Teaching Bits: A Resource for Teachers of Statistics

Topics for Discussion from Current Newspapers and Journals

“What It’s Worth: Field of Training and Economic Status in 2001”, Camille L. Ryan. Issued September 2005 by the U.S. Census Bureau from the Household Economic Studies. URL: www.census.gov/prod/2005pubs/p70-98.pdf

This publication from the U.S. Census Bureau is sure to start some discussion in your classes. The report “explores issues related to school completion and degrees, fields of training occupations pursued, and earnings obtained. It also examines the education and earnings of people who obtain a General Educational Development (GED) certificate, the different educational results for women and men and trends across generations.” The material could be used for students in high school through college, perhaps even junior high. For students without extensive Statistical background, one could simply discuss the figures and tables. For example, many students may find it surprising that in the year 2001, only 1% of the population 18 and older have a Doctorate degree (Figure 1. Educational Attainment in 1984 and 2001). Since most of the tables or figures make comparisons, one can ask students to find percent change for a variety of questions. For example, “find the percent change in average monthly earnings between people with less than a high school degree and those with a high school diploma.” Using the entries from Table D. Monthly Earnings by Educational Attainment: 2001, one determines that there is a 29.0% increase. Perhaps this table might encourage students to finish high school or obtain their Bachelor’s degree (a 40% increase in average monthly earnings between people with some college and those with a Bachelor’s degree).

Table D. also lists the monthly earnings as an average, 25th percentile, median, and 75th percentile for the various educational attainments, and as we would expect, the average monthly earnings is larger than the median monthly earnings for each of the educational attainments. This is a great segue to resistant measures and skewed distributions. Also, one could discuss the Interquartile Range (IQR) as a measure of spread since it is the only possible measure of spread that one can find in the article. Table F. Monthly Earnings by Educational Attainment and Sex: 2001 also gives monthly earnings (average, 25th percentile, median, and 75th percentile), but in this table, one can investigate any sex differences. It does include the earnings ratio, ratio of women’s average earnings to men’s. The article states, “The overall female-to-male average monthly earnings ratio was 0.73. The ratio did not vary by education.” This would be a good opportunity to discuss possible lurking variables with your students.

Table E. Broad Field of Training by Sex for Selected Years: 1984 – 2001 gives the opportunity to make time plots of data. The students can pick a field of training and make two time plots, one for the number of people (in thousands) with that training and the other for the percent of people with that training. Each time plot would have two lines, one for males and one for females. For some of the fields (Education for example), the number increases, but the percent decreases. One could have the students discuss why this would happen and discuss which plot would be the best representation of the data. Of course, students can discuss trends across time and trends affecting the different sexes. This table also gives the opportunity for students to make pie charts or bar charts. For example, concentrating on the year 2001, students can compare the distribution of field of training between males and females. The article itself discusses the different patterns in fields of training between the sexes.

For more advanced students, statistical inference is used throughout the article. Concerning Table G. Average Monthly Earnings by Educational Attainment, Sex, and Field of Training: 2001, we read “the earnings ratios for several fields were not statistically different from 1.00.” Here, one can discuss the importance of the ratio being 1.00, as well as, what does it mean not to be statistically different from 1.00. Also, the footnotes are very interesting. For example, footnote 9 says, “the earnings of people with some college, no degree were not statistically different from the earnings of people with a vocational certificate or an associate’s degree.” Another opportunity to discuss statistical inference as well as encourage students to continue their education!

Table A. Detailed Fields of Postsecondary Degrees of the Adult Population: 2001 gives the number of people (in thousands) with a specific degree in different fields as well as a 90-percent confidence interval. Since we usually find confidence intervals in this type of situation in terms of a proportion, this table gives us the opportunity to discuss why and how this article can give confidence intervals on the number of people with a degree in the specified field. We usually do not know the total number in the population, but here, since this information is from the Census, we do have the total number in the population (or at least a very good approximation); therefore, our usual proportion confidence interval can be made into a number confidence interval.

In several places, the article discusses its limitations to make statistical inference. For example, footnote 11 indicates that “Data for the Asian population and the American Indian and Alaska Native population are not shown in this report because of their small sample size.” Towards the end of the article, there is a section called “Source of the Data”. Another place for instructors to lead discussion with their students.

Overall, this article contains a plethora of discussion material for your students as well as interesting information. Each instructor can tailor this article to the ability of his or her students which makes this article excellent for a wide range of students. This article is bound to make Statistics a little more interesting to your students. After all who doesn’t want to know -- How long does it take to complete a Bachelor’s degree on average? (5.6 years) How long does it take for a woman versus a man to complete a Doctorate degree? (11.6 years versus 8.3 years, respectively). Both answers are from Table I. Average Number of Years to Start and Complete Postsecondary Certification and Degrees: 2001. I hope you and your students enjoy this article!

Marjorie E. Bond
Department of Mathematics and Computer Science
Monmouth College
Monmouth, IL 61462

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