Becoming a Teacher of Statistics
Portfolio
by
Susan Sexton
Data Analysis
Probability and Statistics for Secondary
Teachers
STAT 6070
University of Georgia
Fall 2007
Instructor: Christine Franklin
Analysis of a Data Set
Background:
America is known as the land of opportunities. One opportunity available to all Americans is entrepreneurialship, or the ability to begin a business. Data collected from a survey on administered between 1996 to 2006 on people (between the ages of 20-64) Òwho do not own a business in the first survey month that start a business in the following month with fifteen or more hours worked per weekÓ were analyzed. The survey provides data on gender, race, age, education, and the list goes on.
Source:
The data comes from the Kauffman Index of Entrepreneurial Activity website. The goal of the Kauffman Foundation is to act as an Òindicator of new business creation in the United States.Ó The aim of the measures is to provide Òthe earliest documentation of new business development across the countryÓ and does so by providing a variety of Òseparate estimates for specific demographic groups, states, and select metropolitan statistical areas.Ó The Kauffman Index uses information taken from the U.S. Census BureauÕs Current Populations Survey to compare Òthe percent of the population of adult non-business owners who start a business over time.Ó
Available from (in Excel
format):
http://www.kauffman.org/kauffmanindex/files_biblio.cfm
Teaching with this Data:
Why?
Entrepreneurialship is a possibility for all Americans, those with or without education. Thus this data set can engage and enlighten students of entrepreneurialship that can exist in America regardless of educational level. To dive further into the data, students can investigate the age, gender, and/or race of entrepreneurialship. They may even investigate entrepreneurialship by state.
What?
Students can investigate a variety of trends over time using time plots. They can investigate whether or not age, gender or educational level is a factor in the percentage of entrepreneurialship over time. They can also investigate the types of jobs or the states that appear to have the most entrepreneurialship. Students can compare, using the five-number summary, gender or educational level to each over the 10 year period. They can decide on which visual presentation conveys the most useful information. For example, would a regular bar graph or a Pareto chart be more helpful in displaying each of the United StatesÕ percentage index? Of course, all of these investigations and visualizations would be done with the aid of technology.
Some Analyses:
Next are some visual plots done with three different types of technology to illustrate the types of investigations possible.
A comparison of females and males over time with an Excel time plot:
The gender data available from the site:
Another visual with boxplots of gender using the TI-83 graphing calculator:
The top left boxplot represents females, while the
bottom right represents males.
The five number summary from the TI-83:
Females Males
Students can use the visual to see that the trend over the 10 year period indicate that men tended to be more entrepreneurial than women. The boxplots also indicate that their proportions in the population are also different, again indicating more men start businesses than women. This analysis can also be done with age and educational level. Parts of these analyses are done next.
A comparison of educational level over time:
Over time, people who did not finish high school appeared to be more entrepreneurial than any other group in the study.
A boxplot comparison of those with only a high school degree to those with a college degree:
The top boxplot represents those with only a high school
degree. The bottom boxplot represents those with a college degree.
The five number summary of the two groups:
High School Graduate only College Graduate
Since it is difficult to compare the high school graduates with the college graduates, students can use the five number summary to find that the two groups are not so different with close medians. However the college graduates have more of a spread of representation over the years.
The education data available from the site:
One additional visual analysis can be done with the information on the percentage of entrepreneurialship by state for the year 2006. Students can choose which graph would convey the most useful information. Hopefully they will chose a Pareto chart!
A Pareto chart by state using SPSS:
Using the Pareto chart, students can quickly see (with the tiny font) that Montana has the most entrepreneurialship while Michigan has the least. This would not be easily seen with a regular bar graph.
The state data for 2006 available from the website. It
also contains the confidence intervals which would be a means to introduce
the topic to the students through the context of the analyses.
Since I was curious, I decided to look at the age brackets of the entrepreneurialship shown below in the timeplots:
One can see that those who are 55-64 generally pursue a business much more than those in the other age brackets, especially ages 20-34.
The age data provided on the website:
One more interesting piece of information provided by the website is the cohort of ages polled over the years:
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Age in survey year for different birth cohorts |
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birth years |
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survey year |
1935 |
1944 |
1945 |
1954 |
1955 |
1964 |
1965 |
1974 |
1975 |
1984 |
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1996 |
|
61 |
52 |
51 |
42 |
41 |
32 |
31 |
22 |
21 |
12 |
|
1997 |
|
62 |
53 |
52 |
43 |
42 |
33 |
32 |
23 |
22 |
13 |
|
1998 |
|
63 |
54 |
53 |
44 |
43 |
34 |
33 |
24 |
23 |
14 |
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1999 |
|
64 |
55 |
54 |
45 |
44 |
35 |
34 |
25 |
24 |
15 |
|
2000 |
|
65 |
56 |
55 |
46 |
45 |
36 |
35 |
26 |
25 |
16 |
|
2001 |
|
66 |
57 |
56 |
47 |
46 |
37 |
36 |
27 |
26 |
17 |
|
2002 |
|
67 |
58 |
57 |
48 |
47 |
38 |
37 |
28 |
27 |
18 |
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2003 |
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68 |
59 |
58 |
49 |
48 |
39 |
38 |
29 |
28 |
19 |
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2004 |
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69 |
60 |
59 |
50 |
49 |
40 |
39 |
30 |
29 |
20 |
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2005 |
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70 |
61 |
60 |
51 |
50 |
41 |
40 |
31 |
30 |
21 |
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2006 |
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71 |
62 |
61 |
52 |
51 |
42 |
41 |
32 |
31 |
22 |
One question to pose: Who is representing those born from 1976 to 1983? This could affect the results of the data. Would the data show more young entrepreneurials? Definitely during the mid- to late 90Õs there was an increase in Internet businesses created by young professionals. Is this market being represented by these surveys? It would not appear to be so.
One final note:
The website has other data available on race, state region, entrepreneurialship of states spanning over the 10 years and nativity (whether a citizen or immigrant). Students can explore these data as well to enhance their statistical thinking and become critical statisticians.