FCAT scores and poverty. Refer to the Journal of Educational and Behavioral Statistics (Spring 2004) analysis of the link between Florida Comprehensive Assessment Test (FCAT) scores and sociodemographic factors, presented in Exercise.
FCAT scores and poverty. In the state of Florida, elementary school performance is based on the average score obtained by students on a standardized exam, called the Florida Comprehensive Assessment Test (FCAT). An analysis of the link between FCAT scores and sociodemographic factors was published in the Journal of Educational
Elementary School | FCAT—Math | FCAT—Reading | % Below Poverty |
1 | 166.4 | 165.0 | 91.7 |
2 | 159.6 | 157.2 | 90.2 |
3 | 159.1 | 164.4 | 86.0 |
4 | 155.5 | 162.4 | 83.9 |
5 | 164.3 | 162.5 | 80.4 |
6 | 169.8 | 164.9 | 76.5 |
7 | 155.7 | 162.0 | 76.0 |
8 | 165.2 | 165.0 | 75.8 |
9 | 175.4 | 173.7 | 75.6 |
10 | 178.1 | 171.0 | 75.0 |
11 | 167.1 | 169.4 | 74.7 |
12 | 177.0 | 172.9 | 63.2 |
13 | 174.2 | 172.7 | 52.9 |
14 | 175.6 | 174.9 | 48.5 |
15 | 170.8 | 174.8 | 39.1 |
16 | 175.1 | 170.1 | 38.4 |
17 | 182.8 | 181.4 | 34.3 |
18 | 180.3 | 180.6 | 30.3 |
19 | 178.8 | 178.0 | 30.3 |
20 | 181.4 | 175.9 | 29.6 |
21 | 182.8 | 181.6 | 26.5 |
22 | 186.1 | 183.8 | 13.8 |
Based on Tekwe, C. D., et al. “An empirical comparison of statistical models for value-added assessment of school performance.” Journal of Educational and Behavioral Statistics , Vol. 29, No. 1, Spring 2004.
and Behavioral Statistics (Spring 2004). Data on average math and reading FCAT scores of third graders, as well as the percentage of students below the poverty level, for a sample of 22 Florida elementary schools are listed in the accompanying table and saved in the FCAT file.
a. Propose a straight-line model relating math score ( y ) to percentage ( x ) of students below the poverty level.
b. Use the method of least squares to fit the model to the data in the FCAT file.
c. Graph the least squares line on a scatterplot of the data. Is there visual evidence of a relationship between the two variables? Is the relationship positive or negative?
d. Interpret the estimates of the y -intercept and slope in the words of the problem.
e. Now consider a model relating reading score ( y ) to percentage ( x ) of students below the poverty level. Repeat parts a–d for this model.
Data on average math and reading FCAT scores of third graders, as well as the percentage of students below the poverty level, for a sample of 22 Florida elementary schools are saved in the FCAT file.
a. Compute and interpret Spearman’s rank correlation between FCAT math score ( y ) and percentage ( x ) of students below the poverty level.
b. Compute and interpret Spearman’s rank correlation between FCAT reading score ( y ) and percentage ( x ) of students below the poverty level.
c. Determine whether the value of rs in part a would lead you to conclude that FCAT math score and percent below poverty level are negatively rank correlated in the population of all Florida elementary schools. Use α =.01 to make your decision.
d. Determine whether the value of rs in part b would lead you to conclude that FCAT reading score and per cent below poverty level are negatively rank correlated in the population of all Florida elementary schools. Use α =.01 to make your decision.
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