2 Ingredients of Change: Non-Linear Models

Project 2.1: Compulsory School Laws

Setting

In 1852, Massachusetts became the first state to enact a compulsory school attendance law. Sixty-six years later, in 1918, Mississippi became the last state to enact a compulsory attendance law. Table 2.72 lists the first 48 states to enact such laws and the year each state enacted its first compulsory school law.

TABLE 2.72

Source: Richardson, "Variation in Date of Enactment of Compulsory School Attendance Laws," Sociology of Education vol. 53 (July 1980), pp. 153&endash;163.

6. Examine scatter plots for the two data sets in Task 5. Do you believe that logistic models are appropriate for these data sets? Explain.

7. Find logistic models for each set of data in Task 5. Comment on how well each model fits the data.

8. It appears that the northern and western states were slow to follow the lead established by Massachusetts and New York. What historical event may have been responsible for the time lag?

9. One way to reduce the impact of unusual behavior in a data set (such as that discussed in Task 8) is to group the data in a different way. Tabulate the cumulative northern and western state totals for the following 10-year periods:

 1852-1861 1862-1871 1872-1881 1882-1891 1892-1901 1902-1911

10. Fit a logistic curve to the data in Task 9. Comment on how well the model fits the data. Compare models for the data grouped in 10-year intervals and the data grouped in 5-year intervals (Task 6). Does grouping the data differently significantly affect how well the model fits? Explain.

11. Find a model that fits the data for the southern states better than the logistic model. Explain your reasoning.

1. Tabulate the cumulative number of states with compulsory school laws for the following 5-year periods:

 1852-1856 1887-1891 1857-1861 1892-1896 1862-1866 1897-1901 1867-1871 1902-1906 1872-1876 1907-1911 1877-1881 1912-1916 1882-1886 1917-1921

2. Examine a scatter plot of the data in Task 1. Do you believe a logistic model is appropriate? Explain.

3. Fit a logistic model to the data in Task 1.

4. What do most states in the third column of the original data have in common? Why would these states be the last to enact compulsory education laws?

5. The seventeen states considered to be southern states (below the Mason-Dixon Line) are AL, AR, DE, FL, GA, KY, LA, MD, MO, MS, NC, OK, SC, TN, TX, VA, and WV. Tabulate cumulative totals for the southern states and the northern/western states for these dates:

 Northern/Western States Southern States Years Years 1852-1856 1891-1895 1857-1861 1896-1900 1862-1866 1901-1905 1867-1871 1906-1910 1872-1876 1911-1915 1877-1881 1916-1920 1882-1886 1887-1891 1892-1896 1897-1901 1902-1906

Reporting

1. Prepare a written report of your work. Include scatter plots, models, and graphs. Include discussions of each of the tasks in this project.

2. (Optional) Prepare a brief (15-minute) presentation on your work.