1 identifies the standard deviations causing inhomogeneity of the determined variances. The data sets of the laboratories concerned were not taken into account for any further calculations. The Dixon test was subsequently applied to the data sets screened in this way, to find out whether significant differences exist between the mean values.

According to the Dixon test the given data set has first to be arranged in order of magnitude:

X(h), h = 1, 2,3,. . . , H (A.7)

Then (in the case of 3 <H < 7) the larger of the two expressions:

X(2) -X(l)

X(H) -X(l) and X(H)--XH-- 1)

X(H)--(l) (A-8)

has to be compared to the critical values in Table A.4. A superscript b in Table A.1 marks all means which differ signifi-

cantly from the joint mean value: the data sets of these laboratories

TABLE A.3 Critical Values of the Cochran Test (Significance Level 5%) According to Goetsch

ef al. (1978).

m n=2 n=3 n=4 n=5 n=6

2 - 0.975 3 0.967 0.87 1 4 0.906 0.768

0.939 0.906 O-877 0.798 0.746 0.707

O-684 0.629 0.590

5 0.841 O-684 0.598 6 0.781 0.616 0.532 7 0.727 0.561 0.480 8 0.680 0.516 0.438 9 O-638 0.478 0.403

0.544 0.506

0.480 o-445 0.43 1 o-397 0.391 0.360 O-358 0.329

10 0.602 o-445 0.373 0.331 0.303 11 0.570 0.417 0.348 0.308 0.281 12 0.541 0.392 0.326 0.288 0.262 13 o-515 0.371 0.307 0.27 1 0.246 14 0.492 0.352 O-29 1 0.255 0.232

15 0.47 1 o-335 0.276 0.242 0.220 16 0.452 0.319 0.262 0.230 0.208 17 0.434 o-305 0.250 0.219 0.198 18 0.418 0.293 0.240 0.209 0.189 19 0.403 0.281 0.230 0.200 0.181

20 O-389 0.270 0.220 0.192 0.174 21 0.377 0.261 o-212 O-185 0.167 22 0.365 0.252 0.204 0.178 0.160 23 0.354 0.243 0.197 O-1 72 0,155 24 0.343 0.235 o-191 0.166 o-149

2s 0.334 0.228 0.185 0.160 0.144 26 0.325 o-22 1 0.179 0.155 0.140 27 0.316 0.215 0.173 0.150 0.135 28 0.308 0.209 0.168 0.146 0.131 29 0.300 0.203 0.164 0.142 0.127

30 0.293 0.198 0.159 0.138 0.124 31 0.286 0.193 0.155 o-134 0.120

32 0.280 O-188 0.151 0.131 0.117

33 0.273 0.184 0.147 0.127 0.114

34 0.267 0.179 0.144 0.124 0.111

35 0.262 o-175 o-140 0.121 0.108

36 0.256 0.172 0.137 0.111 0.106

37 0.25 1 0.168 0.134 0.116 0.103

38 0.246 0.164 0.131 0.113 0.101

39 0.242 0.161 0.129 0.111 0.099

40 O-237 0.158 0.126 0.108 0.097

72 W. Wolf et al.

TABLE A.4 Critical Values of the Dixon Test

According to Goetsch et aE. ( 1978)

n fil Significance level

8 9

10

11 12

5% 1% ___

0.970 0.994 0.819 0.926 0.710 0.82 1 0.628 0.740 0.569 0.680

0.608 0.717 0,564 0.672. 0.530 0.635 0.501 0.605 0.479 0.579

had to be eliminated as well (however, before elimination, a background analysis should be made in each case).

Using the remaining data sets the repeatability Y and the reproducibility R are calculated using eqns [A.B) to (A. 15):

I’ = '7.83~~ CA.91

R = 2.83~~

where the factor 3.83 represents the 95% probability level.

s,, the repeatability standard deviation. is defined as:

(A.lO)

and sR. the reproducibility standard deviation, is defined as: I<

(A.1 1)

CA.12)


where

m n(i)2 a= &+-I~ ( i=l 1

(A.13)

(A. 14)

(A.15)

the water-vapour sorption isotherms of

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