The study of human populations involves working not PART 2. Cemetery Investigation: An Exercise in Simple Statistics POPULATIONS

Transcription

1 PART 2 POPULATIONS Cemetery Investigation: An Exercise in Simple Statistics 4 When you have completed this exercise, you will be able to: 1. Work effectively with data that must be organized in a useful manner. 2. Make generalizations about a specific population based on the analysis of data collected. 3. Define and explain the meaning of common statistical terms. 4. Collect information for a stratified random sample. 5. Generalize statistical models to analyze other biological populations. 6. Compare and contrast materials used to construct grave markers. 7. Identify vegetation found in a local cemetery in terms of plant diversity. Characterizing Populations Your instructor will assign you to a cemetery within a reasonable traveling distance of your school. Rural and smalltown cemeteries usually give the best picture of a stable population over time, while urban communities tend to be more mobile and thus show more variation due to relocation. This is especially true in the United States in the periods directly following the Civil War, World War I, the Great Depression, World War II, and the latter half of the twentieth century. If you are gathering data from a cemetery in a part of the country where Euro-Americans were recent arrivals, gravestones may only date back to the turn of the century. On the other hand, graves in the eastern United States exist from the 1670s and earlier, and in the southwestern part of the country, the graves of Spanish colonizers are even older than that. The study of human populations involves working not only with statistics, a branch of mathematics, but also with cultural practices and innovations from the social sciences. In the last century, several scientific and technological advances in the areas of medicine, nutrition, architecture, and transportation have had an impact on human survivorship, the probability of surviving to a particular age. Because survivorship may be reflected in average life spans and gravestones usually record the dates of births and deaths, cemeteries can be sources of survivorship data. All statistical problems involve the collection, description, or analysis of data, the raw material collected by a researcher. In this exercise, you will gather data in a cemetery, analyze the population trends it reveals, and practice using basic statistical terminology. By the way... In looking at contemporary practices, there is a growing trend toward cremation rather than cemetery interment. Some people are concerned that embalming fluid (mostly formaldehyde) is toxic, making the embalmed body toxic material. Actually, there are few laws requiring that embalming be done; it has merely become accepted practice because it preserves the body longer while distant relatives travel to the funeral. Given all the complex social dimensions of a cemetery investigation and its potential for yielding information about the human population of a region, searching county records offices can help provide an accurate picture of the human population in your specific region over time. We suggest that you complete this cemetery investigation lab first and follow with Exercise 5, Community Population Analysis. 19

2 Using the Language of Statistics Because the analysis of data requires us to use the language of statistics, you will need to be familiar with certain basic terms and methods before completing this lab exercise. In statistics, the word population is used to refer to the group to which the researcher would like the results of the study to be generalizable; it includes all individuals with certain specified characteristics. In this lab exercise, your population will be individuals buried in the cemetery in marked graves. Also, with statistical methods, the larger the sample of data points gathered, the more likely it is that the data will accurately reflect the overall population. A random sample is chosen in such a way that each individual member of the population has an equal chance of being selected. In this lab exercise you will not be working with a purely random sample because you are bound by the variable of distance and cannot select a cemetery from a purely random set of possibilities. In addition, the following factors could influence your sample: (1) All graves in a cemetery may not be marked since infants and stillborn children were occasionally interred on top of the existing graves of family members and left otherwise unmarked; (2) grave markers may disintegrate, may become damaged, or may never have been placed; (3) nineteenth- and twentieth-century stone and wooden grave markers are notorious for becoming illegible; and (4) larger municipal cemeteries are often deliberately subdivided following cultural practices (religious affiliations, socioeconomic status, age [children versus adults], military status, or membership in secret societies or fraternal orders). Stratified random sampling is the process of selecting a sample in such a way that subgroups in the population are represented in the same proportion as they exist in the population; this is the type of sampling you will be doing in this exercise. Using Graphs Statistical data are often displayed using graphs, and this exercise will provide you with experience in interpreting such graphs as well as creating your own. You are probably familiar with graphs like the one shown in Figure 4.1 in the lab report, a type that is frequently used in statistical analysis. Such graphs are based on the Cartesian coordinate system and consist of a horizontal axis, the x-axis, and a vertical axis, the y-axis. At other times, data are summarized on a type of graph called a histogram. This graphic representation consists of vertical rectangles of the scores in a distribution, wherein the height of the rectangle indicates the frequency of each score or group of scores. The sum of the scores in the distribution divided by the number of scores in the distribution is known as the arithmetic mean, symbolized by X. The arithmetic mean is the most commonly used measure of central tendency, a set of numbers that shows the tendency of the data to cluster around certain numerical values (Wagner, 1992). Lab Activity Materials Clipboard Black, waterproof pen or marker Dry marker board and markers Newsprint or tracing paper (optional) Large crayons (optional) Procedure 1. Members of the class will be assigned different parts of the cemetery in which to collect data. Note the boundaries of your assigned cemetery section. 2. Make sure permission has been obtained if a large group will be working in the cemetery all at once, and remember to be respectful of the graves and flower memorials. 3. Proceed through your assigned area in an organized fashion, recording from each gravestone the following information: last name (for reference), date of birth (month and year), and date of death (month and year). Using the data sheet provided (Table 4.1 in the lab report), record data from the first 30 tombstones you encounter. If a tombstone is illegible or missing any data, skip it. Record your data in black ink so that it may be photocopied and shared with your classmates. Because in statistical research it is generally accepted that a sample size should be no smaller than 30, you should collect at least 30 data points for your analysis. 4. After the data have been shared, calculate the life span for each individual by subtracting the year of birth from the year of death. Record this information in the fourth column of Table Continue the exercise by completing steps 17 of the lab report. Additional Activities 1. How many different gravestone materials are represented in your sample population? Note: Possible materials include wood, granite, sandstone, limestone, and metal. 2. When was your study cemetery founded? Is there a correlation between the age of the markers and the material used? Note: In earlier times, transportation was an issue. People tended to use locally available material for gravestones. What stone is available locally? 3. Cemeteries are often places where local native plant populations are protected from development or collection. Sometimes even rare or endangered plants find refuge in cemeteries. For example, a small-town cemetery might provide habitat for as many as 300 different plant species, some of them endangered. In a short visual survey, count the number of different plants within and around the borders of the cemetery. Differentiate between trees and forbes (wildflowers). 20 Part 2 Populations

