TITEL : calories KEYWORDS (statist) : ANOVA , Boxplot , Histogram , Median , Transformation ANWENDUNGSGEBIET : Lebensmitteltechnologie VERW.(VORL./J.-S.) : E in Statistik, H.R. Roth Ws 96/97 Ueb.aufgabe : "ad.calories.tex" -------------------------------------------------------------------------------- KURZE BESCHREIBUNG : Results of a survey of 40 food items claiming to be "lite," "reduced-calorie," "low-calorie," "diet," "low-fat," "no-fat," or "health" foods. Each food is classified based on its distribution as either nationally advertised, regionally distributed, or locally prepared. The researchers measured the caloric content of each food by bomb calorimetry, and converted these readings into an estimate of total metabolizable energy (the type of energy the calories on a food label are supposed to reflect). Finally, they calculated the percentage difference between the measured calories and the labeled calories for each item and per gram. Abstract: "Let the buyer beware" is a phrase that comes to mind when buying a used car, not when buying food. However, Allison, Heshka, Sepulveda, and Heymsfield (1993) think that this phrase should apply to purchasing "diet" and "health" foods as well. They purchased 40 such food items in Manhattan, New York and compared the caloric content of each to the calories listed on the label. They discovered that some labels on food packages understated the calorie content by more than 85%. Examination of the data shows that the distribution of percentage difference per gram is symmetric, but information is missing for all of the "locally prepared" foods. This variable cannot be used for a full investigation of the relationship between distribution area and underreporting of calories. The distribution of percentage difference per item is skewed right with median 24. A one sample sign test of Ho: Median=0 is appropriate to determine whether there is an overall underreporting of calories on food labels. Boxplots suggest that national products are not systematically under reporting caloric content, regional products are somewhat under reporting, and local products are most prone to under reporting. There is also an increase in the variability as the classification changes from local to regional and national. One-way ANOVA can be used to address the relationship between distribution area and underreporting of calories. Because of the skewness and non-constant variance, the data should be transformed first. First, eliminate the negative differences in the data set by adding 100 to each number before transforming it. A reciprocal transformation (1/(100+percentage difference per item) results in an approximately normally distributed variable. A one-way ANOVA with this transformed difference as the dependent variable shows a significant difference in underreporting among the different distribution area categories. SPEZ. EIG. : -------------------------------------------------------------------------------- DIM.(VAR./FAELLE) : 4 * 40 1.Food: Kind of food 2.Per_gram: Percentage difference between measured calories and labeled calories per gram (100% x (measured-labeled)/labeled) 3.Per_item: Percentage difference between measured calories and labeled calories per item 4.Classification: N if nationally advertised, R if regionally distributed, L if locally prepared Einlesen mit S-plus: read.table("/u/sfs/ueb/datasets/calories.dat", header = T) DATENFORMAT IN SAS : INFILE INPUT -------------------------------------------------------------------------------- * / LITERATUR : /Allison, D., Heshka, S., Sepulveda, D., and * Heymsfield, S. (1993), "Counting Calories -Caveat Emptor," JAMA, v. 270, pp. 1454-1456. * D=Daten, vA=volle Analyse, tA=teilweise Analyse, K=Kommentar -------------------------------------------------------------------------------- BEMERKUNGEN : -------------------------------------------------------------------------------- USERS : DATUM/UNTERSCHRIFT :