Status of Education in Rural America
NCES 2007-040
June 2007

Appendix B. Technical Notes

Technical notes

This report includes data from both universe and sample surveys. In the case of universe data, all individuals or institutions of interest are included in the data collection. There is no sampling error; thus, observed differences are reported as true. In the case of sample surveys, a nationally representative set of respondents is selected and asked to participate in the data collection. In order to allow for representative samples at the locale level, the samples are stratified. Since the sample represents just one of many possible samples that could be selected, there is error associated with the sample. To avoid reaching false conclusions about differences between groups or differences over time measured by sample survey data, sampling error is taken into account in statistical tests that are conducted to support statements about differences. Thus, all statements about differences in this report are supported by the data, either directly in the case of universe surveys or with statistical significance testing in the case of sample survey data. In addition, there are occasional references to apparent differences that are not statistically significant. Apparent differences that are not statistically significant are discussed in order to aid the reader in interpreting the data.

All significance tests of differences are tested at the .05 level of significance. Several test procedures were used, depending on the type of data interpreted and the nature of the statement tested. The most commonly used test procedures were t tests, linear trend tests, and equivalency tests. The t tests were not adjusted to compensate for multiple comparisons being made simultaneously. Equivalence tests at the 0.15 level were used to determine whether two statistics were substantively equivalent or different by using a hypothesis test to determine whether the confidence interval of the difference between sample estimates was significantly greater or less than a preset substantively important difference. In most cases involving percentages, a difference of 3.0 percentage points was used to determine substantive equivalence or difference. In some indicators involving only very small percentages, a lower value was used.

The appearance of a "!" symbol (meaning "Interpret data with caution") in a table or figure indicates an unstable estimate; therefore, the reader should use caution when interpreting the data. These unstable estimates are discussed, however, when statistically significant differences are found despite large standard errors.

The indicators in this report present data from a variety of sources. The sources and their definitions of key terms are described in appendix C. Most of these sources are federal surveys and many are conducted by the National Center for Education Statistics (NCES). The majority of the sources are sample surveys; these are the sources of the estimates for which standard errors are provided on the NCES website. A few sources provide universe data, meaning that they collect information on the entire population of interest, and therefore no standard errors are needed.

Although percentages reported in the tables are generally rounded to one decimal place (e.g., 76.5 percent), percentages reported in the text and figures are rounded from the original number to whole numbers (with any value of 0.50 or above rounded to the next highest whole number). Due to rounding, cumulative percentages may sometimes equal 99 or 101 percent, rather than 100. In addition, sometimes a whole number in the text may seem rounded incorrectly based on its value when rounded to one decimal place. For example, the percentage 14.479 rounds to 14.5 at one decimal place, but rounds to 14 when reported as a whole number.

Counts or numbers from universe data are reported unrounded. Estimated counts or numbers from sample survey data are reported rounded to hundreds when they are four-and five-digit numbers, and to thousands when they are six-digit numbers.


Comparison of poverty measures

In this report, the definition of poverty varies by data source. A comparison of these different poverty definitions is provided below.

Data on household income and the number of people living in the household are combined with estimates of the poverty threshold published by the Bureau of the Census to classify children (or adults) as "below the poverty threshold" or "at or above the poverty threshold" in indicator 1.5. The thresholds that are used to determine whether an individual is below or at or above poverty differ for each survey year. (For background on how poverty is measured, click here. For the weighted average poverty thresholds for various household sizes and years, click here.)

Indicators 1.7, 2.4, and 2.9 use the categories of "poor," "near-poor," and "nonpoor." Poor is defined to include those families below the poverty threshold, near-poor is defined as those at 100–185 percent of the poverty threshold, and nonpoor is defined as those above 185 percent of the poverty threshold.