3 4. Use separate paper to respond in summary form. What can you conclude about the population you studied today? Consider information about life span, childhood mortality, ethnicity, health care evolution, advances in building design, nutrition, and family size. 5. If time permits in the field, use the dry marker board to sketch graphs and show initial population trends. For the next class session, your instructor may make copies of each person s graphs and raw data and provide each student with copies. 6. To make an aesthetic record of your experiences, you may create what some artists call gravestone rubbings. It is essential that your instructor contact the authority that manages the cemetery to get permission for this activity. Choose a stone or marker with clear inscriptions. Place a piece of newsprint or tracing paper over the inscription. As you gently rub a large crayon across the paper, the imprint of the stone will emerge. Be careful not to press too hard or the paper might tear and the stone be damaged. The archival quality of some rubbings is outstanding. History enthusiasts use a special rectangular crayon called gravestone rubbing wax, which is often available in art stores. Reference Wagner, S Introduction to statistics. New York: HarperCollins. Lab Report Your lab report may be written in standard lab report format (see Appendix A). Alternatively, your instructor may require that you use the lab report form on the following pages. Exercise 4 Cemetery Investigation: An Exercise in Simple Statistics 21

4

5 Name Lab Report 4 Cemetery Investigation: An Exercise in Simple Statistics Table 4.1 Cemetery Data Date of Birth Date of Death Life Span Last Name (Month and Year) (Month and Year) (Years) Category Exercise 4 Cemetery Investigation: An Exercise in Simple Statistics 23

6 1. In the far right-hand column of the lab report data sheet, classify and record each individual by year of death according to the letter categories on the following list. Then calculate the average life span (the arithmetic mean) for each category and record it in the spaces provided. (If you have no data for a category, leave the space blank.) _ A. (Before 1671) J. (192130) _ B. ( ) K. (193140) C. ( ) L. (194150) D. ( ) M. (195160) E. (180150) N. (196170) F. (185170) O. (197180) G. (187190) H. ( ) I. (191120) P. (198190) Q. (1991Present) 2. On the following graph, find each death category on the x-axis and the average age on the y-axis and make a dot at the point where these two pieces of information (known as quantitative variables) intersect. By doing this for each category, you will have created a scatter plot. A regression line on a scatter plot is a measure of how much the line s predicted y-value differs from the actual y-value. If a recognizable regression line emerges, highlight the line in a different color of ink. y-axis Life Span (Years) A B C D E F G H I J K L M N O P Q x-axis Category of Death Figure 4.1 Graphs in this style are commonly used to plot data for statistical analysis. 24 Part 2 Populations

7 3. The score that occurs most frequently in a distribution is called the mode. Determine the mode for your distribution:. 4. The point in a distribution at which 50% of the scores fall above and 50% fall below is the median. Calculate the median for your distribution:. 5. Calculate the number of deaths per month (January through December) for individuals who died prior to 1930 (categories A through J), and represent the data by completing the following histogram so that the column for each month on the horizontal axis reaches to the appropriate level on the vertical axis. Number of Deaths per Month Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Month 6. Draw a histogram to show the data for individuals who died after Draw a histogram to represent deaths both before and after Differentiate between the two time periods visually. Note: Penicillin became available around What effect might this have had on humans death rate or life span? Do your data reflect this development? Exercise 4 Cemetery Investigation: An Exercise in Simple Statistics 25

8