The case takes a quantitative approach in exploring the value of higher education for Native Americans. Descriptive statistical methods are applied to empirical data from the US Census Bureau. Students are asked to consider and analyze educational attainment and its correlation to median income levels, labor force participation, and poverty rates. Other statistical measures (median, ratios, and tables and charts critiques) are performed, analyzed, and interpreted. The quantitative measures and calculations can be tailored to fit the audience – depending on the level of complexity and involvement the instructor and audience wish to pursue. Hence, the questions at the end of the case are organized into two levels: Level One (treatment is less rigorous and involved, less time is available for study) and Level Two (treatment is more rigorous, more time is available to study the case. The quantitative approach of the case attempts to provide an informed answer to the all-important question: For Native Americans, is there real value in getting a college education? Ajo (pronounced ‘axo’), Arizona is a small rural community, population 4,500, that shares a border with the Tohono O’odham Indian reservation. The median income levels in the area are quite low, and the unemployment rate in the Tumbleweed area, as in several rural communities, is quite high. The local high school, Ajo State High School (AJS), has approximately 400 students, with 72% of the students being Native American. AJS operates on a minimal budget, and adequate funding is hard to come by. Academic programs at AJS suffer as a result. Nonetheless, AJS’s Native American counselor, Inez Begay, has been able to set up some academic counseling and an after-school tutoring program for native students, using Johnson O’Malley funds.2
Assisting Inez in her efforts with native students is Matthew Candu. Matthew is a mathematics teacher at Ajo High School . He has been teaching and coaching at AJS for less than a year, but he seems to be well received and well respected by the students.
Primarily through Inez’s leadership and efforts, AJS has gotten more Native students interested in going to college. It’s been a struggle, as state standardized test scores at AJS have been below average and dropout rates remain high.
In spite of the obstacles, Inez continued to stress the importance of going to college. She has found an ally in the new math teacher, Matthew Candu. Inez knew math was a real obstacle and teachers were important mentors for students. Consequently, she was happy when Matthew expressed interest in collaborating with her to explore new ways to interest students in going to college.
With the support of the school principal, Matthew and Inez decided to spearhead a school-wide campaign that focused on the importance of going to college. To kick off the campaign, they put on a seminar entitled “Is college worthwhile?” The two-hour seminar was conducted in Matthew’s classroom, during the afternoon “flex-time” period. Teachers were very gracious in letting students out of class to attend the seminar. The turnout was fairly good – twenty-five in all – with over half of the group comprised of seniors planning to graduate in the spring.
When putting the seminar together, Inez and Matthew decided to take a quantitative approach and use data from the U.S. Census bureau. They felt the point would be better made with students if real-world data were used. More specifically, they thought it would be good for the students to work with actual, empirical data to answer questions about educational attainment and its impact on median earnings, labor force participation, and poverty reduction.
After an introduction and overview, Mathew and Inez had the students break out into small groups of five. Each group was asked to work through and answer various questions about educational attainment and its relationship to earnings, labor force participation, and poverty rates. Groups reconvened a couple of hours later to compare their results and findings. The significant data needed from these figures, to answer the questions below, are summarized in the following tables.
Table 1: Educational attainment and annual earnings, labor force participation,
Source: U.S. Census “We the People: American Indians and Alaska Natives in the United States: Census 2000 Special Reports,” pages 8-12, and the website: http://www.census.gov/prod/2006pubs/censr-28.pdf
Tribe'>Table 2: Median Earnings by Sex: 1999
Source: U.S. “We the People: American Indians and Alaska Natives in the United States: Census 2000 Special Reports,” page 11, and the website http://www.census.gov/prod/2006pubs/censr-28.pdf.
Table 3: Labor Force Participation Rate By Sex: 2000
(Percent of specified population 16 and older that is in the labor force.
Data based on sample.)
