² For response rates, see tables A3 and A4 in A. Malizio, National Postsecondary Student Aid Study: Student Financial Aid Estimates for 1999-2000 (NCES 2001-209)(Washington, DC: U.S. Department of Education, National Center for Education Statistics, 2001).(NCES 2001-209) (Washington, DC: 2000). (return to text)

³ The NPSAS samples are not simple random samples, and therefore, simple random sample techniques for estimating sampling error cannot be applied to these data. The DAS takes into account the complexity of the sampling procedures and calculates standard errors appropriate for such samples. The method for computing sampling errors used by the DAS involves approximating the estimator by the linear terms of a Taylor series expansion. The procedure is typically referred to as the Taylor series method.(return to text)

⁴ A Type I error occurs when one concludes that a difference observed in a sample reflects a true difference in the population from which the sample was drawn when no such difference is present. (return to text)

⁵ U.S. Department of Education, National Center for Education Statistics, A Note from the Chief Statistician, no. 2, 1993. (return to text)

⁶ Ibid. (return to text)

⁷ The standard that p<.05/k for each comparison is more stringent than the criterion that the significance level of the comparisons should sum to p<.05. For tables showing the t statistic required to ensure that p<.05/k for a particular family size and degrees of freedom, see Olive Jean Dunn, "Multiple Comparisons Among Means," Journal of the American Statistical Association 56 (1961): 52-64.(return to text)

⁸ For more information about least squares regression, see Michael S. Lewis-Beck, Applied Regression: An Introduction, Vol. 22 (Beverly Hills, CA: Sage Publications, Inc., 1980); and William D. Berry and Stanley Feldman, Multiple Regression in Practice, Vol. 50 (Beverly Hills, CA: Sage Publications, Inc., 1987). (return to text)

⁹ Although the DAS simplifies the process of making regression models, it also limits the range of models. Analysts who wish to estimate other types of models, such as logit models, can apply for a restricted data license from NCES. (return to text)

¹⁰ The adjustment procedure and its limitations are described in C.J. Skinner, D. Holt, and T.M.F. Smith, eds., Analysis of Complex Surveys (New York: John Wiley & Sons, 1989). (return to text)