Eligibility for the National School Lunch Program also serves as a proxy measure of poverty status. The National School Lunch Program is a federally assisted meal program operated in public and private nonprofit schools and residential child care centers. Unlike the poverty thresholds discussed above, which rely on dollar amounts determined by the Census Bureau, eligibility for the National School Lunch Program relies on the federal income poverty guidelines of the Department of Health and Human Services. To be eligible for free lunch, a student must be from a household with an income at or below 130 percent of the federal poverty threshold; to be eligible for reduced-price lunch, a student must be from a household with an income at or below 185 percent of the federal poverty threshold. Title I basic program funding relies on free and reduced priced lunch eligibility numbers as one (of four) possible poverty measures for levels of Title I federal funding. In indicators 1.8 and 1.9, moderate-to-high poverty schools are defined as schools with more than 50 percent of students eligible for free or reduced-price lunch.

In indicators 3.1 and 3.2, district poverty was determined by ranking school districts by the percentage of enrolled children aged 5–17 from families with an income below the poverty threshold, and then dividing these districts into five categories with equal proportions of the total enrollment. The low-poverty district category consists of the 20 percent of students nationally in districts with the lowest percentages of poor school-age children. Conversely, the high-poverty district category consists of the 20 percent of students nationally in districts with the highest percentages of poor school-age children.


Measures of educational attainment

Various measures of educational attainment have been developed to provide information about the highest level of formal education completed by individuals or various population groups.

Indicator 2.4 uses American Community Survey (ACS) data to report on the high school status dropout rate among 16- to 24-year-olds. The high school status dropout rate is defined as the percentage of the civilian, noninstitutionalized population ages 16 through 24 who are not in high school and who have not earned a high school credential (either a diploma or equivalency credential such as a General Educational Development [GED] certificate), irrespective of when they dropped out. Status dropout rates measure the extent of the dropout problem for a population and as such can be used to estimate the need for further education and training in that population.

Indicator 2.5 examines the percentage of public high school students who graduate by using the averaged freshman graduation rate (AFGR). The AFGR is an estimate of the percentage of the incoming freshman class that graduates with regular diplomas 4 years later. The AFGR is the number of graduates with regular diplomas divided by the estimated count of freshmen 4 years earlier as reported through the NCES Common Core of Data (CCD), the survey system based on state education departments' annual administrative records. The estimated count of freshmen is calculated by summing 10th-grade enrollment 2 years before the graduation year, 9th-grade enrollment 3 years before the graduation year, and 8th-grade enrollment 4 years before the graduation year and dividing this amount by 3. The intent of this averaging is to account for the high rate of grade retention in the freshman year, which adds 9th-grade repeaters from the previous year to the number of students in the incoming freshman class each year. Enrollment counts include a proportional distribution of students not enrolled in a specific grade.

Indicators 1.14 and 2.9 use American Community Survey (ACS) data to examine levels of educational attainment among parents of school-age children and among adults age 25 and over, respectively. The levels of educational attainment reported by ACS include less than a high school diploma or equivalent, a high school diploma or equivalent, some college or an associate's degree, a bachelor's degree, and a graduate or professional degree. The "less than a high school diploma or equivalent" category includes those currently enrolled in high school, while the "high school diploma or equivalent" category includes those currently enrolled in college. ACS data do not differentiate between those who graduated from public schools, graduated from private schools, or who earned an equivalency credential such as a GED. The data include individuals who never attended high school in the United States and is limited to the civilian, noninstitutionalized population. Indicator 1.14 reports on the percentages of students ages 6–18 with a mother who had completed the various levels of attainment and the percentages of such students with a father who had completed these levels of educational attainment. Indicator 2.9 examines the percentages of adults age 25 and older with these levels of educational attainment.

Indicator 1.15 uses National Household Education Survey (NHES) data to report on parents' expectations for their children's highest level of educational attainment. The levels of attainment used by NHES differ slightly from those used by ACS. They include less than a high school diploma, a high school diploma, vocational or technical school, 2 or more years of college, a 4- or 5-year college degree, and a graduate or professional degree.