Correlating Data to Formula Creation: The Egg Experiment. understand that formulas are created to develop correlations between real world data

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Betty Bailey
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1 Correlating Data to Formula Creation: The Egg Experiment Introduction: The purposes of this exercise is to 1) learn to use Excel proficiently and 2) understand that formulas are created to develop correlations between real world data and the human need for classification systems. One example of a classification system is the body mass index, BMI (1-6). The human population varies in height, weight and hip and waist circumferences. The chronic health conditions, overweight and obese are classifications of body fat as determined from the BMI. Other methods to determine body fat include the skin fold thickness test and immersion tests. The BMI equation was determined by studying various parameters such as height, weight and circumference and creating correlating equations that best matched body fat. For example, weight over height and weight over height cubed were studied along with the accepted equation. Thus, multiple measures and permutations of measures can be chosen and examined for their discerning ability for body fat. In the end, equation #1 was the final equation that was put forth to be used. Table 1 lists the divisions. Notice that the divisions occur in increments of 5 BMI values. W 2 4 BMI = x10 Equation #1 H W in kg, H in cm, C is circumference at width in cm Table 1. Size distribution for BMI BMI Size Underweight <20 Normal Overweight Obese >30

2 Eggs from chickens are sold in grocery stores for consumption. The sizes are medium, large, extra-large and jumbo. Other factors with respect to the purchase of eggs are whether the chickens were cage-free or not. Eggs can also be brown but the majority purchased is white. The division of size is based on weight and total weight of the carton (7,8). Is this the best measure for selecting the size of an egg? The goal of this investigation is to determine which permutation, if any, provides the best correlation of the division of eggs by size by applying analytical measurements to eggs. Experimental Procedure Group Discussion (verbal discussion with group) Four groups are created. Examine Figure 1 and discuss the following within your group. Decide what analytical principles should be used to determine where a separation/division between sizes occurs. Decide what would constitute as an analytical measurement that would provide a good separation and one that does not. Write a short proposal detailing the analytical protocol of analysis that will be undertaken to determine the best correlation of the division of eggs. Once the proposal is submitted to the instructor and approved, a carton of eggs will be given to the group. Measurement (in groups) Each group will make the same measurements on a different set of eggs. These measurements are 1) mass, 2) circumference at width, and 3) height. Each group will analyze a dozen eggs, such that each size is analyzed (medium, large, extra-large and jumbo). Care must be taken in handling the eggs to avoid breakage. Egg shell pieces caused by breakage may cause cuts and infection. Safety glasses must be worn.

3 Mass of Egg (g) The mass will be determined on an analytical balance (do not use a top-loading balance) by placing the egg on a vacuum adapter (conical in shape) on a balance that has been tared with the adapter on it. The egg should not be allowed to roll. The circumference and height will be analyzed by using a measuring tape. Once the data has been collected, the data should be typed into an Excel spreadsheet and shared with the class through the on-line class management system. Data Analysis Step One (in pairs or singles): Use Excel to tabulate and compute the averages, standard deviations and coefficient of variation (relative standard deviation) for each set of measurements using the functions available on Excel TM. Create a graph of average mass of egg versus size of egg as depicted below in Figure 1, including the standard deviation of each mass as the error bars and the trendline and r 2 value. Repeat this for height and then for circumference. Ask the instructor or teaching assistant for assistance in using Excel TM if needed y = 7.1x R 2 = medium large extra-large Size of Egg Figure 1. Example of Mass of Egg Versus Size of Egg.

4 Step Two (in pairs or singles): Create a list of the egg data such that the first column is the size name, the second column is the mass measured, the third column is the height and the fourth column is the circumference. This provides a list of 48 eggs in a column with their respective data appearing in each row. Graph using a scatter plot, the mass of each egg versus height, the mass of each egg versus circumference, and the height or each egg versus circumference. Add trendlines and r 2 values. Ask the instructor or teaching assistant for assistance. Calculate using Excel, the BMI for each egg using Equation #1. This requires creating an equation using the references to cell locations. Ask the instructor or teaching assistant for assistance. Graph BMI and the standard deviations versus egg size as in Figure 1. Graph a scatter plot of mass versus BMI. Group Work: Once the majority of your group has completed steps 1 and 2, meet with your group to discuss these questions. Are there any trends that can be discussed based on the first three graphs? Are there any trends that can be discussed based on the next three graphs? Compare and contrast these six graphs. Refer back to your proposal. Use the list of 48 eggs and divide the eggs based on your separation/division criteria and calculate the new average and standard deviation and graph the results. How well have you followed the original criteria? Is the separation of the eggs superior based on BMI versus any of the other measures? Which measure (mass, height, circumference, BMI) separates the eggs based on size the best. What separation/division criteria are you using to determine this selection? Share the results (spreadsheets and graphs) of this discussion with all group members.

5 Step Three (in pairs or singles): Develop a different formula using Excel TM that will separate the eggs based on size and your separation/division criteria. Graph the result of this formula. Individual Discussion for Report In your discussion comment on the graphs created and the group discussions and group answers to questions. Comment on the precision of the work in general and the methods that could be employed to increase precision. Is it better to just use mass or to use BMI or another predictor to separate the eggs into their sizes? Create a conclusion as to which method is best to separate eggs by size. References 1. Keys, A. Fidanza, F. Karvonen, M.J. Kimura, N., Taylor, H.L Indices of relative weight and obesity, Journal of Chronic Diseases, 25(6-7), Tran, M.H., Lellouch, J. Richard, J.L. 1973, Fat Body Mass II. Its Relationship with some biological parameters, blood pressure and physical training in a population of 8660 men aged 20 to 55. Biomedicine, 18, Thomas, a. E. McKay, D.A., Cutlip, M.B A nomograph method for assessing body weight. The American Jounal of Clinical Nutrition29: Killeen, J. Vanderburg, D. Harlan, W.R Application of weight-height ratios and body indices to juvenile populations The National Health Examination Survey Data. J. Chron. Dis. 31, Hsu, P-H, Mathewson, F.A.L., Rabkin, S.W Blood pressure and body mass index patterns a longitudinal study, 30,

6 6. Dyer, A.r. Stamler, J. Berkson, D.M. Lindberg, H.A Relationship of relative weight and body mass index to 14-year mortality in the Chicago peoples gas company study. J. Chron. Dis. 28,

Broadening Course YPHY0001 Practical Session II (October 11, 2006) Assessment of Body Fat

Sheng HP - 1 Broadening Course YPHY0001 Practical Session II (October 11, 2006) Assessment of Body Fat REQUIRED FOR THIS PRACTICAL SESSION: 1. Please wear short-sleeve shirts / blouses for skin-fold measurements.