Source: U.S. Census “We the People: American Indians and Alaska Natives in the United States: Census 2000 Special Reports,” page 9, and the website: http://www.census.gov/prod/2006pubs/censr-28.pdf
Table 4: Poverty Rate: 1999
(Percent of specified group in poverty. Data based on sample)
Source: U.S. Census“We the People: American Indians and Alaska Natives in the United States: Census 2000 Special Reports,” page 12, and the website: http://www.census.gov/prod/2006pubs/censr-28.pdf References
Bluman, A.G. (2008). Elementary Statistics: A Step by Step Approach. New York: McGraw Hill.
U.S. Census (2006) We the People: American Indians and Alaska Natives in the United States: Census 2000 Special Reports, 2006. Downloaded 3/21/10 from: http://www.census.gov/prod/2006pubs/censr-28.pdf
APPENDIX A: The scatter plot, the correlation coefficient, and using technology to find the correlation coefficient
The Scatter Plot:
A less formal, more intuitive measure of correlation is the graph called a scatter plot; amore precise, mathematical measure of correlation is the mathematical formula called the correlation coefficient.
In algebra, we plotted ordered pairs on the xy-coordinate plane. Data comes in ordered pairs (x, y). The first coordinate is called the x-coordinate, the second coordinate is called the y-coordinate. The variable x is the independent (explanatory) variable (it is usually used as the label for the horizontal axis of the scatter plot; the variable y is called the dependent (response) variable (it is usually used as the label for the vertical axis of the scatter plot). A scatter plot, then, is simply a plot of the ordered pairs. After the ordered pairs are plotted, encircle the data points with an oval, then draw a line through the oval, length-wise. If the line through the oval goes uphill from left to right (i.e., the line has a positive slope), then the correlation between x and y is positive (as x increases, y increases). If the line through the oval goes downhill from left to right (i.e., the line has a negative slope), then the correlation between x and y is negative (as x increases, y decreases). If you can’t picture or get a line through the points, then there is no correlation. Correlation, then, is determined by simply looking at the pattern of the dots. The good news is that a scatter plot can be created quickly, but it is less precise, more intuitive, and gives only a “ball park,” visual estimate of correlation.
The Correlation Coefficient
The correlation coefficient is a more precise, less subjective measure of correlation, but it takes more work to find it. It measures not only the strength of the correlation between two variables, it also measures the direction (positive or negative) of the correlation. The formula for the sample correlation coefficient (r) is:
n: number of ordered pairs;
The outcome for r will be a value between 1 and -1 (i.e., positive and negative 100% inclusive). If the value of r is close to 1, then a strong positive correlation exists. If the value of r is close to -1, then a strong negative correlation exists. If the value of r is close to 0, then a weak correlation or no correlation exists. Values that are closer to -0.5 and +0.5 than -1 and 1, respectively, represent weak negative and weak positive correlations, respectively.
Notice that the values in the formula call for summations (sigma is the upper case Greek symbol for summation). It is recommended, then, that you make a table with column headings: x, y, xy, x, y22, then add up the columns. It is the sums of these columns that are needed for the formula.
3. Using technology to find the correlation coefficient:
If you have a Texas Instrument TI-83, TI-83 Plus, or TI-84, you can quickly calculate the correlation coefficient. Here are the steps (TI keystrokes are italicized):
Go to Catalog, and activate DiagnosticsOn (displaying the correlation coefficient has been activated). Then hit Stat, then Edit. Enter the x values under column L1, and the y values under column L2 (make sure the x and y values are paired up correctly). Then hit Stat, Calc, 4: LinReg, Enter. The equation of the regression line and the correlation coefficient (r) will be displayed.
1 This material is based upon work supported by the National Science Foundation under Grant No. 0817624.Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Copyright held by The Evergreen State College. Please use appropriate attribution when using and quoting this case. Cases are available at the Enduring Legacies Native Cases website at http://www.evergreen.edu/tribal/cases/
2 The Johnson O’Malley Act was originally passed in 1934 and has been amended several times. Its main objective is to provide supplementary funding to meet the unique and specialized educational needs of American Indian students