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Color changes in fresh beef during storage


Exploring complex interactions in designed data using GEMANOVA


Data from a severely reduced experimental design was investigated to obtain information on important factors affecting the changes in quality of meat during storage at different conditions.

It was possible to model the response, meat-color, using traditional ANOVA techniques, but the exploratory and explanatory value of this model was somewhat limited due to the number of factors and the fact that several interactions exist.

Using a recently suggested alternative to traditional analysis of variance, GEMANOVA(GEneralized Multiplicative ANOVA), it was possible to analyze the data effectively and obtain a more interpretable solution.

Whereas traditional analysis of variance typically seeks a model with main effects and as few and simple interactions and cross-products as possible, the GEMANOVA model seeks to describe the data primarily by means of higher-order interactions, albeit in a straightforward way. The two approaches are thus complementary. In this case, the GEMANOVA model was simple to interpret, because the GEMANOVA structure is in agreement with the nature of the data.

Furthermore, the GEMANOVA model used was mathematical unique and this leads to attractive simplifying ways of interpreting the model.

Get the data

The data are available in zipped MATLAB 5.x format. Download the data and write load data in MATLAB. If you use the data we would appreciate that you report the results to us as a curtsey of the work involved in producing and preparing the data. Also you may want to refer to the data by referring to  

R. Bro and Marianne Jakobsen. Exploring complex interactions in designed data using 
GEMANOVA. Color changes in fresh beef during storage. Journal of Chemometrics 16(2002)294-304.


Data (Matlab format)


Description of Data

1.1 Meat samples

Longissimus dorsimuscles of fresh beef were used. The muscles were matured in vacuum bags for two weeks at 2°C. Subsequently, the muscles were trimmed free of external fat and cut into 1.5cm thick steaks. Meat from three different animals was used and left and right parts from each animal were treated independently giving a total of six muscles. Meat from the different animals was handled in the same way after slaughter, e.g. maturing time, transportation conditions, etc., and all animals passed the normal quality control at the slaughterhouse. The animals may, however, be of different age, breed etc.

1.2 Storage and packaging conditions

Storage time, temperature, time of light exposure and oxygen content in the package headspace (balanced with carbon dioxide) were varied. The meat samples were placed in polystyrene trays and flow packed using a laminated packaging material with an oxygen transmission rate of 40 cm3/m2/24 h/atm. The samples were kept on refrigerated storage and exposed to light (Philips Fluotone TLD 18w/830 yielding 1000 lux at the packaging surface) for 0, 50 or 100% of the storage time. The temperature was monitored continuously during storage at several places in the refrigerator using data-loggers (TINY Talk II-Temp Loggers, RS Radio Parts, Copenhagen, Denmark).  The meat samples had a volume of 80 ml, and the headspace in the packs was 750 ml.

 1.3 Instrumental analysis

On day 0, 3, 7, 8 and 10 color was measured on the meat surface immediately after opening of the package using a Minolta Colorimeter CR-300 (Minolta, Osaka, Japan) measuring the L, a, b coordinates (CIELAB color system). Red color was expressed as the a-value and only this response-value was used in the analysis. A high a-value represents a red color of the meat sample. The measurement was repeated on five randomly selected locations for each sample and the average used.

 1.4 Experimental design

Table 1. Level of factors in designed experiments for which a-color response is measured.



Storage time (days)

0, 3, 7, 8, 10

Temperature (°C)

2, 5, 8

O2 content in headspace (%)

40, 60, 80

Exposure time to light (%)

0, 50, 100

Muscle no.

1, 2, 3, 4, 5, 6

Table 2. Other characteristics of design.



No. of samples in full design


No. of samples in reduced design


Missing elements in array

60 %

The full factorial design constitutes 5 x 3 x 3 x 3 x 6 = 810 (Storage x Temperature x Oxygen x Light xMuscle x replicate) combinations all measured in five replicates (hence the data are stored as a six-way array including the replicate mode). Due to the limited amount of samples that can be taken from an individual muscle, a reduced design was chosen using a modified quadratic D-optimal design with 324 settings (40% of the 810 initial combinations). The experiment was performed 6 times (during 8 weeks) using meat from three different animals, two samples from each (left and right side muscle of each animal). The measurements were randomized over muscles. The actual measurements on different days are not performed on the same physical piece of meat but rather on samples from the same muscle. On day zero there is no effect of storage and packaging conditions yet, and therefore all variable combinations are assigned the same color a-value calculated as the mean of five analyzed replicates on two samples from each of the six muscles.

See description of GEMANOVA algorithm and another application

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